{"data":[{"id":1037,"title":"Optimal, Integral, Likely Optimization, Integral Calculus, and Probability for Students of Commerce and the Social Sciences","edition_statement":null,"volume":null,"copyright_year":2020,"isbn10":null,"isbn13":null,"license":"Attribution-NonCommercial-ShareAlike","language":"eng","accessibility_statement":"","accessibility_features":[],"description":"Optimal, Integral, Likely is a free, open-source textbook intended for UBC’s course MATH 105: Integral Calculus with Applications to Commerce and Social Sciences. It is shared under the Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.","contributors":[{"id":5468,"contribution":"Author","primary":false,"corporate":false,"title":null,"first_name":"Bruno","middle_name":null,"last_name":"Belevan","location":"The University of British Columbia","background_text":"Bruno Belevan, The University of British Columbia"},{"id":5469,"contribution":"Author","primary":false,"corporate":false,"title":null,"first_name":"Parham","middle_name":null,"last_name":"Hamidi","location":"The University of British Columbia","background_text":"Parham Hamidi, The University of British Columbia"},{"id":5470,"contribution":"Author","primary":false,"corporate":false,"title":null,"first_name":"Nisha","middle_name":null,"last_name":"Malhotra","location":"The University of British Columbia","background_text":"Nisha Malhotra, The University of British Columbia"},{"id":5471,"contribution":"Author","primary":false,"corporate":false,"title":null,"first_name":"Elyse","middle_name":null,"last_name":"Yeager","location":"The University of British Columbia","background_text":"Elyse Yeager, The University of British Columbia"}],"subjects":[{"id":84,"name":"Calculus","parent_subject_id":7,"call_number":"QA150-272.5","visible_textbooks_count":31,"url":"https://staging.open.umn.edu/opentextbooks/subjects/calculus"},{"id":36,"name":"Pure","parent_subject_id":7,"call_number":"QA37.3","visible_textbooks_count":83,"url":"https://staging.open.umn.edu/opentextbooks/subjects/pure"},{"id":7,"name":"Mathematics","parent_subject_id":null,"call_number":"QA1","visible_textbooks_count":177,"url":"https://staging.open.umn.edu/opentextbooks/subjects/mathematics"}],"publishers":[{"id":1015,"url":"https://nisha-malhotra.arts.ubc.ca/","year":null,"created_at":"2021-08-16T10:51:58.000-05:00","updated_at":"2021-08-16T10:54:18.000-05:00","name":"Bruno Belevan, Parham Hamidi, Nisha Malhotra, and Elyse Yeager"}],"formats":[{"id":2539,"type":"PDF","url":"https://nisha-malhotra.arts.ubc.ca/open-textbook/","price":{"cents":0,"currency_iso":"USD"},"isbn":null}],"rating":null,"textbook_reviews_count":0,"reviews":[],"url":"https://staging.open.umn.edu/opentextbooks/textbooks/optimal-integral-likely-optimization-integral-calculus-and-probability-for-students-of-commerce-and-the-social-sciences","updated_at":"2025-12-15T02:33:27.000-06:00"},{"id":948,"title":"Elementary Calculus","edition_statement":null,"volume":null,"copyright_year":2020,"isbn10":null,"isbn13":null,"license":"Free Documentation License (GNU)","language":"eng","accessibility_statement":null,"accessibility_features":["unknown"],"description":"This textbook covers calculus of a single variable, suitable for a year-long (or two-semester) course. Chapters 1-5 cover Calculus I, while Chapters 6-9 cover Calculus II. The book is designed for students who have completed courses in high-school algebra, geometry, and trigonometry. Though designed for college students, it could also be used in high schools. The traditional topics are covered, but the old idea of an infinitesimal is resurrected, owing to its usefulness (especially in the sciences). There are 943 exercises in the book, with answers and hints to selected exercises.","contributors":[{"id":5332,"contribution":"Author","primary":false,"corporate":false,"title":null,"first_name":"Michael","middle_name":null,"last_name":"Corral","location":"Schoolcraft College","background_text":"Michael Corral, Schoolcraft College"}],"subjects":[{"id":84,"name":"Calculus","parent_subject_id":7,"call_number":"QA150-272.5","visible_textbooks_count":31,"url":"https://staging.open.umn.edu/opentextbooks/subjects/calculus"},{"id":36,"name":"Pure","parent_subject_id":7,"call_number":"QA37.3","visible_textbooks_count":83,"url":"https://staging.open.umn.edu/opentextbooks/subjects/pure"},{"id":7,"name":"Mathematics","parent_subject_id":null,"call_number":"QA1","visible_textbooks_count":177,"url":"https://staging.open.umn.edu/opentextbooks/subjects/mathematics"}],"publishers":[{"id":927,"url":"http://www.mecmath.net/","year":null,"created_at":"2021-01-11T18:04:56.000-06:00","updated_at":"2021-01-11T18:04:56.000-06:00","name":"Michael Corral"}],"formats":[{"id":2079,"type":"PDF","url":"http://www.mecmath.net/calculus/","price":{"cents":0,"currency_iso":"USD"},"isbn":null},{"id":2080,"type":"LaTeX","url":"http://www.mecmath.net/calculus/","price":{"cents":0,"currency_iso":"USD"},"isbn":null},{"id":2081,"type":"Hardcopy","url":"https://www.lulu.com/en/us/shop/michael-corral/elementary-calculus/paperback/product-j6mggd.html","price":{"cents":0,"currency_iso":"USD"},"isbn":null}],"rating":"5","textbook_reviews_count":1,"reviews":[{"id":34498,"first_name":"Esteban","last_name":"Diaz","position":"Assistant Professor of Instruction","institution_name":"University of Texas at Arlington","comprehensiveness_rating":5,"comprehensiveness_review":"The approach taken by the textbook to begin with infinitesimals is truly commendable. By starting with these fundamental concepts, the reader is able to gain a deep and intuitive understanding of the subject matter. This approach also greatly enhances the understanding of derivatives, as it allows the reader to see how they relate to infinitesimals and the broader context of calculus.\n\nThe treatment of integrals in the textbook is similarly impressive. Every detail is carefully analyzed and explained, making it easy for the reader to follow along and truly grasp the concepts. The author's attention to detail and clear explanations ensure that even complex concepts are presented in a way that is accessible to all readers.","accuracy_rating":5,"accuracy_review":"From the best of my knowledge while reading the book, I didn't see any numerical or logical inconsistency.","relevance_rating":5,"relevance_review":"The content presented in the text is not only current, but has been carefully curated in a way that ensures its relevance and usefulness for the foreseeable future. Rather than relying on fleeting trends or passing fads, the author has focused on presenting foundational concepts that are likely to remain relevant for years to come.\n\nMoreover, the author's thoughtful approach to organizing the material means that updates can be easily incorporated without disrupting the flow of the text. The text is structured in a way that anticipates potential updates and allows for them to be seamlessly integrated without requiring a complete overhaul of the entire book.\n\nThis flexibility is a testament to the author's foresight and attention to detail. By taking the time to structure the text in a way that anticipates changes and allows for easy updates, the author has created a truly valuable resource for students and educators alike. Whether used in a classroom setting or for self-study, this text is sure to remain relevant and useful for many years to come.","clarity_rating":5,"clarity_review":"The language used in the text is impressively clear and accessible, making it easy for readers of all levels to follow along with the material. Even when technical terminology or jargon is used, the author ensures that the necessary context is provided so that readers can fully understand what is being discussed.\n\nFurthermore, the author's ability to provide the appropriate context for technical terms is a testament to their skill as an educator. They recognize that not all readers will have the same level of prior knowledge, and take care to explain concepts in a way that is approachable and informative. This is particularly important in technical subjects such as calculus, where a lack of understanding of key terms and concepts can quickly lead to confusion and frustration.\n\nOverall, the text strikes an impressive balance between technical rigor and accessibility. The language used is consistently lucid and straightforward, while still conveying the necessary complexity of the subject matter. Thanks to the author's skillful use of language and attention to detail, readers are able to engage fully with the material and gain a deep understanding of calculus.","consistency_rating":5,"consistency_review":"The text is notable for its remarkable consistency in terminology and framework, which is essential for helping readers build a strong foundation of understanding. The author has taken great care to ensure that key terms and concepts are presented in a clear and systematic way, making it easier for readers to connect new concepts to the broader framework that has been established. This consistency reflects the author's deep understanding of the material and their commitment to presenting it in a way that is both accurate and accessible. Whether used for self-study or as part of a classroom curriculum, the text's internal consistency ensures that readers are able to engage fully with the material and gain a deep understanding of calculus.","modularity_rating":5,"modularity_review":"The text's well-structured and easily divisible format makes it a versatile resource that can be adapted to a variety of course structures and learning environments. The author's careful attention to avoiding excessive self-referentiality ensures that the text can be easily reorganized without disrupting the reader's learning experience. These features make the text a valuable tool for both educators and students seeking to learn calculus.","organization_rating":5,"organization_review":"The author's mastery of the subject matter is evident in the text's logical and clear presentation of topics. From the foundational concepts of calculus to the more advanced techniques and applications, each chapter builds on the previous one in a way that is easy to follow and understand. The author's skillful organization of the material not only makes it easier for readers to grasp individual topics but also helps them to see how these topics fit together into a broader framework. This approach ensures that readers come away with a comprehensive understanding of calculus and its real-world applications. Whether used for self-study or as part of a classroom curriculum, the text's clear and logical presentation of material makes it an invaluable resource for anyone seeking to learn calculus.","interface_rating":5,"interface_review":"The text's interface design is a standout feature, with the author's attention to detail ensuring a seamless and distraction-free reading experience. Navigation is intuitive, and images/charts are clear with no distortion. Unnecessary display features are avoided, resulting in a functional and aesthetically pleasing resource for students and educators.","grammatical_rating":5,"grammatical_review":"To the best of my knowledge the text contains no grammatical errors.","cultural_rating":5,"cultural_review":"The textbook is for teaching of Calculus.","overall_rating":10,"overall_review":"I recently came across a textbook that has blown me away with its quality. It is one of the best textbooks I have ever seen and I am thoroughly impressed by it. This is the first time I have truly understood infinitesimals and their real-world applications. If I had the opportunity to choose which textbook to teach with, I would undoubtedly choose this one.\n\nThe author's treatment of derivatives is exceptionally elegant, and they have done an excellent job of incorporating numerous pedagogical concepts. While the part on integrations follows a more direct approach, it still perfectly complements the overall structure of the textbook.\n\nThere are a few minor issues, such as the notation for sin dx. Personally, I would prefer something like sin(dx), but this is just a small detail that can easily be corrected.\n\nFurthermore, the sections on exercises are well-organized and contain different exercises tailored to different levels of understanding. The author stays true to their belief that mainstream textbooks are often filled with unnecessary information that only serves to cloud the learning process instead of enhancing it. Overall, I highly recommend this textbook to anyone interested in the subject.","created_at":"2023-04-05T19:55:32.000-05:00","updated_at":"2023-04-05T19:55:32.000-05:00"}],"url":"https://staging.open.umn.edu/opentextbooks/textbooks/elementary-calculus","updated_at":"2025-12-15T02:31:22.000-06:00"},{"id":780,"title":"Multivariable Calculus","edition_statement":null,"volume":null,"copyright_year":2019,"isbn10":null,"isbn13":null,"license":"Attribution","language":"eng","accessibility_statement":null,"accessibility_features":["unknown"],"description":"This book covers the standard material for a one-semester course in multivariable calculus. The topics include curves, differentiability and partial derivatives, multiple integrals, vector fields, line and surface integrals, and the theorems of Green, Stokes, and Gauss. Roughly speaking the book is organized into three main parts corresponding to the type of function being studied: vector-valued functions of one variable, real-valued functions of many variables, and finally the general case of vector-valued functions of many variables. As is always the case, the most productive way for students to learn is by doing problems, and the book is written to get to the exercises as quickly as possible. The presentation is geared towards students who enjoy learning mathematics for its own sake. As a result, there is a priority placed on understanding why things are true and a recognition that, when details are sketched or omitted, that should be acknowledged. Otherwise the level of rigor is fairly normal. Matrices are introduced and used freely. Prior experience with linear algebra is helpful, but not required.","contributors":[{"id":4987,"contribution":"Author","primary":false,"corporate":false,"title":null,"first_name":"Don","middle_name":null,"last_name":"Shimamoto","location":"Swarthmore College","background_text":"Don Shimamoto, Swarthmore College"}],"subjects":[{"id":84,"name":"Calculus","parent_subject_id":7,"call_number":"QA150-272.5","visible_textbooks_count":31,"url":"https://staging.open.umn.edu/opentextbooks/subjects/calculus"},{"id":36,"name":"Pure","parent_subject_id":7,"call_number":"QA37.3","visible_textbooks_count":83,"url":"https://staging.open.umn.edu/opentextbooks/subjects/pure"}],"publishers":[{"id":759,"url":"https://drive.google.com/drive/folders/1VBn7HiZBlvOVbMCcjL1Yh5AoJcB7gj-j","year":2020,"created_at":"2019-10-12T12:54:05.000-05:00","updated_at":"2020-12-27T17:12:10.000-06:00","name":"Don Shimamoto"}],"formats":[{"id":1343,"type":"PDF","url":"https://drive.google.com/drive/folders/1VBn7HiZBlvOVbMCcjL1Yh5AoJcB7gj-j?usp=sharing","price":{"cents":0,"currency_iso":"USD"},"isbn":null},{"id":1365,"type":"Hardcopy","url":"https://www.amazon.com/gp/product/1708246991","price":{"cents":0,"currency_iso":"USD"},"isbn":null}],"rating":"5","textbook_reviews_count":1,"reviews":[{"id":3399,"first_name":"Andy","last_name":"Rich","position":"Professor of Mathematics","institution_name":"PALNI, Manchester University","comprehensiveness_rating":5,"comprehensiveness_review":"Has all the usual topics and then some.  I liked the development of differential forms towards the end and having chapter 11 as a teaser for higher level stuff.  The development was clear enough that I hope most students at this level could get it.\r\nSome of my favorite examples were missing: e.g., the cycloid and deriving Kepler's laws from Newton's laws, but everybody has their own favorites so I am okay with that.  \r\nIn discussing multivariable continuity, it would have been nice to pull out the two path discussion which appears in the text and highlight it as a theorem, but these are all minor points.  I still give this text a 5 for comprehensiveness.","accuracy_rating":5,"accuracy_review":"My only complaint here is in the discussion of torsion.  He describes torsion as \"wobbling\" which to me gives the wrong idea.  Wobbling means going back and forth which can happen in the plane.  Torsion is \"twisting\" out of the plane.\r\nThe mathematics is all correct and the author is honest about where things are being swept under the rug, e.g., in the proof of Green's Theorem.","relevance_rating":5,"relevance_review":"This is not much of an issue for math texts.  ","clarity_rating":5,"clarity_review":"Excellent!  Good clear explanations of the ideas behind the theory, e.g., Lagrange multipliers which are sometimes presented as magic, but here are motivated with geometrical ideas.  Nice treatment of multidimensional chain rule via matrix multiplication with one section on the conceptual picture and one on computations.\r\nGood diagrams throughout, present whenever needed to help with understanding, e.g., showing the relationship of two different parametrizations when proving that the value of the integral is independent of the parametrization.","consistency_rating":5,"consistency_review":"No problems that I saw.","modularity_rating":5,"modularity_review":"The division into parts, chapters, and sections made sense and the sections were not too long.","organization_rating":5,"organization_review":"Good.  The preface and table of contents outline the organization and make it easy to find topics.\r\nIt might be helpful to introduce polar coordinates earlier.","interface_rating":5,"interface_review":"No problems that I saw.  It easy to navigate jumping around with the bookmarks pane in Adobe.  