Calculus Volume 1
Gilbert Strang, MIT
Edwin Herman, University of Wisconsin-Stevens Point
Pub Date: 2016
ISBN 13: 978-1-9381680-2-4
Conditions of Use
From the start, this book gives a comprehensive (yet straight forward) review of the necessary function knowledge. There is even a “Review of read more
From the start, this book gives a comprehensive (yet straight forward) review of the necessary function knowledge. There is even a “Review of Pre-Calculus” at the end of the text, which contains all relevant formulas and identities. Before diving into calculus, there is a section which shows the student the basic ideas covered in differential and integral calculus. After limits, differentiation is covered (with applications contained in a following section) and then integration is covered (with applications in the subsequent section). For my institution, all relevant topics are covered. Plenty of exercises are placed throughout the text and include solutions for about half of them, similar to what is done for the odd numbered problems in a physical textbook.
The book is accurate, although I did not complete all exercises in order to check their solutions. In reading through the written portions, I did not find any glaring mistakes. Not only is this textbook accurate, it is concise as well.
Calculus is a classic subject, so the topics here will not need to change. Since the text is thorough and organized in a clear way, instructors can easily select the topics to cover for a given course. As course topics change, the fact that the topics are presented separately here will make course changes straight forward. There won’t be too much picking and choosing of things from within a section.
The book is clear in its written language, definitions, and figures. There isn’t an overuse of greek letters, which I like. For the most part, functions are in x or t. The figures used throughout are clear, support learning, and are free of extraneous visual information.
All sections have a similar flow and the depth feels even. Exercises are place consistently throughout the written text.
This text is broken up nicely by topic. Each topic has a little backstory or introduction that may reference a previous section, but it does not heavily reference past sections. It feels like the sections could easily be selected and ordered at the instructor’s discretion, without too much confusion.
The topics are structured clearly as: function background, limits, derivatives, derivative applications, integrals, integral applications. In each section has 7-10 subsections. My only complaint is that the limits at infinity is listed with applications. I wish it were listed in the limits section.
The fact that this text has an online version is a huge plus for me. I wouldn't use a text that didn't. Also, the website is modern-looking and organized. There are enough colors used so that the user doesn't feel bored immediately or over time with the aesthetic. The images are of good quality and seem to be used at pretty much every opportunity. My one complaint here is that the exercises don’t have numbers. It would be hard to assign specific problems without them having a label. Maybe you just assign all of them?
The grammar in this text is good and it is well written. Commas are used in correct places, which adds to clarity.
This text is a bit of a cultural void. Although the majority of the real-world objects referenced inanimate, the humans referenced are male. It seems like the text was intentionally written to be gender and culture free. The hes should be eliminated, if that is the case. Otherwise, the message is that only men are of note.
I really like this text book and would use it in the future if my college didn’t already have their own open textbook available for this course. I do find this text superior, though, and will recommend it to my students for use as supplementary study material.
The book is comprehensive. It covers the entirety of the usual Calculus I curriculum and includes sections with applications that are particularly helpful. read more
The book is comprehensive. It covers the entirety of the usual Calculus I curriculum and includes sections with applications that are particularly helpful.
Alas, there are many errors in the print version of the book, some of which are also in the PDF version. I'm not sure why these could not be fixed at least in the electronic version as they are discovered. Some of these errors are minor typos, but others significantly change the meaning of the text, e.g. f'' where f' is meant, cos instead of sin, and so on.
The bulk of the material is timeless, but the examples used are modern and applicable.
The book is easy to understand, and most material is presented in a sensible order. To a large extent this is the traditional Calc I curriculum, in the traditional order.
The book is quite consistent. The terminology used, names of concepts and theorems, and so on are all standard in the discipline.
I have been very happy with how the text is broken up. Generally speaking, with few exceptions, it is possible to cover one section in a 50-minute class period. Sections that can be skipped are fairly evident. Of course, this is a subject which requires that prerequisite material be learned before later material, but the later sections to rely overmuch on the previous ones in terms of examples or definitions.
Again, the book uses the traditional sequence of topics for calculus I, as follows: 1. A review of algebra concepts 2. Introduction to limits 3. Derivatives 4. Integrals
The online version of the book and the downloadable PDF are both very easy to load, navigate, and read on-screen. However, the problems at the end of each section are not numbered in the online version of the book, and this makes it difficult for students to find the assigned problems unless they have a download (which they do not if, for example, they're working on a phone) or a hard copy.
I haven't noticed any English grammar errors, although as I said earlier there are some issues with mathematical errors (typos).
The text is about calculus, which is relevant to all cultures.
I recommend the book. The biggest problem I have had is with the errors that change meaning, but these are easy enough to spot and do not seem to be a problem in the online version. I have not had students complain about them much. A smaller but still irritating issue is the lack of numbers on the problems in the online version, which makes it difficult for students using the book on a mobile device to locate the homework. However, beyond those two things I find the book to be of excellent quality, particularly given that it is free.
The test covered all necessary topics for an introductory calculus course with a particularly strong eye to understanding functions. Glossaries read more
The test covered all necessary topics for an introductory calculus course with a particularly strong eye to understanding functions. Glossaries appeared at the end of each section, and the index was useful and contained all expected references. A universal glossary would have been useful.
I did not encounter any errors.
The material is timeless, and the examples used aren't too topical.
The text is easy to read and is pleasantly presented.
There are no consistency errors which I found.
The material is broken into manageable chunks and foundational material is covered before advanced material.
The text is well organized.
There are no interface issues.
I found very few typos or grammatical errors.
The book doesn't make a particular effort to include examples that contain a breadth of cultural relevance.
This is overall a very good text for an introductory calculus course.
This book covers all major topics in a typical first calculus course. Our curriculum also includes numerical integration, which is in the read more
This book covers all major topics in a typical first calculus course. Our curriculum also includes numerical integration, which is in the corresponding Calculus II text, but that single section could be easily incorporated into our Calculus I course. Extensive further-reaching problems and Student Projects for each chapter make this text suitable for honors sections as well. A comprehensive Table of Contents and Index are easily located at the beginning and end of the text, respectively. A variety of application problems requiring the use of technology (denoted with [T]) accompany solid pure math exercises.
No obvious errors jumped out at me.
The theoretical content is fairly timeless. Broad applications in biology, engineering, business, statistics, chemistry, and computer science for calculus are included. The real-world data will eventually require updating – a regular necessity for all textbooks – but individual problems can be seamlessly modernized as needed.
Corresponding diagrams and figures are strong. The addition of colored definition boxes (light blue) and problem-solving strategy boxes (light orange) makes key concepts easy to find. I appreciate that the authors took the time and space in example problem solutions to include algebraic steps that other texts tend to omit. I noticed some minor spacing problems with mathematical symbols, but this was more prominent in the online version than on the pdf.
Formatting is clear and consistent. This text provides a wide variety of examples and problems for each section.
The topics in this course are easily divided into the 6 chapters offered here. Each section is divided into subsections by objective, which can be customized to any curriculum. The text is organized in such a way to accommodate both Early Transcendental and Late Transcendental approaches.
The explanations of