Good color illustrations showing geometric pictures when helpful.","grammatical_rating":5,"grammatical_review":"Fine.","cultural_rating":5,"cultural_review":"Not really relevant.","overall_rating":10,"overall_review":"I really liked this text.  It is more theoretical, more proof-based than what I usually teach, and I might skip some of that if I were teaching from this text, but I think it is good to include the proofs in the text.  \r\nI liked the presentation of differential forms towards the end.  I think one addition to chapter 11 as a further teaser and to try to show the relationship of the various theorems, would be to set up the deRham sequence in R^3 and show how gradient, curl, and divergence come into that single unifying sequence.  (This tiptoes up to topology of the underlying space which the author has already alluded to at various places.)\r\nThe conversational style was great: \"trying to find the maximum of a function like ... is silly\" for example.  Humor is scattered throughout, for example, including a picture of a porcupine as an example of a mammal with an orientation. \r\nThere seemed to be plentiful exercises.  \r\nOverall, I think this is an excellent text for multivariable calculus.","created_at":"2019-12-19T09:23:55.000-06:00","updated_at":"2019-12-19T09:23:55.000-06:00"}],"url":"https://staging.open.umn.edu/opentextbooks/textbooks/multivariable-calculus","updated_at":"2025-12-15T02:16:56.000-06:00"},{"id":198,"title":"APEX Calculus","edition_statement":null,"volume":null,"copyright_year":2014,"isbn10":null,"isbn13":null,"license":"Attribution-NonCommercial","language":"eng","accessibility_statement":null,"accessibility_features":["unknown"],"description":"This text comprises a three–text series on Calculus. The first part covers material taught in many “Calc 1” courses: limits, derivatives, and the basics of integration, found in Chapters 1 through 6.1. The second text covers material often taught in “Calc 2:” integration and its applications, along with an introduction to sequences, series and Taylor Polynomials, found in Chapters 5 through 8. The third text covers topics common in “Calc 3” or “multivariable calc:” parametric equations, polar coordinates, vector–valued functions, and functions of more than one variable, found in Chapters 9 through 14. More information, including free downloads of .pdf versions of the text, is available at www.apexcalculus.com.","contributors":[{"id":3487,"contribution":"Author","primary":true,"corporate":false,"title":null,"first_name":"Gregory","middle_name":null,"last_name":"Hartman","location":"Virginia Military Institute","background_text":"Gregory Hartman, PhD. Author. Associate Professor of Mathematics at Virginia Military Institute, where he has been on faculty since 2005. He earned his PhD in Mathematics from Virginia Tech in 2002."},{"id":3488,"contribution":"Author","primary":false,"corporate":false,"title":null,"first_name":"Brian","middle_name":null,"last_name":"Heinold","location":"Mount St. Mary’s University","background_text":"Brian Heinold, PhD. Contributor. Associate Professor, Mathematics and Computer Science Department, Mount St. Mary's University. Heinold came to Mount St. Mary's in 2006, after receiving his doctorate from Lehigh University. Since then he has taught a variety of math and computer science courses. He has mentored several honors projects, coordinated the department's Smalltalk colloquium series and advised a number of COMAP teams. He has given presentations on fractals and mathematical imagery, teaching and graph theory."},{"id":3489,"contribution":"Author","primary":false,"corporate":false,"title":null,"first_name":"Troy","middle_name":null,"last_name":"Siemers","location":"Virginia Military Institute","background_text":"Troy Siemers, PhD. Contributor. Head of the Applied Mathematics program at VMI. He earned his Ph. D. from the University of Virginia and previously led a summer program abroad in Lithuania."},{"id":3490,"contribution":"Author","primary":false,"corporate":false,"title":null,"first_name":"Dimplekumar","middle_name":null,"last_name":"Chalishajar","location":"Virginia Military Institute","background_text":"Dimplekumar Chalishajar, PhD. Contributor. Assoicate Professor, Department of Applied Mathematics and Computer Science, Virginia Military Institute."},{"id":3491,"contribution":"Editor","primary":false,"corporate":false,"title":null,"first_name":"Jennifer","middle_name":null,"last_name":"Bowen","location":"The College of Wooster","background_text":"Jennifer Bowen, PhD. Associate Professor and Department Chair of Mathematics and Computer Science, The College of Wooster. Bowen earned a BA in Mathematics with Honors from Boston College, and both an MS and PhD in Mathematics from The University of Virginia. Bowen teaches a range of courses, including Math in Contemporary Society, Basic Statistics, Calculus I, Calculus II, Multivariate Calculus, Transition to Advanced Mathematics, and Abstract Algebra."}],"subjects":[{"id":84,"name":"Calculus","parent_subject_id":7,"call_number":"QA150-272.5","visible_textbooks_count":31,"url":"https://staging.open.umn.edu/opentextbooks/subjects/calculus"},{"id":36,"name":"Pure","parent_subject_id":7,"call_number":"QA37.3","visible_textbooks_count":83,"url":"https://staging.open.umn.edu/opentextbooks/subjects/pure"},{"id":7,"name":"Mathematics","parent_subject_id":null,"call_number":"QA1","visible_textbooks_count":177,"url":"https://staging.open.umn.edu/opentextbooks/subjects/mathematics"}],"publishers":[{"id":76,"url":"http://www.apexcalculus.com/","year":null,"created_at":"2018-09-07T12:22:37.000-05:00","updated_at":"2018-09-26T13:10:21.000-05:00","name":"APEX Calculus"}],"formats":[{"id":90,"type":"PDF","url":"https://drive.google.com/file/d/1bDsqf4u3rNz_dVnlViE_AXrhWpJoBi3H/view","price":{"cents":0,"currency_iso":"USD"},"isbn":null},{"id":91,"type":"Hardcopy","url":"http://www.apexcalculus.com/purchase","price":{"cents":1100,"currency_iso":"USD"},"isbn":null}],"rating":"4.5","textbook_reviews_count":5,"reviews":[{"id":326,"first_name":"Anne","last_name":"Nelson Fisher","position":"Mathematics Instructor","institution_name":"Central Lakes College","comprehensiveness_rating":4,"comprehensiveness_review":"The text covers all necessary topics for Calculus I and II. However, no justification or proof for the derivatives of the natural exponential and natural logarithmic functions are provided. They are simply stated among the basic rules for differentiation without development. Most topics in Multivariable Calculus are included, with the exception of vector fields. No review of Precalculus topics is included, nor is any historical development of calculus. Conversational discussions of theorems are used in place of formal proofs in many cases throughout the entire text. An index is included, and the search function is accurate.\r\n\r\nIf the text is to be used for Calculus I and II only, I would rate its overall comprehensiveness at 4-5, based on the comments above. For Multivariable Calculus, I would rate it at 3.\r\n ","accuracy_rating":5,"accuracy_review":"For the most part, the accuracy of the mathematical content is excellent.  In a careful reading of the Calculus I material, a few typographical errors and one mathematical error (which might also have been typographical) were found. Since there is no discussion of people in the text, it contains no content that I would construe as biased.","relevance_rating":4,"relevance_review":"There is no topic in the text which would make the material outdated, though a lack of interactive apps, web links, and computer-generated graphics may make it appear less stimulating than the modern for-profit, online textbook.  Updates may be made difficult by the choice of numbering definitions, theorems and key ideas from 1 to n throughout the text, rather than by chapter and number (e.g. Thm. 2.5).","clarity_rating":5,"clarity_review":"The text is extremely readable for the first-time calculus student. My notes repeatedly include the words \"clear\", \"understandable\", and  \"straightforward\". The explanations of the concepts of the limit, the derivative, differentials, integration, sequences, and series are conversational, accurate, and lucid. Applications are well-explained, though in some cases (e.g. the disk and washer methods of determining volumes) more and better graphs and pictures would be appreciated.","consistency_rating":5,"consistency_review":"Notation and terminology are consistent.  ","modularity_rating":5,"modularity_review":"For the most part, chapter sections are divided as expected for a calculus text. Section 6.1 is remarkably long, including not only integration by substitution, but trigonometric integrals as well. Institutions that include only basic u-substitutions in Calculus I and trigonometric integrals in Calculus II will need to divide this section. As noted earlier, the text is quite readable, and the division of chapters into sections, and further into segments of concept development, and examples are appropriate.","organization_rating":4,"organization_review":"The organization of the text is logical and consistent, and its flow is smooth. As previously noted, theorems are not generally justified with formal proofs but with conversational discussions. Topics are ordered appropriately, except, in my opinion, for the presentation of the derivatives of exponential and logarithmic functions without background development.","interface_rating":5,"interface_review":"Navigating by use of the table of contents, bookmarks, or by page number is error-free. Highlighting and \"sticky notes\" are available. An index is included, but the search tool is quick and easy to use.  Graphs are clear. No other pictures or images are included, and no internet links are included (which could become outdated). If students/instructors choose to print a hard copy of the text, there is blank space at the bottom of each page for hand-written notes.","grammatical_rating":5,"grammatical_review":"The only grammatical errors found (notably, all in section 2.1) were likely typographical. Sentence structure, choice of words, and punctuation were all very good. ","cultural_rating":5,"cultural_review":"This item is not very applicable to the text, as no mention of culture or ethnicity is made. A check of several examples and application problems that refer to people appear to refer to women as often as they refer to men.","overall_rating":9,"overall_review":"Problem sets are included at the end of each section, and answers to selected problems (most of the odd problems) are found at the end of the text. However, the sets of problems are generally more limited that what is found in a traditional textbook, and answers are sometimes spare. (For example, proofs are \"left to the reader\".) No review sections or problem sets are included at the end of chapters.","created_at":"2016-01-07T18:00:00.000-06:00","updated_at":"2016-01-07T18:00:00.000-06:00"},{"id":925,"first_name":"Samuel","last_name":"Horelick","position":"instructor","institution_name":"J. Sargeant Reynolds Community College","comprehensiveness_rating":5,"comprehensiveness_review":"The text covers all areas and skills of Calculus I, Calculus II, and Calculus III. This is an excellently written standard Calculus text that includes all ideas and skills of comprehensive college Calculus sequence. The text provides answers to exercises and an effective index.","accuracy_rating":5,"accuracy_review":"The content is accurate, error-free, very-well written, professionally organized and unbiased.","relevance_rating":5,"relevance_review":"The content is perfectly up-to-date. This comprehensive college Calculus textbook will not become obsolete. The text is professionally written and arranged in such a way as to make any future updates easy and straightforward to implement.","clarity_rating":5,"clarity_review":"The text is written clearly and lucidly, with great variety of excellent examples and clear, concise explanations. It provides adequate context for mathematical terminology used in the text.","consistency_rating":5,"consistency_review":"The text is effectively organized into a standard Calculus sequence. It is professionally written and arranged. The text is internally consistent in terms of terminology and framework.\n","modularity_rating":5,"modularity_review":"The text is effectively organized into smaller sections and units that can be assigned at the appropriate points within the course. The text is professionally written, arranged, and properly formatted into easily manageable units well-suited for college students. The text can be easily reorganized and realigned with the requirements of any Calculus course without presenting any disruption to the reader.","organization_rating":5,"organization_review":"The textbook is very effectively organized. The topics in the text are presented clearly and arranged logically.","interface_rating":5,"interface_review":"The text is user-friendly. It is easy to navigate. All text images, graphs, and charts are clear. PDF file is up-to-date and easily navigable. Nothing to distract or confuse the reader..","grammatical_rating":5,"grammatical_review":"The text contains no mathematical or grammatical errors.","cultural_rating":5,"cultural_review":"This is an excellent Calculus textbook. The text is professionally written and edited. It is not culturally insensitive or offensive in any way. This very effective text is aimed at all college students regardless of race, ethnicity, creed, or background.","overall_rating":10,"overall_review":"I have been using this book since 2015 for both lecture and online Calculus classes. My students are from various racial, ethnic, cultural, and religious backgrounds, as well as different countries of origin. Some students use an online version of the textbook while other purchase a printed copy. This book is well-liked by virtually all students. It is clear, excellently organized, and easy to use. Highly recommended.","created_at":"2017-02-08T18:00:00.000-06:00","updated_at":"2017-02-08T18:00:00.000-06:00"},{"id":996,"first_name":"Bryan","last_name":"Faulkner","position":"Associate Professor","institution_name":"Ferrum College","comprehensiveness_rating":5,"comprehensiveness_review":"The text covers material for a first semester course in differential calculus and begins integral calculus with antiderivatives and Riemann sums. The book begins with limits (even the epsilon-delta definition) and continuity before delving into derivatives and their applications (e.g. curve sketching, Newton's method, related rates, and optimization).","accuracy_rating":5,"accuracy_review":"Content is accurate, error-free and unbiased.","relevance_rating":5,"relevance_review":"Content is up-to-date and should remain so indefinitely. The non-mathematical application primarily used are those dealing with position, velocity, and acceleration.","clarity_rating":5,"clarity_review":"The text has the appropriate amount of prose with adequate mathematically written explanations.","consistency_rating":5,"consistency_review":"The text is internally consistent in terms of terminology and framework. The text terminology standard to most differential calculus books, such as product rule, quotient rule, and chain rule.","modularity_rating":5,"modularity_review":"The section lengths within chapters are appropriate for a one hour class meeting, if the students have read and thought through the section beforehand.","organization_rating":5,"organization_review":"The organization of the book is standard: limits and continuity, differentiation rules, curve sketching, applications. The book doesn't take too much time in connecting the ideas of limits and differentiation. Instructors should expect to spend more time explaining this connection.","interface_rating":5,"interface_review":"The book is freely available as a PDF with hyperlinked table of contents. The third volume's (i.e. for multivariable calculus) PDF allows the user to manipulate the graphics.","grammatical_rating":5,"grammatical_review":"The text contains no grammatical errors.","cultural_rating":5,"cultural_review":"The text is not culturally insensitive or offensive in any way.","overall_rating":10,"overall_review":"As the author points out in the preface, the number of exercises at the end of each section is not too large. Students can be expected to complete all of the exercises. \nThe reader of this text can skip the \"epsilon-delta\" definition for limits without too much frustration.","created_at":"2017-02-08T18:00:00.000-06:00","updated_at":"2017-02-08T18:00:00.000-06:00"},{"id":2184,"first_name":"Bethany","last_name":"Downs","position":"Mathematics Instructor","institution_name":"Portland Community College","comprehensiveness_rating":4,"comprehensiveness_review":"This a is a comprehensive text that covers all the basic material presented in a standard calculus sequence.  It is clearly written, with easy-to-understand explanations. Many formal proofs are omitted, but the theorems and ideas are explained well.","accuracy_rating":5,"accuracy_review":"The text is accurate, error-free, and unbiased.","relevance_rating":5,"relevance_review":"The content is up-to-date.  It is relevant and in no way seems dated.  The use of the \"classic\" position-velocity-acceleration example  will remain applicable indefinitely.","clarity_rating":5,"clarity_review":"The writing is clear and easy to understand.  The explanations are concise and to-the-point.  The examples are well chosen and show a variety of different situations and problem-solving techniques.","consistency_rating":5,"consistency_review":"The text is consistent in its use of notation, symbols, terminology, and framework.","modularity_rating":5,"modularity_review":"The section length is appropriate for the material presented and a typical class period.  The text is well organized within each chapter and section.","organization_rating":5,"organization_review":"The organization of the book is standard and presents the material in a logical and clear fashion.","interface_rating":5,"interface_review":"The interface is user-friendly.  The table of contents and search features works well.  The type-face is easy to read, and the graphs and tables are clear.","grammatical_rating":5,"grammatical_review":"The text contains no grammatical errors.","cultural_rating":5,"cultural_review":"The text is not culturally insensitive or offensive in any way.","overall_rating":10,"overall_review":"Overall, this is a concise, compact, straightforward, understandable, but complete approach to a calculus textbook.  It doesn't include some of the \"extras\" that one would expect from a more traditional textbook such as a pre-calculus review, interesting application problems, larger projects for students to complete, or rigorous proofs of all the theorems.  However, all the basic material is included.","created_at":"2018-06-19T19:00:00.000-05:00","updated_at":"2018-06-19T19:00:00.000-05:00"},{"id":3913,"first_name":"Joel","last_name":"Berman","position":"Professor","institution_name":"Valencia College","comprehensiveness_rating":4,"comprehensiveness_review":"I have used this the semester-based courses Calculus 1 and Calculus 2.  I will not comment on Calculus 3.  The text addresses all of the required areas for the courses, though I would like to see a couple other areas: \r\n(1) a section providing some of the motivation for the development of Calculus.  Some information is provided in a couple paragraphs at the beginning of the Limits Chapter [Chapter 1], but no examples or exercises related to the motivation.  In fact, the motivation for limit is not really addressed until Chapter 2.  I supplement this on day 1 of my course. \r\n(2) While approximations with differentials is well-addressed, the related \"Linear Approximation\" topic is not.  There is an example of a Linear Approximation in section 2.2 of the text, and several exercises related to it, but it is rarely addressed afterward. This is another topic I supplement. \r\n(3) Applications tend to be only addressed in specific application sections, rather than introduced early and called back upon after learning new rules or techniques.\r\n(4) Most of the conceptual exercises are either true/false, or open ended.  I would like to see more conceptual exercises with graphical or numerical data.\r\n\r\nThe text lacks proofs of most of the stated theorems.  I am fine with that, and supplement the proofs that I think are most instructive.  My classes see very few Mathematics majors and many Engineering majors, so I do not think that showing the proofs for all of the theorems is necessary, as most of my students will never need the proofs, but will need the appropriate techniques.","accuracy_rating":5,"accuracy_review":"I have not found any errors in the writing, nor areas of bias.","relevance_rating":5,"relevance_review":"I have not found any use of \"current\" data for examples or exercises, so there should not be any issues with the updating.","clarity_rating":5,"clarity_review":"Text is readable, using notation appropriate for the level of students that are taking the course.","consistency_rating":5,"consistency_review":"The terminology of the text is consistent throughout. I have not found any issues.","modularity_rating":5,"modularity_review":"The text is well structured.  Sections always start on new pages.  Examples and Theorems have specific \"call-outs\" that are used consistently throughout the text.  There are clear Sub-Headings within sections for sub-topics.  Exercise sets always start on new pages.","organization_rating":4,"organization_review":"Very good, overall.  Though there are a couple areas that I have concerns with:\r\n(1) The section on Hyperbolic Functions is presented in Chapter 6 with Techniques for Antidifferentiation.  The derivatives and antiderivatives are presented in the section, but I think I would have broken that up into two separate topics, and placed the derivative techniques in an earlier chapter.\r\n(2) L'Hopital's Rule is also presented in Chapter 6 with Techniques for Antidifferentiation, immediately before Improper Integration.  I think that L'Hopital's Rule is useful for curve sketching, so I prefer to teach it as an application of differentiation.","interface_rating":5,"interface_review":"I have not found any issues with the interface.  The text has appropriate bookmarks that are all linked correctly.  Graphs show correctly.  The large-size version of the PDF has graphs that can be dragged to show different perspectives (useful for Calculus 3).","grammatical_rating":5,"grammatical_review":"I have not found any grammatical issues.","cultural_rating":3,"cultural_review":"There is nothing offensive in the course.  But the examples do not show any inclusiveness.","overall_rating":9,"overall_review":"Overall an excellent text, though there are some areas that I tend to supplement.  If you are interested in getting into using OER textbooks for a Calculus course.  This one would be a good choice to start with.","created_at":"2020-06-04T12:05:32.000-05:00","updated_at":"2020-06-04T12:05:32.000-05:00"}],"url":"https://staging.open.umn.edu/opentextbooks/textbooks/apex-calculus","updated_at":"2025-12-15T02:01:27.000-06:00"},{"id":674,"title":"APEX PreCalculus","edition_statement":null,"volume":null,"copyright_year":2017,"isbn10":null,"isbn13":null,"license":"Attribution-NonCommercial","language":"eng","accessibility_statement":null,"accessibility_features":["unknown"],"description":"This text was written as a prequel to the APEXCalculus series, a three–volume series on Calculus. This text is not intended to fully prepare students with all of the mathematical knowledge they need to tackle Calculus, rather it is designed to review mathematical concepts that are often stumbling blocks in the Calculus sequence. It starts basic and builds to more complex topics. This text is written so that each section and topic largely stands on its own, making it a good resource for students in Calculus who are struggling with the supporting mathemathics found in Calculus courses. The topics were chosen based on experience; several instructors in the Applied Mathemathics Department at the Virginia Military Institute (VMI) compiled a list of topics that Calculus students commonly struggle with, giving the focus of this text. This allows for a more focused approach; at first glance one of the obvious differences from a standard Pre-Calculus text is its size.","contributors":[{"id":4793,"contribution":"Author","primary":false,"corporate":false,"title":"Ph.D.","first_name":"Amy","middle_name":"Givler","last_name":"Chapman","location":"Virginia Military Institute","background_text":"Amy Givler Chapman, Ph.D., Department of Applied Mathematics, Virginia Military Institute"},{"id":4794,"contribution":"Author","primary":false,"corporate":false,"title":"Ph.D.","first_name":"Meagan","middle_name":null,"last_name":"Herald","location":"Virginia Military Institute","background_text":"Meagan Herald, Ph.D., Department of Applied Mathematics, Virginia Military Institute"},{"id":4795,"contribution":"Author","primary":false,"corporate":false,"title":"Ph.D.","first_name":"Jessica","middle_name":null,"last_name":"Libertini","location":"Virginia Military Institute","background_text":"Jessica Libertini, Ph.D., Department of Applied Mathematics, Virginia Military Institute"}],"subjects":[{"id":84,"name":"Calculus","parent_subject_id":7,"call_number":"QA150-272.5","visible_textbooks_count":31,"url":"https://staging.open.umn.edu/opentextbooks/subjects/calculus"},{"id":36,"name":"Pure","parent_subject_id":7,"call_number":"QA37.3","visible_textbooks_count":83,"url":"https://staging.open.umn.edu/opentextbooks/subjects/pure"}],"publishers":[{"id":652,"url":"http://www.apexcalculus.com/other-texts","year":null,"created_at":"2019-02-28T11:44:48.000-06:00","updated_at":"2019-02-28T11:44:48.000-06:00","name":"APEX Calculus"}],"formats":[{"id":1158,"type":"PDF","url":"https://drive.google.com/file/d/12b2cwH7afXhsYSDb-QCWKmFK2QCq7UfY/view","price":{"cents":0,"currency_iso":"USD"},"isbn":null}],"rating":"4.5","textbook_reviews_count":1,"reviews":[{"id":33394,"first_name":"Cynthia","last_name":"Huffman","position":"University Professor","institution_name":"Pittsburg State University","comprehensiveness_rating":4,"comprehensiveness_review":"As mentioned in the preface, the text is “designed to review mathematical concepts that are often stumbling blocks in the Calculus sequence.”  There are three chapters – Numbers \u0026 Functions, Basic Skills for Calculus, and Solving \u0026 Trigonometric Functions.   The authors do a good job of covering all the common precalculus areas with which students struggle in calculus. (Factoring doesn’t include the cases where the leading coefficient is not equal to 1.)  There is no index or glossary, however, solutions to the exercises are included.","accuracy_rating":4,"accuracy_review":"The content is unbiased, however it is not error-free.  While reading the text, I noticed more typographical, grammatical, and mathematical errors than I expected.  (I plan on sending a copy of the errors that I found to the authors.)","relevance_rating":5,"relevance_review":"The text is current and relevant for its intended audience.  The authors do a good job connecting the topics to the real world to explain to the students why each topic is important.","clarity_rating":5,"clarity_review":"The text is well-written and at a level that makes it very readable for students.  It is clearly written with students as the intended audience.  The explanations and solutions of examples are very clear and easy to follow.","consistency_rating":5,"consistency_review":"The text is very consistent with content and worked examples and exercises.  The consistency of the exercise sets especially stood out with questions about “Terms \u0026 Concepts” followed by problems of varying difficulty","modularity_rating":5,"modularity_review":"There are a few places where the text refers to something done previously, but for the most part, an instructor could assign individual sections as needed.","organization_rating":4,"organization_review":"For the most part the text is very well-organized and the topics are presented in a logical clear fashion.  I did find the title of Chapter 3 (Solving and Trigonometric Functions) confusing.  Since “Solving” and “Trigonometric Functions” are separate topics, I would suggest they be split into separate chapters.","interface_rating":5,"interface_review":"The text is a pdf.  There are no navigation problems.  The graphics are clear and very helpful for the reader.","grammatical_rating":4,"grammatical_review":"There are some grammatical errors.  For example, in the first section there are several times when the singular “parenthesis” is used, when it should be the plural form “parentheses”. The word “term” is used at times, when it should be “factor” or “expression”.  Of more concern are the mathematical errors scattered throughout the text.","cultural_rating":5,"cultural_review":"I did not notice any places of concern for being culturally insensitive or offensive.","overall_rating":9,"overall_review":"With a bit more editing, this will be a great text for students needing support with the common precalculus areas in which calculus students struggle.  There are excellent examples throughout the text to illustrate the concepts.  It is obviously intentionally written for students, with clear explanations, the inclusion of alternate wording students might run across, and motivation for learning the techniques and concepts.  A wonderful resource!","created_at":"2021-09-26T22:38:50.000-05:00","updated_at":"2021-09-26T22:38:50.000-05:00"}],"url":"https://staging.open.umn.edu/opentextbooks/textbooks/apex-precalculus","updated_at":"2025-12-15T02:15:51.000-06:00"},{"id":557,"title":"Introduction to GNU Octave: A brief tutorial for linear algebra and calculus students","edition_statement":null,"volume":null,"copyright_year":2017,"isbn10":null,"isbn13":null,"license":"Attribution-ShareAlike","language":"eng","accessibility_statement":null,"accessibility_features":["unknown"],"description":"This brief book provides a noncomprehensive introduction to GNU Octave, a free open source alternative to MatLab. The basic syntax and usage is explained through concrete examples from the mathematics courses a math, computer science, or engineering major encounters in the first two years of college: linear algebra, calculus, and differential equations.","contributors":[{"id":4500,"contribution":"Author","primary":true,"corporate":false,"title":null,"first_name":"Jason","middle_name":null,"last_name":"Lachniet","location":"Wytheville Community College","background_text":"Jason Lachniet, Wytheville Community College"}],"subjects":[{"id":83,"name":"Algebra","parent_subject_id":7,"call_number":"QA150-272.5","visible_textbooks_count":29,"url":"https://staging.open.umn.edu/opentextbooks/subjects/algebra"},{"id":84,"name":"Calculus","parent_subject_id":7,"call_number":"QA150-272.5","visible_textbooks_count":31,"url":"https://staging.open.umn.edu/opentextbooks/subjects/calculus"},{"id":36,"name":"Pure","parent_subject_id":7,"call_number":"QA37.3","visible_textbooks_count":83,"url":"https://staging.open.umn.edu/opentextbooks/subjects/pure"},{"id":7,"name":"Mathematics","parent_subject_id":null,"call_number":"QA1","visible_textbooks_count":177,"url":"https://staging.open.umn.edu/opentextbooks/subjects/mathematics"}],"publishers":[{"id":523,"url":"http://www.wcc.vccs.edu/sites/default/files/Introduction-to-GNU-Octave.pdf","year":null,"created_at":"2018-09-07T12:22:40.000-05:00","updated_at":"2020-01-02T23:48:16.000-06:00","name":"Jason Lachniet"}],"formats":[{"id":882,"type":"PDF","url":"http://www.wcc.vccs.edu/sites/default/files/Introduction-to-GNU-Octave.pdf","price":{"cents":0,"currency_iso":"USD"},"isbn":null},{"id":883,"type":"Hardcopy","url":"http://www.lulu.com/shop/jason-lachniet/introduction-to-gnu-octave/paperback/product-23933033.html","price":{"cents":0,"currency_iso":"USD"},"isbn":null}],"rating":"4.5","textbook_reviews_count":2,"reviews":[{"id":2706,"first_name":"Julia","last_name":"Varbolow","position":"Associate Professor","institution_name":"Thomas Nelson Community College","comprehensiveness_rating":5,"comprehensiveness_review":"The text seems to cover all the introductory topics for a new user to GNU Octave. The index and glossary were effective. \r\nI believe I could readily use this for a great deal of the computational or graphing my students use in my Introductory Linear Algebra, Introduction to ODE, or Multivariate Calculus courses. ","accuracy_rating":4,"accuracy_review":"The text is unbiased, and specifically states where MATLAB is more efficient. I found no errors in the textbook's descriptions and examples of the commands \u0026 syntax that I tested: matrix operations, LU decomps, single-variable differentiation, single-variable definite \u0026 indefinite integration, 2D graphs, 3D graphs of curves and surfaces, Double Integrals, solving simple ODEs, Direction Fields, etc. However, there is still a great deal of material that I did not test.","relevance_rating":4,"relevance_review":"The textbook can easily be updated as the software changes. The only issue I potentially see is that many free software programs have trouble creating and maintaining robust support, development, debugging, etc, depending on the community. This could make it difficult for the textbook to keep up lists of discovered bugs, corercted bugs, and such within the text itself; however, this could be addressed if there is online site for this information.\r\n\r\nAs far as I am concerned, this is the nature of the material and not the textbook itself.","clarity_rating":4,"clarity_review":"As I have never used GNU Octave before, and I have not used MATHLAB in decades, so I was testing the material in the text as a complete beginner. I generally found the explanations of commands and syntax clear. I suspect those not clear to me simply require more practice on my part.","consistency_rating":5,"consistency_review":"The text is consistent in terms of technology and framework.","modularity_rating":5,"modularity_review":"The text is readily divisible into smaller sections. Any problems created by skipping or reordering material is easily addressed by constructing a reduced index specific to your reduced coverage. \r\nE.g. I went to solve ODE before reading about some of the necessary syntax; I simply went to the index and found the sections that I required for the commands I was learning.","organization_rating":5,"organization_review":"The text has organzied the material in a logical order. Each Chapter covers related topics using related commands of increasing complexity, and the Chapters do cover the topics in a logical order.","interface_rating":3,"interface_review":"Many of the figures were not directly below (or even above) the relevant material. Some were actually in the middle of the next example. This was terribly distracting and caused me to have to switch back and forth between pages multiple times as I tried to follow the materials and examples.\r\n\r\n","grammatical_rating":5,"grammatical_review":"I noticed no grammatical or spelling errors.","cultural_rating":5,"cultural_review":"Not applicable. \r\n\r\nThere are not even gendered pronouns used in the text, only \"you\".","overall_rating":9,"overall_review":null,"created_at":"2019-03-28T17:30:24.000-05:00","updated_at":"2019-03-28T17:30:24.000-05:00"},{"id":3664,"first_name":"Jeff","last_name":"Graham","position":"Associate Professor","institution_name":"Susquehanna University","comprehensiveness_rating":4,"comprehensiveness_review":"For an introduction, it has all the things one would need.  I expect that once one got the hang of Octave, it would be easy to figure out the things that one might need that are not covered.  The index appears to cover all of the major topics.  It might be too difficult to do, but linking the index items to to their page in the text would be really nice.  Also, the ability to go from the table of contents to a section and back to the table of contents would be really nice.  Maybe this is too difficult to achieve.\r\nIt might be nice if there was a discussion of floating point arithmetic in the book.  Students will be surprised otherwise they start getting weird answers in some places.  In particular, in the section on limits in calculus, if you try to  calculate some limits simply by evaluating at values of x closer and closer to the limiting value of x, you can get some strange and misleading answers due to the nature of floating point computations.","accuracy_rating":5,"accuracy_review":"I've spot checked commands given and everything seems in order.  I know the software changes from time to time, so I would not be surprised to find a command or two that doesn't work as advertised, but I found none that didn't work.","relevance_rating":5,"relevance_review":"The topics that are covered are pretty timeless.  Octave should be pretty stable as a mature software product.  I think this book will remain relevant.  Updating periodically will be necessary since new features will undoubtedly be added to Octave in the future.  I doubt the basic commands given in this book will change much though.","clarity_rating":5,"clarity_review":"I found the book to read well.  It is written in very straightforward prose that I believe students could easily follow.","consistency_rating":5,"consistency_review":"Much of the consistency is probably due to Octave itself, but I found no glaring inconsistent terminology.  The author uses screenshots or something similar to display the Octave commands in action.  The graphs are the output from the graphics commands in Octave, so it would be easy to follow along.  What you see in the book will be very similar to what you see on your screen.","modularity_rating":5,"modularity_review":"The author uses sectioning commands.  The chapters seem to be divided into logical sections.","organization_rating":4,"organization_review":"The optimal order of the topics I think is going to depend on who is using the book.  For instructors using the book for a calculus class, it might seem strange to start with vectors and matrices, but that's the nature of the program so there is no way around it.  For instructors using the book for a linear algebra class, I'd imagine they'd ignore the calculus chapters.  Short of writing two different books, I'm not sure what else the author could do.","interface_rating":3,"interface_review":"As mentioned above, more internal links would be nice.  I'm not sure if there is another version that has these in place.  I've just got the pdf version I believe.  One of the little annoyances is you can click on something in the table of contents and you go there, but there is no back button that I can find, so jumping around in the book seems a bit clunky.  It could be I'm missing something.  If I were to adopt the book, I'd probably send it to my campus print shop and have them print and bind it for me.  I much prefer working from print.  That wouldn't stop me from using it though.","grammatical_rating":5,"grammatical_review":"I may not be the best judge of this characteristic.  No glaring grammatical errors jump out at me.  Are all the commas in the right place?  Beats me.  The language usage seems consistent with the dialect spoken by mathematicians though.","cultural_rating":5,"cultural_review":"I found no gender or ethnic references at all.  The text seems to stick with just math and Octave lingo.","overall_rating":9,"overall_review":"This seems to be a useful supplemental book for a lot of math classes looking to add some computational emphasis to the course.  Octave has come a ways since I last used it and is definitely a viable alternative to pricey proprietary software.","created_at":"2020-03-19T13:58:43.000-05:00","updated_at":"2020-03-19T13:58:43.000-05:00"}],"url":"https://staging.open.umn.edu/opentextbooks/textbooks/introduction-to-gnu-octave-a-brief-tutorial-for-linear-algebra-and-calculus-students","updated_at":"2025-12-15T02:12:17.000-06:00"},{"id":525,"title":"Ordinary Differential Equations","edition_statement":null,"volume":null,"copyright_year":2017,"isbn10":null,"isbn13":null,"license":"Attribution","language":"eng","accessibility_statement":null,"accessibility_features":["unknown"],"description":"This book consists of ten weeks of material given as a course on ordinary differential equations (ODEs) for second year mathematics majors at the University of Bristol. It is the first course devoted solely to differential equations that these students will take. This book consists of 10 chapters, and the course is 12 weeks long. Each chapter is covered in a week, and in the remaining two weeks I summarize the entire course, answer lots of questions, and prepare the students for the exam. I do not cover the material in the appendices in the lectures. Some of it is basic material that the students have already seen that I include for completeness and other topics are \"tasters\" for more advanced material that students will encounter in later courses or in their project work. Students are very curious about the notion of chaos, and I have included some material in an appendix on that concept. The focus in that appendix is only to connect it with ideas that have been developed in this course related to ODEs and to prepare them for more advanced courses in dynamical systems and ergodic theory that are available in their third and fourth years.","contributors":[{"id":4408,"contribution":"Author","primary":true,"corporate":false,"title":null,"first_name":"Stephen","middle_name":null,"last_name":"Wiggins","location":"University of Bristol","background_text":"Stephen Ray Wiggins is an American applied mathematician, born in Oklahoma City, Oklahoma and best known for his contributions in nonlinear dynamics, chaos theory and nonlinear phenomena, influenced heavily by his PhD advisor Philip Holmes, whom he studied under at Cornell University. He is actively working on the advancement of computational applied mathematics at the University of Bristol, where he was the head of the Mathematics Department until 2008. Previously he was a professor at Caltech in Pasadena, California"}],"subjects":[{"id":84,"name":"Calculus","parent_subject_id":7,"call_number":"QA150-272.5","visible_textbooks_count":31,"url":"https://staging.open.umn.edu/opentextbooks/subjects/calculus"},{"id":36,"name":"Pure","parent_subject_id":7,"call_number":"QA37.3","visible_textbooks_count":83,"url":"https://staging.open.umn.edu/opentextbooks/subjects/pure"},{"id":7,"name":"Mathematics","parent_subject_id":null,"call_number":"QA1","visible_textbooks_count":177,"url":"https://staging.open.umn.edu/opentextbooks/subjects/mathematics"}],"publishers":[{"id":462,"url":"https://figshare.com/articles/Ordinary_Differential_Equations/5311612","year":null,"created_at":"2018-09-07T12:22:40.000-05:00","updated_at":"2020-01-02T23:32:28.000-06:00","name":"Stephen Wiggins"}],"formats":[{"id":784,"type":"PDF","url":"https://math.libretexts.org/Bookshelves/Differential_Equations/Book%3A_Ordinary_Differential_Equations_(Wiggins)","price":{"cents":0,"currency_iso":"USD"},"isbn":null}],"rating":"4.5","textbook_reviews_count":1,"reviews":[{"id":2483,"first_name":"Malgorzata","last_name":"Marciniak","position":"Assistant Professor","institution_name":"LAGCC","comprehensiveness_rating":4,"comprehensiveness_review":"Elegant and relatively short textbook is written on less than 150 pages but covers a 12-week course in 10 chapters and 6 appendices. The appendices take about a quarter of the book and could serve as review materials or lessons on their own.\r\n","accuracy_rating":4,"accuracy_review":"In the Preface the author claims that he uses this textbook for the first course of ordinary differential equations for mathematics students, but it seems that this material is suitable for the second course. The book does not furnish proofs of theorems, but each chapter contains problem sets and few examples. The book contains the list of contents, biography, list of figures, list of tables, and index. Additional comments are provided on the margins. ","relevance_rating":4,"relevance_review":"For most US institutions the book appears to be an excellent complementary textbook for those who would like to gently introduce a little bit of mathematical theory but do not aim for too heavy load of theorems and definitions. Majority of the book is devoted to discussion about stability of two-dimensional autonomous systems. The emphasis is on the concept rather than calculations. The text is generously furnished with pictures. \r\nThe textbook will remain valuable regardless the flow of time. ","clarity_rating":5,"clarity_review":"The textbook is extremely well written but with some overuse of language. Majority of the material is devoted to analysis of the stability of autonomous systems in two variables. The word “manifolds” used in the titles of chapters does not reflect on the generality used in the text that limits examples to curves on the plane. The manifold that actually appears in the textbook is a plane curve.\r\n The book contains the list of contents, biography, list of figures, list of tables, and index. It is easy to navigate through and the comments on the margins provide suggestions about the interconnections of topics.","consistency_rating":5,"consistency_review":"All terms related to differential equations used in the textbook are introduced in a form of a definition. Many examples are assisted by pictures which significantly improve the clarity of the exposition. Notation, terminology and appearance are consistent throughout the book.","modularity_rating":5,"modularity_review":"The book is conveniently divided into 10 chapters and 6 appendices with material carefully selected into a logical flow. Chapters do not carry additional subdivisions except steps of procedures, examples or sets of problems.","organization_rating":5,"organization_review":"The content of the book is organized into a logical flow and contains a significant amount of cross references provided by comments on the generous margins. Each chapter begins with definitions, followed by examples or steps of procedures and ends with sample problems.","interface_rating":5,"interface_review":"The interface is well organized according to TeX standards of books with broad margins left for comments. The author uses the margins skillfully providing cross references, footnotes, references and additional comments.","grammatical_rating":5,"grammatical_review":"The text is grammatically excellent.","cultural_rating":5,"cultural_review":"The book topic does not touch sensitive topics of race, culture, religion, background.","overall_rating":9,"overall_review":"Suggestions for the textbook: few suggested reflexive problems for consideration may make a use of the vast margins.\r\nFor example: in chapter 1 the author defines autonomous equations. In chapter 2 he proves that they have the time-shift property. A sharp student may develop curiosity whether every ODE having the time-shift property must necessarily be autonomous and how the proof may be approached in an elementary way using methods presented in the book.","created_at":"2018-12-26T21:45:45.000-06:00","updated_at":"2018-12-26T21:45:45.000-06:00"}],"url":"https://staging.open.umn.edu/opentextbooks/textbooks/ordinary-differential-equations","updated_at":"2025-12-15T02:10:39.000-06:00"},{"id":178,"title":"Active Calculus 2.0","edition_statement":null,"volume":null,"copyright_year":2017,"isbn10":null,"isbn13":null,"license":"Attribution-NonCommercial-ShareAlike","language":"eng","accessibility_statement":null,"accessibility_features":["unknown"],"description":"Active Calculus is different from most existing calculus texts in at least the following ways: the text is freely readable online in HTML format and is also available for in PDF; in the electronic format, graphics are in full color and there are live links to java applets; version 2.0 now contains WeBWorK exercises in each chapter, which are fully interactive in the HTML format and included in print in the PDF; the text is open source, and interested users can gain access to the original source files on GitHub; the style of the text requires students to be active learners — there are very few worked examples in the text, with there instead being 3-4 activities per section that engage students in connecting ideas, solving problems, and developing understanding of key calculus concepts; each section begins with motivating questions, a brief introduction, and a preview activity, all of which are designed to be read and completed prior to class; following the WeBWorK exercises in each section, there are several challenging problems that require students to connect key ideas and write to communicate their understanding.","contributors":[{"id":3688,"contribution":"Author","primary":true,"corporate":false,"title":null,"first_name":"Matt","middle_name":null,"last_name":"Boelkins","location":"Grand Valley State University","background_text":"Matt Boelkins, Professor, Department of Mathematics, Grand Valley State University. PhD in College Teaching of Mathematics, Syracuse University."},{"id":3689,"contribution":"Author","primary":false,"corporate":false,"title":null,"first_name":"David","middle_name":null,"last_name":"Austin","location":"Grand Valley State University","background_text":"David Austin, Professor, Department of Mathematics, Grand Valley State University."},{"id":3690,"contribution":"Author","primary":false,"corporate":false,"title":null,"first_name":"Steve","middle_name":null,"last_name":"Schlicker","location":"Grand Valley State University","background_text":"Steve Schlicker, Professor, Department of Mathematics, Grand Valley State University. PhD, Northwestern University, specializing in Algebraic K-Theory and the Cohomology of Groups."}],"subjects":[{"id":84,"name":"Calculus","parent_subject_id":7,"call_number":"QA150-272.5","visible_textbooks_count":31,"url":"https://staging.open.umn.edu/opentextbooks/subjects/calculus"},{"id":36,"name":"Pure","parent_subject_id":7,"call_number":"QA37.3","visible_textbooks_count":83,"url":"https://staging.open.umn.edu/opentextbooks/subjects/pure"},{"id":7,"name":"Mathematics","parent_subject_id":null,"call_number":"QA1","visible_textbooks_count":177,"url":"https://staging.open.umn.edu/opentextbooks/subjects/mathematics"}],"publishers":[{"id":425,"url":"http://scholarworks.gvsu.edu/books/15/","year":null,"created_at":"2018-09-07T12:22:39.000-05:00","updated_at":"2018-09-07T12:22:39.000-05:00","name":"Grand Valley State University"}],"formats":[{"id":796,"type":"PDF","url":"http://scholarworks.gvsu.edu/books/15/","price":{"cents":0,"currency_iso":"USD"},"isbn":null},{"id":797,"type":"Online","url":"https://activecalculus.org/single/","price":{"cents":0,"currency_iso":"USD"},"isbn":null}],"rating":"4.5","textbook_reviews_count":13,"reviews":[{"id":144,"first_name":"Milos","last_name":"Savic","position":"Assistant Professor","institution_name":"University of Oklahoma","comprehensiveness_rating":5,"comprehensiveness_review":"I thought that the book was thorough in the subjects that were listed, including limits, derivatives, integrals, differential equations, and sequences and series. I would have liked a few chapters on multi-variable calculus, but that wish should not degrade the comprehensiveness of the book. The book is hyperlinked throughout, so if on the PDF you look up a terming the index, clicking on the link will bring you right to the page that the term is introduced.","accuracy_rating":5,"accuracy_review":"The book builds upon 400 years of calculus understanding, so most of the book is accurate and unbiased in terms of the content. ","relevance_rating":5,"relevance_review":"The text will not be obsolete for a long period of time. The topics covered, and the problems presented are relevant. I conjecture that if an application problem is ever out-of-date, it could be easily replaced.","clarity_rating":5,"clarity_review":"This book is written contrary to many mathematics textbooks in a fresh, active, and accessible manner. The layout of each section of the text has a summary of what will be discussed, preview activities to get the reader situated, activities throughout the prose, and a summary of what was discussed prior to exercises. It seemed as though the activities and the mathematics had purpose and understanding built in, which I cannot say the same for some other textbooks. I was excited to move to the next section when reading.","consistency_rating":5,"consistency_review":"The consistency of the textbook is fine. Every section has the same layout, and problems at the end of the section are probing no matter which section is discussed.","modularity_rating":4,"modularity_review":"I think that it is slightly difficult to be modular with a mathematics textbook. With that being said, I thought that the authors had a different approach than other textbooks in terms of what they wanted to introduce first. For example, I have always learned to prove the fundamental theorem, I would need the interplay between derivatives and integrals. The authors prefer to conjecture the fundamental theorem from observations of velocity and position, and in the next chapter approach the proof.","organization_rating":4,"organization_review":"I have already commented on the flow in the modularity section. I think that many parts flow in this textbook, but there were some parts that I had trouble with initially.","interface_rating":5,"interface_review":"I was so pleased with the interface of this textbook. There are links to javascript modules where students can interact with the exact topics they are reading about. If there is any textbook that shows us the slight capabilities of the 21st century, it is this textbook.","grammatical_rating":5,"grammatical_review":"I found little to no grammatical errors in this textbook.","cultural_rating":5,"cultural_review":"I did not see any portion of this text that referred to any ethnicity or race, so technically it is inclusive of all races and ethnicities.","overall_rating":10,"overall_review":"If you adopt this textbook in your classrooms, please adhere to the active learning modules in the text. They are written in a way that tries to empower the student mathematically. I really enjoyed the previews, recaps, and activities throughout each section. I enjoyed the references back to certain activities. Most of all, I enjoyed the javascript applets that accompanied this text, thus making it a textbook that takes advantage of the 21st century. I would highly recommend this textbook to any educator that wants their students to thoroughly understand the calculus material.","created_at":"2015-01-12T18:00:00.000-06:00","updated_at":"2015-01-12T18:00:00.000-06:00"},{"id":381,"first_name":"Carrie","last_name":"Kyser","position":"Master Instructor","institution_name":"Clackamas Community College","comprehensiveness_rating":5,"comprehensiveness_review":"This book is thorough and up-to-date in all areas of a single-variable differential and integral calculus course. I have been using it in my courses for over a year now, and I haven't found it to be lacking any topic, theorem, or technique. \n\nIt is current in its reduced emphasis on algebraic technique and greater attention to the underlying concepts and engineering-based applications. For example, integration techniques have been reduced in coverage and in emphasis in most calculus textbooks and this book is no exception. Substitution and Integration by Parts are featured, Partial Fractions gets a nod, and then students are introduced to the idea of a CAS (Computer Algebra System). This is in keeping with the reduced treatment of \"by hand\" integration techniques in most modern calculus textbooks. ","accuracy_rating":5,"accuracy_review":"There are no issues with the book's mathematical accuracy. \n\nAnother kind of accuracy, though, is how well an individual activity \"hits its mark\" in taking the student through an illuminating example of a topic. Generally, I think the text succeeds here, but there are some edits I might suggest. \n\nFor example, in Activity 1.15, after working through this activity in class with students, I altered the graph a bit to create more variation so the resulting discussion about displacement, velocity, and acceleration would be a bit more fleshed out. Teaching with this new version of this activity has had better results in terms of student understanding. ","relevance_rating":4,"relevance_review":"The content is not only up-to-date, but I think very forward-looking in its approach to the subject matter. The book has an almost conversational tone that I find very appealing. \n\nHowever, to remain relevant going forward, I would like to see the \"book\" revised to take advantage of its medium. It's presented and used (especially by students, who are perhaps more open to using electronic resources than their older, more traditional instructors) as an *online* resource. To remain relevant, I hope that future editions will take advantage of the power of the computing devices on which this book is often read, and feature more video, applets, maybe some Desmos-type graphs with movable parts. When students want to learn how to do something, they are searching YouTube, not looking for a page of text that describes how they might do a thing. They want to try it on, see it in action, engage with it. We should encourage and provide more opportunities for students to do that. ","clarity_rating":4,"clarity_review":"My students did not much care for the text. I am teaching this course using a flipped model, so there is reading and also instructional videos that students are asked to do outside of class. Not surprisingly, most students prefer the videos. Some student comments (from an anonymous end-of-course survey) about the assigned reading in the text:\n\n--I didn't find the textbook explanations very user-friendly, as they were much more difficult to comprehend than the videos. I don't know if there are textbooks with clearer explanations? About mid-way through the course, I also didn't find the reading to be necessary for most modules, as the videos and class explanations were clearer teachings of the same book concepts.\n\n--The book tends to be confusing, as student that learns from examples, I find this book to be hard to understand.\n\n--I liked that the textbook wasn't expensive, but I don't think the examples given were very helpful. I think they were a bit distracting from the point of the section at times.\n\n--more videos less reading\n\nI am not surprised that students prefer videos, but I don't think this is the fault of the text, but rather that they would prefer video explanations over ANY text. Nor am I surprised that they wanted more \"example problems\" from the text. Students have been taught that math is mostly manipulating expressions and equations. This book takes a very different approach. One student expressed his discomfort:\n\n--...also there aren't very good examples and explanations in the text. For instance; A section has about a paragraph and then the preview activity.....there's no explanation or good examples of problems. We are kind of just thrown into a pit of fire.\n\n...which is exactly the point of the text, that you learn this content by interacting with it. \n\nThe text is interspersed with Activities (as the book's title implies). I used most of the activities (either as-is or modified a bit) as group work in my Calc I and II classes. Students resoundingly preferred this \"active\" approach to learning calculus to the traditional lecture-based approach, and I think the quality of these activities was a big factor in students' satisfaction. \n\n","consistency_rating":4,"consistency_review":"The book is consistent in terminology and framework, absolutely. \n\nThere is a bit of variation in the consistency of the relative difficulty of the activities, however. \n\nFor example, in the section on Implicit Differentiation--a topic that students often find challenging--Activity 2.20 features an expression that is algebraically quite complicated for students. I used this once in class. Students just laughed out loud, most refused to try it! I removed it from the set of activities I use. \n\nAt other times, there are questions that seem to confuse students because they are \"too easy\", like (d) in Preview Activity 1.3:\n\n\"Write a meaningful sentence that explains how the average rate of change of the function on a given interval and the slope of a related line are connected.\"\n\nStudents ask \"Do they just want me to say that they are the same? Is that all?\" ","modularity_rating":5,"modularity_review":"The text is easy to pull apart and put back together. It is suitably modular. ","organization_rating":4,"organization_review":"The text gets full points for organization/structure/flow. \n\nI would like to suggest perhaps an alternate version of the text where it is organized more like a workbook, with more room left between the questions/problems where students might write their responses. I don't like asking students to copy down the text of a problem when they are working; their resistance to doing so is firm and vocal! But a bunch of answers on a piece of paper with no context is not good work product, nor very helpful as a study device. \n\nA version of this text that invited that kind of \"active\" participation from the reader would be a marked improvement, I think. ","interface_rating":5,"interface_review":"The interface is fine; I've encountered no issues. ","grammatical_rating":5,"grammatical_review":"I think the book is not only grammatically correct, but very well-written. Not always the case with math textbooks!","cultural_rating":5,"cultural_review":"I have encountered nothing even remotely insensitive or offensive in this text. ","overall_rating":9,"overall_review":"This book helped me to understand how I might teach calculus in a more learner-centered way, and for that I sing its praises! I recognize, though, that the \"active\" approach is a bit different from what most students are used to/expect, and they will need instructor support to make the most of this book and what it has to offer. ","created_at":"2016-01-07T18:00:00.000-06:00","updated_at":"2016-01-07T18:00:00.000-06:00"},{"id":400,"first_name":"M. Paul","last_name":"Latiolais","position":"Professor","institution_name":"Portland State University","comprehensiveness_rating":4,"comprehensiveness_review":"PLEASE BEGIN BY READING THE \"OTHER COMMENTS\" SECTION AT THE BOTTOM FIRST.\n\nIt seems to cover all of what we need for the first two quarters of calculus except surface integrals, which we could add or move to the third term.","accuracy_rating":5,"accuracy_review":"i found no errors","relevance_rating":5,"relevance_review":"It is the most up-to-date book on Introductory Calculus that I have seen so far.","clarity_rating":5,"clarity_review":"This is a book designed to teach.  As such, it will not be a good resource for student who have already studied calculus.  That would be a very different book.","consistency_rating":5,"consistency_review":"consistent","modularity_rating":4,"modularity_review":"not appropriate question for this subject.","organization_rating":5,"organization_review":"Excellenet.  See \"other comments\" for more details.","interface_rating":5,"interface_review":"Very clear","grammatical_rating":5,"grammatical_review":"I found no grammatical errors.","cultural_rating":1,"cultural_review":"While that would be a great idea, no one has yet attempted to write a calculus textbook which was \"inclusive\".  The closest thing was an environmental calculus book, but that included only covered the applied calculus material.","overall_rating":9,"overall_review":"It is hard to get a good sense of how well a book will work before one has taught a class using it.  Nonetheless, the approach articulated in the preface follows the the best of what is known about student learning as it relates to calculus. The approach would be challenging for graduate teaching assistants to accomplish, but possible with sufficient support and worth the effort toward the improvement of student learning.  \n\nI would do a \"Dan Meyer\"  ( https://www.ted.com/talks/dan_meyer_math_curriculum_makeover?language=en ) on the activities and the initial questions.  However, the formatting of questions and then activities seems a sound one.  For example, I would not foreshadow the answer to the questions by using terminology too soon. \n\nFor example, I would change the question \"How does the notion of limit allow us to move from average velocity to instantaneous velocity?\" to \"How do we manipulate average velocity to compute instantaneous velocity?\"\n\nExample 2: Instead of  \"What is sigma notation and how does this enable us to write Riemann sums in an\nabbreviated form?\", say \"How can we write Riemann sums in an abbreviated form?\"\n\nI should have more examples, after testing this book in a class.\n\nOur challenge is that this book would cover only 2 quarters, not the 3 quarters that we teach.  We would be required to use a more traditional book (presumably open source) for the third term.  Likely do-able, but challenging.\n\n","created_at":"2016-01-07T18:00:00.000-06:00","updated_at":"2016-01-07T18:00:00.000-06:00"},{"id":1373,"first_name":"Bethany","last_name":"Downs","position":"Mathematics Instructor","institution_name":"Portland Community College","comprehensiveness_rating":4,"comprehensiveness_review":"The book covers all major topics of differential and integral calculus.  However, the emphasis is on \"big-picture\" understanding of the topics and has relatively few (in comparison to other texts) formally stated theorems and even fewer proofs.  This could be seen as an asset, if the goal is introducing students to the overall ideas of calculus.","accuracy_rating":5,"accuracy_review":"The text is accurate.","relevance_rating":5,"relevance_review":"This is as up-to-date of a calculus textbook as I've seen.  The examples and activities are interesting and draw from a number of disciplines (physical and social sciences, etc.) which gives the reader a sense that calculus has many applications.  While specific, the examples will not feel dated in a decade or two and could be replaced with new examples or new data as the need arises.","clarity_rating":5,"clarity_review":"This is a really well written book. The style is clear and easy to understand.  The tone is conversational and uses appropriate vocabulary and description of the mathematics - it doesn't \"dumb down\" the topics, but also doesn't rely too heavily on \"mathy\" words when an explanation using regular language would suffice.\n\n However, there is a lot of text between and explaining the very few examples and it is hard to say, having never taught with this text, whether or not students would enjoy reading it as much as I did.\n\nThe authors choose not to state many formal theorems or show detailed proofs.  The emphasis is on overall understanding of the topics, not the underlying theory that makes the mathematics possible.  This approach is successful for this textbook.  If, however, you prefer a formal step-by-step build-up of theory and theorems, this is not the textbook for you.  Also, the flow of this book and paucity of detailed examples and homework problems would make it difficult to use as a reference book.","consistency_rating":5,"consistency_review":"Very consistent in layout and use or terms/vocabulary.","modularity_rating":5,"modularity_review":"The chapters and sections of the book are of the appropriate length for breaking over class periods throughout the term.","organization_rating":5,"organization_review":"The organization of each section is nicely done: \"Motivating Questions\", text with examples, activities for students, and the a \"Summary\" at the end followed by a homework set.","interface_rating":5,"interface_review":"The interface is fine.","grammatical_rating":5,"grammatical_review":"No errors found.","cultural_rating":5,"cultural_review":"I have yet to see a culturally relevant calculus textbook!  This particular text is in no way insensitive or offensive.","overall_rating":10,"overall_review":"To take full advantage of the unique approach of this textbook would need a lot of instructor planning/preparation before class.  The text has very few examples and the instructor would need to provide many of his or her own examples during lecture.  This is especially true for the more algebra-intensive topics.\n\nIn class, students would need a lot of involvement from the instructor.  It would be very important for the instructor to make sure that the students were completing and drawing the correct conclusions from the Activities within the text before moving on.  With the right preparation and implementation by the instructor, this \"lab\"-style approach could be very successful and enjoyable for the students.\n\nThere are only a few homework problems listed for each section.  Additional problems from elsewhere (either another textbook or something like WebWork) would be helpful.","created_at":"2017-06-20T19:00:00.000-05:00","updated_at":"2017-06-20T19:00:00.000-05:00"},{"id":1627,"first_name":"Erika","last_name":"Rappold","position":"Instructor","institution_name":"Virginia Tech","comprehensiveness_rating":3,"comprehensiveness_review":"The text was fairly comprehensive. The first portion of the book, which is dedicated to differential calculus, was very thorough. However, the sections on integral calculus was lacking in some of the integration techniques and methods commonly taught in a Calc II course (such as trig sub, higher order partial fractions, etc.) and the Differential equations and Series sections were nice introductions. ","accuracy_rating":3,"accuracy_review":"Overall, the accuracy was decent in the book. I found some of the notations to be confusing. In the sequences and series sections, s_n was used to represent terms of the sequence, while later a_n was used for the terms of a series, which are just a sum of the terms of a sequence. Then the partial sum was S_n, which could easily be confused with s_n. It's also not consistent with other math texts I've seen that discuss this topic, which could also be confusing. \n\nThere is also a slight question mark over the topic of continuity as far as what constitutes being continuous over it's domain. ","relevance_rating":5,"relevance_review":"The text could be easily rearranged or updated if necessary. The examples were relevant to the topics at hand and there weren't any examples that were outdated. ","clarity_rating":4,"clarity_review":"The text was quite clear and should be accessible to most students. The only trouble I had was with some of the notation, as mentioned above. ","consistency_rating":5,"consistency_review":"The book was very internally consistent with it's terminology. ","modularity_rating":5,"modularity_review":"The text could be rearranged without much disruption to the reader, however can only be rearranged to a certain extent. (As with most math texts, certain topics have to go together.)","organization_rating":5,"organization_review":"I really enjoyed the structure of this text. I liked that each section started with some motivational questions to start conversations, then progressed to a discussion of the topic and hitting the high points I appreciated that there were places for students to help build up the material themselves alone with the instructor. \n\nI also enjoyed that there was a summary at the end of each section.","interface_rating":5,"interface_review":"I had the e-book version of the text, and the only issue I had was that the table of contents page wouldn't take me to an individual section, it would only take me back to the cover page. ","grammatical_rating":5,"grammatical_review":"There were only a handful of errors that I saw in the wording of some of the questions. For example, in chapter one, there is a graph about calories burned and the question asks if the number of calories increased or decreased, instead of the number of calories used/ burned increased or decreased. Still, over 500 pages and a handful of grammatical errors is impressive!","cultural_rating":5,"cultural_review":"There were no culturally insensitive examples that I found. These topics don't generally involve examples that could potentially be racially or culturally offensive, but those that were included were appropriate. ","overall_rating":9,"overall_review":"On the whole, I felt this was a great Calculus I (differential calculus) and introductory Calculus II (integral calculus) / Differential Equations text. I feel it would be a great addition to a Calculus I course, but would caution against using it in an upper level course or in a more in depth program (such a math or engineering majors.)","created_at":"2018-02-01T18:00:00.000-06:00","updated_at":"2018-02-01T18:00:00.000-06:00"},{"id":1817,"first_name":"Cesar","last_name":"Martínez-Garza","position":"Associate Professor","institution_name":"The Pennsylvania State University - Berks College","comprehensiveness_rating":3,"comprehensiveness_review":"This textbook is intended for a two semester Single Variable Calculus sequence. I was mostly pleased with the textbook, although it lacks  sections on the Mean value Theorem and parametrization/polar coordinates. However, the book is presented in both online and pdf formats. The online version is somewhat interactive, so one simply has to click on the appropriate section and the web browser is directed to the respective section of the text. On the other hand, the book includes a section on the Qualitative Behavior of Solutions of Differential Equations, as well as a section on Euler's Method.\n\nOverall, the book could be used for a standard 2-semester Calculus sequence, however, the instructor will have to introduce additional material and proofs.","accuracy_rating":5,"accuracy_review":"The concepts are presented clearly and accurately. I did not find any errors on concepts, notation, or grammar. ","relevance_rating":5,"relevance_review":"As a Calculus textbook, this book will remain relevant for generations to come. It mostly follows in the typical layout of a traditional Calculus textbook. It's online format, though, has opened interesting venues since the book contains links to Java applets using GeoGebra in the author's website. This ability makes it outperform paper or PDF texts. Additionally, the book can be downloaded and customized (if the instructor is experienced in web publishing).","clarity_rating":4,"clarity_review":"The material is presented clearly. Each sections begins with \"Motivating Questions\" as a means to introduce the material. In general, I found this text to be less \"wordy\" than a traditional Calculus textbook. However, I found the lack of proofs to be a considerable weakness in the presentation. Calculus without proofs transforms from an exercise in logic to a belief system. ","consistency_rating":5,"consistency_review":"The structure throughout the textbook is very consistent. All sections are organized in the same format and the notation is very clear and consistent. The exercises are appropriate, although the problems at the end of the text are few.","modularity_rating":5,"modularity_review":"The essential ideas of Calculus cannot be segmented, and this book succeeds in presenting the material very cohesively. However, the material is grouped in a traditional format, so the sections in any one chapter are relevant to each other.","organization_rating":5,"organization_review":"Every section in the book has the same structure and organization. The sections begin with a \"Motivating Question\" followed by conceptual explanations. In may of sections there are \"Preview Activities\" and WeBWorK exercises at the end of the section.  Each section is properly referenced to relevant chapters, sections, and graphs throughout the text, so a simple click on a link will open a window with the information pertinent to the material being presented. I found this to be very valuable.","interface_rating":5,"interface_review":"The interface works well and the full online version is available on github. The only problem I found was my computer not being able to open an Java Applet in the author's website in one instance. On a different day, I was able to open the same applet without a problem. ","grammatical_rating":5,"grammatical_review":"I did not find a single grammatical error. While I may have missed a run-on sentence, nothing distracted my attention to recognize as an obvious grammatical flaw.","cultural_rating":5,"cultural_review":"Calculus has been relevant for 400 years and will continue to be relevant for generations to come. No issues here.","overall_rating":9,"overall_review":"I liked the presentation in general. This book has a lot of potential. Using WeBWork exercises is great because the students can practice concepts on their own textbook with immediate feedback. As mentioned earlier, lack of mathematical proofs is a serious omission for a well-rounded Calculus textbook, which this one can be. The hyper links and applets make this book an interactive tool that can be continuously improved to become a  fully interactive Calculus website.","created_at":"2018-02-01T18:00:00.000-06:00","updated_at":"2018-02-01T18:00:00.000-06:00"},{"id":2247,"first_name":"Brian","last_name":"Katz","position":"Associate Professor","institution_name":"Augustana College (IL)","comprehensiveness_rating":5,"comprehensiveness_review":"This text contains all of the core ideas that I would include in Calculus I \u0026amp; II. It is not trying to be a comprehensive tome, which is for the best, especially because it allows for a text that is readable for learners of Calculus, which is the stated purpose.","accuracy_rating":5,"accuracy_review":"Most of Calculus is in the canon at this point, so there is little controversy about the concepts. However, many of the root concepts, such as limits, are extremely subtle and are not usually discussed accurately until Real Analysis courses. I still like to talk with students about these subtleties, but I think there is almost no chance that they would be able to do that work by reading a written text (and I like to have them reinvent it anyway), so it's appropriate for limits and other similar-level concepts to be defined more heuristically, as they are in this text.\n\nLike most mathematics texts, there is a Platonic bias","relevance_rating":5,"relevance_review":"As above, the Calculus canon seems quite stable at this time, so I expect that this text will have great longevity. This text has been revised successfully, demonstrating that such work is sufficiently straightforward when desired.\n\nMovements like integration-first, series-first, project-based, integrated STE(A)M, or community- and culturally-relevant approaches to Calculus would require large changes for this text, but that is true of almost every Calculus textbook. Moreover, I think it will be a very long time before there is not a sector of Calculus courses that would still want a text like this. Conversely, this text is much better aligned with active learning pedagogies than texts like Stewart's, so calls to incorporate active, constructivist teaching at all levels will make those other texts obsolete soon while making this text even more appealing to a wide audience.","clarity_rating":5,"clarity_review":"The stated purpose of this text is as a readable resource for Calculus students, and it succeeds in being accessible while also maintaining concision and appropriate depth. Readers are asked to connect work across the text, which is hard for many Calculus students, but this work is not possible without it. An instructor will certainly have to teach students to read effectively (both in general and for mathematics specifically), but this is true of all university-level course work.\n\nThis text uses physical motion as a context regularly, though there are other contexts present. This text would be a better fit for a STEM population than a Business Calc population.","consistency_rating":5,"consistency_review":"This text is extremely consistent. The concepts build on each other and are connected, making use of the consistency. The guiding goals and values of the text are also consistently employed; for example, the motivating questions and preview activities are used throughout and are central to the structure of the text.","modularity_rating":5,"modularity_review":"This text uses subsections well; they are appropriate sizes and well titled. It would be easy to add a section for a special topic of interest to a course; most of the sections are important to later work, but it seems that the few topics that could be skipped are stand-alone sections, making that skip straightforward. It would also be easy to use a single section or some sections from this text as a module to replace other course materials in a course if, for example, an instructor preferred this development of a particular topic.","organization_rating":5,"organization_review":"The flow of the concepts is logical and clear. Each section is consistently and appropriately structured with motivating questions, preview activities, development, examples, activities, summaries, and exercises.","interface_rating":5,"interface_review":"The online interface for this book is REALLY strong. The table of contents is useful and fluid. The expandable content works well, especially the WeBWorK exercises, which are user-friendly and focused. The use of subsections keeps individual pages manageable. It might be nice to have PDF or printed versions for reading, in-class usage, and note-taking, but this text lives online.","grammatical_rating":5,"grammatical_review":"This text is well edited. In some ways, Calculus is about learning to be precise with vague and intuitively defined terms such as approaching and smooth, and this text handles language professionally without a hint of pedantry.","cultural_rating":3,"cultural_review":"This text is abstract and symbolic in a way that is normative and expected; many students and instructors will find it neutral and hence appropriate. In a larger context, the assumption that mathematics and its artifacts are culture-free is a deeply problematic issue with which we are not engaging. I am not aware of better models for university-level topics. This text is at least as relevant as texts for comparable courses.","overall_rating":10,"overall_review":"What is the purpose of a Calculus textbook? In the authors' words: \"It is our opinion that in the 21st century—an age where the internet permits seamless and immediate transmission of information—no one should be required to purchase a calculus text to read, to use for a class, or to find a coherent collection of problems to solve.\" This text is clearly a success for these goals.\n\nI think, for many people, a textbook is a resource like an encyclopedia in which the concepts of a discipline are collected. Viewing a textbook in this way makes us focus on the ways that the textbook transmits information to a reader or structures their thinking. This text meets those needs and goes beyond by offerings easy on-ramps for educators to help students engage the concepts of Calculus actively.\n\nHowever, I structure my courses using inquiry-based learning, and the presence of a pre-set authoritative summary of the concepts can be at odds with my goals. How does this text fit in this context? Well, the sections start with questions, which I think it EXCELLENT. The very first is \"How do we measure velocity?\", which is great. This question is a section title; however it is the only section title that is a question - the rest are topics. In the second section, the text asks \"What is the mathematical notion of limit and what role do limits play in the study of functions?\". In contrast to the first question, this question makes a lot of sense from the perspective of the expert and even the student who has learned a little Calculus. In my assessment, most of the motivating questions in this text are of this type; they frame Calculus as an existing body of knowledge that is to be learned rather than something that the reader is participating in building. This is not a critique of this text, since this isn't what it's trying to accomplish, but it does mean that I don't see how to use this text as the core element of an inquiry-based course.\n\nIf you are looking for a text you can ask students to read before class, such as a flipped/blended or project-based context, this text is a strong choice. If you are looking for a text students can read after class discussions and when reviewing for high-stakes assessments, this is an excellent option because it does a great job of making the core questions and goals that structure Calculus visible to the reader with enough experience to engage those questions from within the topic. In particular, if I had to have a text for a course but didn't intend to ask students to read it regularly (such as in my inquiry-based courses), this would be a top option because it focuses on conceptual questions, asks the reader to read actively, and is free! And if you are looking for a text from which you can pull active preview, exploration, and extension tasks to make your course active, this is a great choice.","created_at":"2018-06-19T19:00:00.000-05:00","updated_at":"2018-06-19T19:00:00.000-05:00"},{"id":2294,"first_name":"Steve","last_name":"Leonhardi","position":"Professor of Mathematics and Statistics","institution_name":"Winona State University","comprehensiveness_rating":3,"comprehensiveness_review":"Reviewer’s note:  Please read my “Other Comments”  in section #11 first, where I’ve written most of my review, and then return here to read my condensed, individual section comments.\n\nComprehensiveness:  The text covers most areas and ideas that I would expect, although there are some “missing” sections and additional exercises that I would like to see included, as described in the “Comments” section.","accuracy_rating":5,"accuracy_review":"The text is very well-written and includes appropriate diagrams.","relevance_rating":4,"relevance_review":"The subject matter is relatively timeless, but I would like to see more contemporary examples using recent real-world data.","clarity_rating":5,"clarity_review":"The exposition is straightforward and comprehensible, at a level appropriate to my students.","consistency_rating":5,"consistency_review":"The exposition and notation are internally consistent.","modularity_rating":4,"modularity_review":"The modularity is generally good, except for the presentation of Antiderivatives being sprinkled throughout Chapter 4 rather than presented as a separate section.","organization_rating":4,"organization_review":"The organization is generally good, except for the presentation of Antiderivatives being sprinkled throughout Chapter 4 rather than presented as a separate section.","interface_rating":4,"interface_review":"The interface is generally good.  I do wish that each “activity” could be linked as pop-up pdf page for easy printing when desired.","grammatical_rating":5,"grammatical_review":"I found only a very few typographical errors when using the text for a full semester.","cultural_rating":3,"cultural_review":"The text is not offensive or insensitive in any way, but includes very little mention of the history of the subject or biographical information.  I understand the desire to “streamline,” but I would prefer greater inclusion of this context.","overall_rating":8,"overall_review":"As implied by the textbook title, the design of Active Calculus 2.0 is based on the view that an active, inquiry-based approach is the best way to help students learn Calculus. The experience of the instructor and the students using this textbook will depend largely upon (1) the extent to which they agree with this inquiry approach, and (2) their interpretation of how “active learning” is most effectively implemented.\n\nI used this textbook in a first semester Calculus course in the Spring 2018 semester. Students were asked to read the assigned section before class and attempt to complete the Preview Activities for each section via WeBWork exercises.  In class, students worked in pairs through two to four “activities” from the text. (I required that students purchase a printed $10 “course pack” of the activity worksheets from our campus bookstore, available as a pdf file from the authors upon request, so that they could easily turn in their work at the end of each class period.)  I circulated throughout the room checking students’ progress and answering questions, and then typically spent the last 10 to 15 minutes of each class summarizing possible approaches and results (with as much input as possible from the students), then collected their worksheets and gave credit for effort and participation (about 10% of their final grade).  As the semester progressed, I adjusted this approach by starting most classes with a brief (10 minute) introduction to the material or sometimes completing the preview activity in lecture format, rather than simply starting the class with them working on worksheets.  I also learned to break the class into smaller “chunks” of activity, so that by the end of the semester we were generally alternating between 5-10 minutes mini-lectures or recaps directed by me, interspersed with having students work on activities for only 10-15 minutes at a time rather than longer stretches.\n\nThe reason I go into such detail describing my pedagogical approach in this textbook review is to clarify that this textbook’s effectiveness and suitability will be highly dependent upon the instructor’s preferred pedagogical approach.  If your own approach to teaching matches the active-learning approach that I have described, then you will find this text to be a valuable resource, especially compared to OER alternatives for Calculus.  If you and your students prefer the lecture-discussion model, this textbook is not a good choice, at least not as your primary text.\n\nOverall, using this textbook and this approach was a very positive experience for me and my students.  I used a variety of resources associated with this text, generously provided by the primary author Matt Boelkins in response to my email requests.  As previously mentioned, he sent me the pdf file of the activity worksheets only. (I would recommend using this separate pdf file, as I could not figure out a way to easily print the activities only from either the pdf or live versions of the online text.)  Matt also shared with me sets of WeBWork exercises that align well with the Active Calculus sections.  Instructors at Carroll College (MT) have developed a free “Chapter 0-Preliminaries” of Precalculus review as a supplement to this text.  Instructors at Grand Valley State University (MI) have posted a series of instructional “screencasts” (videos) on YouTube that are matched to the sections of this text.  The authors also suggest using the online Calculus applets developed by Marc Renault at Shippensburg College (PA).  My students found these all these additional resources quite useful.\n\nMy comments so far have focused on the suitability of this text with an active-learning approach.  I would next like to shift now to my second initially-posed question:  How is “active learning” most effectively implemented?  \n\nMy own experience with active learning has led me to believe that active learning using worksheets in groups is most effective when the following ingredients are present:  engaging questions, student-led discovery, and supportive scaffolding. \n\nActive Calculus succeeds for the most part in providing all three of these ingredients, to different degrees in different sections and different activities.  If I use this text again, I would select more carefully which activities I reuse unaltered, which activities I use with some edits, and which activities I skip entirely or replace with my own personal worksheets.\n\nDespite the active learning spirit embodied throughout the text, its contents are remarkably similar to a traditional text.  I wish that the text included more real-world data and examples, in the spirit of a text such as the Hughes-Hallett Calculus.  My students find such problems and examples more engaging and compelling than such questions as “How do we find the slope of the tangent line?” and “How do compute the area beneath a curve?”  \n\nI concur with the review comments of Professor M. Paul Latiolais (Portland State University) that some of the “motivating questions” at the beginning of sections could be reworded to better facilitate student discovery of the relevant concepts as opposed to just asking students “How do we define [fill in the standard Calculus term]?” and then proceeding to tell them in the following exposition.  I also think that some of the activities could be improved by providing more scaffolding.  Most of my students had difficulty correctly completing the Preview Activities (inWeBWork) before each class, to the point that I decided that scoring 50% on a Preview Activity would count as 100%, and any score above 50% would count as extra credit.\n\nFor example, Preview Activity 3.1.1 on critical numbers and extreme values was an especially effective activity because it breaks the concepts up into small enough questions and concepts that allow the students to proceed step by step to feel like they are discovering the notions of critical values and Fermat’s Theorem for Extrema on their own.  Preview Activity 3.5.1 on related rates is also effective because it poses an interesting question and lays out a series of steps for the student to develop understanding of a procedure to answer the question.\n\nOn the other hand, some of the Preview Activities (1.8.1, 2.4.1, 2.7.1, to name a few) felt simply like homework problems and did not generate much student interest or feelings of discovery.\n\nSeveral other features of the text could be improved, in my opinion.  The text is missing several sections that I would expect to see in any Calculus text, even if included only as an optional section. The definition of “limit” is stated correctly but somewhat informally, in the sense that the epsilon-delta clarification of “sufficiently close” is never introduced.  I agree that a strong case can be made for delaying and underemphasizing the formal definition and notation until students are better able to appreciate and understand it, but I would prefer to see the formal definition presented and explored intuitively.  More surprisingly, the Mean Value Theorem is not included.  Again, I am sympathetic to the view that most first semester Calculus students are not ready to appreciate rigorous proof or lengthy formal derivations, but I choose to introduce these notions to my students in intuitive visual contexts, so that they can gradually absorb their meaning and significance over several semesters.  Of course, these “missing” sections are easily filled in using personal notes and/or other, more traditional texts (such as the OpenStax Calculus).\n\nAlso, I would prefer that the text contained both more examples in the exposition, and more exercises at the end of each section. Active Calculus does contain most of the standard examples found in any Calculus text, and any instructor using WeBWork has access to as many additional exercises as they could ever care to assign.  I believe that the authors were intentionally trying to keep the text streamlined to force students to discover","created_at":"2018-08-02T19:00:00.000-05:00","updated_at":"2018-08-02T19:00:00.000-05:00"},{"id":3111,"first_name":"John","last_name":"Carter","position":"Associate Professor","institution_name":"Metropolitan State University of Denver","comprehensiveness_rating":4,"comprehensiveness_review":"The text covers all of the core ideas one would expect in a standard 2 semester calculus course. The authors clearly prioritized readability over exhaustiveness, and may be seen as skipping/missing material depending on your priorities. For example there are no sections on the Mean value Theorem or parametrization/polar coordinates. ","accuracy_rating":5,"accuracy_review":"The material is accurate. ","relevance_rating":5,"relevance_review":"The calculus concepts are timeless of course. I didn't notice any examples that will seem quickly dated. My only concern would be that the electronic text could end up with broken links and or links to broken or outdated programs. As long as it is supported there should be no problems. The active student centered approach is more aligned with modern pedagogy and so might keep Active Calculus relevant (and supported) for a long time.","clarity_rating":5,"clarity_review":"I think this is where the text truly shines. The writing is clear and compelling. Each section has a clear narrative thread and all of the example are included to further the narrative. I think the author's big picture/idea driven approach more accurately reflects the nature of calculus than a traditional exhaustive reference like textbook.","consistency_rating":5,"consistency_review":"The style and exposition are consistent from section to section. However, I would add that the activities  vary greatly in difficulty can derail a class if you are not careful.","modularity_rating":5,"modularity_review":"The sections cover an appropriate amount of material and are as independent as one could expect in a calculus course.","organization_rating":5,"organization_review":"Another strong point for this book.","interface_rating":5,"interface_review":"No issues.","grammatical_rating":5,"grammatical_review":"Fewer typos/errors than the last two books our dept. required.","cultural_rating":5,"cultural_review":"The text is not culturally insensitive or offensive in any way that I can see.","overall_rating":10,"overall_review":"This book will work best if used in a student centered active classroom. Each section includes activities embedded in the exposition designed to get the students to engage the material and make conjectures.  The activities  are not great as lecture examples and so lecturing through them will fall flat. If you take the time to allow students to struggle through them, you will be rewarded. ","created_at":"2019-07-24T13:10:59.000-05:00","updated_at":"2019-07-24T13:10:59.000-05:00"},{"id":4320,"first_name":"Shelly","last_name":"Ray","position":"Department Chair of Mathematics","institution_name":"Community College of Aurora","comprehensiveness_rating":3,"comprehensiveness_review":"For this review I am focusing on Calculus I versus the entire sequence.  The issues that I see in the first course in the sequence, I have no doubt will persist through the remainder of the sequence.  While the topic list addresses the majority of the major concepts, there is not the same level of depth and exploration that I have seen in the Stewart and Thomas texts.  Some of the learning outcomes that are required for MAT 201 based on GT Pathways are not included and would have to be supplemented.  \r\nThere is also only a short table of integrals vs the standard 120 integrals that are include with the text.  While only the first 20 integrals are used in MAT 201, it is useful have students get comfortable seeing the table and understand that they will eventually explore all 120 integrals through the sequence.  Also missing are some Algebra and Trig quick reference pages.  If students did not build course portfolios, these are quick reference guides for students who need to look something up vs search the web.","accuracy_rating":4,"accuracy_review":"I am very confident in the book's accuracy as it has been in use for some time and it is the second edition.  The problems that I worked through are level appropriate but there are not additional supplemental exercises if students need more practice.  The problems are written from a mathematics lens are do have contextualized settings.  It provides a very generic and unbiased approach to the content.","relevance_rating":4,"relevance_review":"Mathematics texts in general are written in such a way that they can be easily updated.  The content does not change only the context of some of the application problems.  This text is the same.  Calculus has been around since the 17th century.  There is an order of topics that allows concepts to be connected and scaffolded.  This does not change by author.  Limits must be introduced first as derivatives are based on understanding rate of change and instantaneous rate of change.  Derivative explore the slope of the tangent line for a family of curves.  Once students can visualize the curves and connect how the curve changes based on first, second, and third derivatives, area under the curve can be explored.  This leads us into integrals.  I still have concerns about the depth, or lack there of, for many of the concepts.  Limits at infinity and their connection to continuity is missing.  Also missing is the precise definition of a limit and relationships within limit laws.  Derivatives of inverse trig functions and logs are not introduced early and relate to limits at infinity.  It also appears that hyperbolic functions are not explored at all in Calculus I.","clarity_rating":3,"clarity_review":"The text is written so it does provide adequate context but is written in a way that is I feel is dry.  There is not real introduction to each section of material.  A real-world context is not shared to set the stage for the concept being explore.  The lack of visual aids and applets do not make the concept come to life in a way other texts do.  I like all of the applications and explorations within the material but feel there is more work to be done to make this rise to the same level of other publisher materials that are available.  Active links to terminology would be helpful as would using color to highlight some of these terms.","consistency_rating":3,"consistency_review":"Once students begin the course, they will see the framework is consistent in terms of both terminology and framework.  The structure for each Unit, section, and preview is the same.  The language of the course is used appropriately and consistently throughout the text but more could be done to enhance the introduction of each unit, creating relevant context within fields of study of the students enrolled in the course, and exploration across and within concepts.  This is essential in Calculus I as we are trying to help students create a foundation for making more of these connections on their own as we move through the Calculus sequence.  While we focus on it in class and within problem solving activities, having a text that supports the efforts is helpful as well.","modularity_rating":3,"modularity_review":"There are large blocks of text with some included examples.  The format of the modules could be structured better so that Preview item are highlighted differently to capture students' attention.  Key concepts are in boxes with a different color background but could be set differently on the page to indicate significance.  It would also be nice if the sub modules were easy to access within the menu of topics.  There are section headings, but no sub headings under those to easily find key concepts within the section.","organization_rating":4,"organization_review":"As mentioned previously, Calculus has been around since the 17th century.  There is an order of topics that allows concepts to be connected and scaffolded.  This does not change by author.  Limits must be introduced first as derivatives are based on understanding rate of change and instantaneous rate of change.  Derivative explore the slope of the tangent line for a family of curves.  Once students can visualize the curves and connect how the curve changes based on first, second, and third derivatives, area under the curve can be explored.  This leads us into integrals.  Depth of some topics is my biggest concern.","interface_rating":3,"interface_review":"The text does not contain enough images to add clarity to the mathematical concepts.  The Rule of 4 in learning mathematics is fundamental.  Table form, equation form, graph form, and written form all play a role in conceptual development and making connections across and within concepts.  If students see more visual aids early on in the course, they learn to use them as part of their problem-solving approach.  This text has minimal use of graphs, applets, and other engaging tech tools.  It also is primarily a two-color text.  To emphasize mathematical definitions, theorems, axioms, etc., it would be better if four colors were used to guide students through the text and to enhance the images that are included. The text feels monotonous to me.","grammatical_rating":5,"grammatical_review":"The text is well written but a bit dry. I would say it is above the reading leveling I would normally select for a course as many of our students English is not their first language.  Learning the vocabulary of the course is critical to success in the course.  If the reading level is challenging along with learning the vocabulary of the course, students may have challenges understand key concepts, making deep conceptual connections, and completing assignments when they are unable to attend class.","cultural_rating":3,"cultural_review":"I would say this section of the review does not apply well to this text.  There are no examples written in a way that mentions races, ethnicities, or backgrounds.  That may make text culturally insensitive overall as the only culture within the text is the culture of advanced mathematics.","overall_rating":7,"overall_review":"I would use the text as a supplemental resource but not a primary text for the course.  While the majority of the learning outcomes are included in the text, there are some that would have to be supplemented.  In addition, there are no included homework exercises, extension questions, or technology explorations that support deep connection across concepts.  These may be addressed in the activities workbook.  I requested a copy of the workbook but it was never emailed to me.","created_at":"2020-08-14T11:20:31.000-05:00","updated_at":"2020-08-14T11:20:31.000-05:00"},{"id":33419,"first_name":"Vira","last_name":"Babenko","position":"Assistant Professor","institution_name":"Drake University","comprehensiveness_rating":5,"comprehensiveness_review":"The text appropriately covers all areas and ideas of the Calculus 1 and Calculus 2 course topics we currently have at Drake University. Has effective and interactive index for the online version, A Short Table of Integrals, Answers to Activities, and Answers to Selected Exercises.","accuracy_rating":5,"accuracy_review":"Content is accurate but seems to be geared toward “pure” math and physics students as there are very few examples from other disciplines.","relevance_rating":4,"relevance_review":"It would be hard to make calculus content not up-to-date, and I am sure it will be relevant for years to come. However, I would certainly prefer to have more applied-oriented examples rather than pure math “analyze this random function” type of exercises. Most of the students who take our calculus 1 or even Calculus 2 are not actually math majors. For them, we would need to supplement with various “real-life” examples and projects to make sure their interest and motivation are sustainable.","clarity_rating":4,"clarity_review":"It is an active calculus textbook, so I am sure some students will find it very unclear and “strange” format. The text will need great support from the instructor and a lot of explanation and motivation presented to students to defend the untraditional choice of presenting the material. It might be a very effective way to learn the concepts, and retention of the material might be much better this way, but it certainly will meet some resistance, especially from students that are not initially fond of mathematics but are required to take a Calculus class to fulfill other majors’ requirements. Each section starts with the motivating questions, then has a preview activity, after that, another activity or exercise that is usually explained (but not always). Ends with a summary and exercises.","consistency_rating":5,"consistency_review":"The text is consistent.","modularity_rating":5,"modularity_review":"The text is already divided into appropriate sections, and sections can be re-arranged if needed.","organization_rating":5,"organization_review":"The topics in the text are presented in a logical, standard to calculus sequence order. I would prefer to have a little review of pre-calc material at the beginning of the text, but it can be easily supplemented from other sources.","interface_rating":5,"interface_review":"The web version of the text is full of in-context links to previous activities and exercises whenever they are mentioned. Some of the exercises have buttons “Preview my answer”, “Check answer”, and finally “Show correct answers”. Examples have “hidden” solutions that you can unfold once ready. The interactivity of the interface is very impressive. Links to various visual applets seem to be very helpful for various topics.","grammatical_rating":5,"grammatical_review":"I did not find any grammatical errors.","cultural_rating":4,"cultural_review":"I didn’t find any examples that include a variety of races, ethnicities, and backgrounds. It is unfortunately common to calculus text, in general, not to have examples/discussions that contain any of these.","overall_rating":9,"overall_review":"It might be an excellent text for inquiry-based learning classes or as supplemental material to lead classroom activities in more traditionally thought courses. The instructor would need to provide and supplement more motivational “real-world” examples for most topics. It can be very difficult to follow for the first-year students who are non-math or other STEAM majors, but for those interested in mathematics, it is a great resource.","created_at":"2021-10-20T11:25:23.000-05:00","updated_at":"2021-10-20T11:25:23.000-05:00"},{"id":34499,"first_name":"Michele","last_name":"Intermont","position":"Associate Professor","institution_name":"Kalamazoo College","comprehensiveness_rating":5,"comprehensiveness_review":"The text has the topics I expected to find. Perhaps your favorite application of integration, or your favorite test for the convergence of an infinite series etc is absent, but this is a small price to pay for a concise text. It should be noted, however, that this text does not contain the multitude of exercises at the end of each section that most traditional books do.","accuracy_rating":5,"accuracy_review":"I didn't note any errors.","relevance_rating":5,"relevance_review":"The content is standard, and the examples neutral.","clarity_rating":5,"clarity_review":"Each section begins with motivating questions in easy to read language. The graphics are clear and illustrative.","consistency_rating":5,"consistency_review":"The terminology is consistent, as is the style and organization of the sections.","modularity_rating":5,"modularity_review":"I found the book easy to navigate, especially the online format.","organization_rating":5,"organization_review":"This text is meant for an active learning approach to Calculus. The sections begin with motivating questions, followed immediately by an introductory activity for students to engage with before ideas are formally presented. There are other activities to engage with throughout the text as well. This is pedagogically sound, and a welcome addition to the literature.","interface_rating":5,"interface_review":"I found the text easy to navigate, with graphics of good quality.  Some of the problems in the sections use Webwork; while that interface didn't work perfectly for me, it did work well enough.","grammatical_rating":5,"grammatical_review":"Typos are few, and the text is easy to read.","cultural_rating":4,"cultural_review":"The author seems to have tried to bypass mention of race and gender as much as possible.","overall_rating":10,"overall_review":"I am pleased to have the pre-activity and activity problems; this suits my teaching style, although it will not suit everyone.  Likewise, the inlcusion of some Webwork problems right in the text is another facet that I particularly like seeing.","created_at":"2023-04-07T14:16:28.000-05:00","updated_at":"2023-04-07T14:16:28.000-05:00"},{"id":34581,"first_name":"Veronica","last_name":"Baker","position":"Assistant Teaching Professor","institution_name":"Montana State University – Bozeman","comprehensiveness_rating":4,"comprehensiveness_review":"Most of the main topics of calculus are present, but there are some noticeable exceptions.  Some missing topics would be hyperbolic functions, Mean Value Theorem, initial value problems.  Some ideas are explored in great detail (like velocity/position) and other areas are only covered superficially (like finding antiderivatives with a stated function).","accuracy_rating":5,"accuracy_review":"The mathematical ideas are sound.","relevance_rating":4,"relevance_review":"The textbook is presented in a way to promote Active Learning and to foster student activities for building mathematical ideas.  The calculus ideas are sound, but pedagogical swings may contribute to another style of teaching.","clarity_rating":4,"clarity_review":"The book is concise which may leave readers wanted to see more worked examples.","consistency_rating":5,"consistency_review":"The book is highly consistent with its framework.  All sections start with an activity to complete before class and an additional 3-4 activities for in-class discussions.  There are a small amount of homework questions available at the end of the section.","modularity_rating":4,"modularity_review":"Each section is broken up into smaller sub-sections.  It would be nice to have them clickable in the provided online table of content to reduce the amount of scrolling necessary.","organization_rating":5,"organization_review":"The order is fairly traditional.  My one suggestion is to cover the Related Rates section currently at the end of Chapter 3 to the end of Chapter 2 closer to Implicit Differentiation.","interface_rating":5,"interface_review":"The online interface of the this textbook is top notch.  It is written in PreText which is ADA complaint and much easier to navigate compared to the PDF versions out there.","grammatical_rating":5,"grammatical_review":"There are very few minor typos.","cultural_rating":4,"cultural_review":"The textbook doesn't seem to have any mention of any race or ethnicities in their examples.","overall_rating":9,"overall_review":"This book is a good source for activities for active learning in your classroom.  It covers the big ideas in calculus, but doesn't necessarily dive into some of its complexities (more involved applications, hyperbolic functions, algebraic manipulations, more complex functions).  There is no review of prerequisite material for a reference for students.  However, it does have some short supplemental videos available to students for each section with the big ideas presented.  There are few worked examples in the book.  It is a good base for information/activities, but will need some supplemental work to form a complete course.","created_at":"2023-05-29T12:58:10.000-05:00","updated_at":"2023-05-29T12:58:10.000-05:00"}],"url":"https://staging.open.umn.edu/opentextbooks/textbooks/active-calculus-2-0","updated_at":"2025-12-15T02:11:07.000-06:00"},{"id":487,"title":"Active Calculus Multivariable","edition_statement":null,"volume":null,"copyright_year":2017,"isbn10":null,"isbn13":null,"license":"Attribution-NonCommercial-ShareAlike","language":"eng","accessibility_statement":null,"accessibility_features":["unknown"],"description":"Active Calculus Multivariable is the continuation of Active Calculus to multivariable functions. The Active Calculus texts are different from most existing calculus texts in at least the following ways: the texts are free for download by students and instructors in .pdf format; in the electronic format, graphics are in full color and there are live html links to java applets; the texts are open source, and interested instructors can gain access to the original source files upon request; the style of the texts requires students to be active learners — there are very few worked examples in the texts, with there instead being 3-4 activities per section that engage students in connecting ideas, solving problems, and developing understanding of key calculus concepts; each section begins with motivating questions, a brief introduction, and a preview activity, all of which are designed to be read and completed prior to class; the exercises are few in number and challenging in nature.","contributors":[{"id":4285,"contribution":"Author","primary":true,"corporate":false,"title":null,"first_name":"Steve","middle_name":null,"last_name":"Schlicker","location":"Grand Valley State University","background_text":"Steve Schlicker is a mathematics professor at Grand Valley State University in Allendale, MI."},{"id":4286,"contribution":"Author","primary":false,"corporate":false,"title":null,"first_name":"David","middle_name":null,"last_name":"Austin","location":"Grand Valley State University","background_text":"David Austin is a mathematics professor at Grand Valley State University in Allendale, MI."},{"id":4287,"contribution":"Author","primary":false,"corporate":false,"title":null,"first_name":"Matthew","middle_name":null,"last_name":"Boelkins","location":"Grand Valley State University","background_text":"Matthew Boelkins is a mathematics professor at Grand Valley State University in Allendale, MI."}],"subjects":[{"id":84,"name":"Calculus","parent_subject_id":7,"call_number":"QA150-272.5","visible_textbooks_count":31,"url":"https://staging.open.umn.edu/opentextbooks/subjects/calculus"},{"id":36,"name":"Pure","parent_subject_id":7,"call_number":"QA37.3","visible_textbooks_count":83,"url":"https://staging.open.umn.edu/opentextbooks/subjects/pure"},{"id":7,"name":"Mathematics","parent_subject_id":null,"call_number":"QA1","visible_textbooks_count":177,"url":"https://staging.open.umn.edu/opentextbooks/subjects/mathematics"}],"publishers":[{"id":428,"url":"http://scholarworks.gvsu.edu/books/14/","year":2018,"created_at":"2018-09-07T12:22:39.000-05:00","updated_at":"2020-12-28T21:08:08.000-06:00","name":"Grand Valley State University"}],"formats":[{"id":735,"type":"PDF","url":"https://scholarworks.gvsu.edu/books/19/","price":{"cents":0,"currency_iso":"USD"},"isbn":null},{"id":1959,"type":"LaTeX","url":"https://github.com/StevenSchlicker/AC3PreTeXt/tree/master/src","price":{"cents":0,"currency_iso":"USD"},"isbn":null},{"id":1960,"type":"Online","url":"https://activecalculus.org/multi/book-1.html","price":{"cents":0,"currency_iso":"USD"},"isbn":null}],"rating":"5","textbook_reviews_count":1,"reviews":[{"id":2755,"first_name":"James","last_name":"Collins","position":"Assistant Professor","institution_name":"University of Mary Washington","comprehensiveness_rating":4,"comprehensiveness_review":"This book covers most areas of multivariate calculus.  However, certain areas, such as Divergence Theorem, and Fundamental Theorem of Line Integrals is not included in the book.  I am told it  will be added in later additions though.","accuracy_rating":5,"accuracy_review":"I found this book very accurate with few errors","relevance_rating":5,"relevance_review":"I don't imagine this book will need updating anytime soon, as Calculus will not be changing.  Any updates will simply be to improve the activities, not the material itself.","clarity_rating":5,"clarity_review":"The book is very clear and easy to understand.  The author specifically avoids any confusing mathematical notation in an attempt to make the material accessible.","consistency_rating":5,"consistency_review":"The book is very consistent.","modularity_rating":5,"modularity_review":"This book does an incredibly good job of subdividing the various sections into subsections.  The author of the book has his students read certain sections before class, as do I.  It is very easy to tell students to read through this section of the book.  Each subsection within a section is usually around a page.","organization_rating":5,"organization_review":"I particularly like how one section flows into the next, telling one coherent story.","interface_rating":5,"interface_review":"The online version of this text was very helpful to demonstrate visual elements of the material to the class.  With multivariate in particular, the visual elements are complex and hard to draw for those of us with little drawing skill.  It was helpful to have various graphs online to demonstrate ideas to the students.","grammatical_rating":5,"grammatical_review":"I found no grammatical errors in my using of the book.","cultural_rating":5,"cultural_review":"The author uses both male and female pronouns where applicable, though pronouns in general are not used often.","overall_rating":10,"overall_review":"I have used this book for Multivariate Calculus and enjoyed it very much.  It is important to stick to doing the activities and having students do the  preview activities before class.  Some students have trouble using this book as a standalone book, as it is very different from what they are used to.  It may be helpful to pair it with a more traditional free textbook, such as APEX.","created_at":"2019-04-09T22:04:04.000-05:00","updated_at":"2019-04-09T22:04:04.000-05:00"}],"url":"https://staging.open.umn.edu/opentextbooks/textbooks/active-calculus-multivariable","updated_at":"2025-12-15T02:31:02.000-06:00"},{"id":462,"title":"Yet Another Calculus Text","edition_statement":null,"volume":null,"copyright_year":2007,"isbn10":null,"isbn13":null,"license":"Attribution-NonCommercial-ShareAlike","language":"eng","accessibility_statement":null,"accessibility_features":["unknown"],"description":"I intend this book to be, firstly, a introduction to calculus based on the hyperrealnumber system. In other words, I will use infinitesimal and infinite numbers freely. Just as most beginning calculus books provide no logical justification for the real number system, I will provide none for the hyperreals. The reader interested in questions of foundations should consult books such asAbraham Robinson's Non-standard Analysis or Robert Goldblatt's Lectures onthe Hyperreals. Secondly, I have aimed the text primarily at readers who already have somefamiliarity with calculus. Although the book does not explicitly assume any prerequisites beyond basic algebra and trigonometry, in practice the pace istoo fast for most of those without some acquaintance with the basic notions of calculus.","contributors":[{"id":4227,"contribution":"Author","primary":true,"corporate":false,"title":null,"first_name":"Dan","middle_name":null,"last_name":"Sloughter","location":"Furman University","background_text":"Dan Sloughter has been teaching Furman students since 1986, and became Professor of Mathematics in 1996. He previously served as an assistant professor at Santa Clara University from 1983-86, and at Boston College from 1981-83. He was also an instructor at Dartmouth College from 1979-81."}],"subjects":[{"id":84,"name":"Calculus","parent_subject_id":7,"call_number":"QA150-272.5","visible_textbooks_count":31,"url":"https://staging.open.umn.edu/opentextbooks/subjects/calculus"},{"id":36,"name":"Pure","parent_subject_id":7,"call_number":"QA37.3","visible_textbooks_count":83,"url":"https://staging.open.umn.edu/opentextbooks/subjects/pure"},{"id":7,"name":"Mathematics","parent_subject_id":null,"call_number":"QA1","visible_textbooks_count":177,"url":"https://staging.open.umn.edu/opentextbooks/subjects/mathematics"}],"publishers":[{"id":385,"url":"http://www.synechism.org/wp/yet-another-calculus-text/","year":null,"created_at":"2018-09-07T12:22:39.000-05:00","updated_at":"2020-01-02T22:42:03.000-06:00","name":"Dan Sloughter"}],"formats":[{"id":664,"type":"PDF","url":"http://yact.synechism.org/","price":{"cents":0,"currency_iso":"USD"},"isbn":null}],"rating":null,"textbook_reviews_count":0,"reviews":[],"url":"https://staging.open.umn.edu/opentextbooks/textbooks/yet-another-calculus-text","updated_at":"2025-12-15T02:09:02.000-06:00"}],"links":{"self":"https://staging.open.umn.edu/opentextbooks/subjects/calculus.json?page=1","total_pages":4,"total_count":36,"next":"https://staging.open.umn.edu/opentextbooks/subjects/calculus.json?page=2"}}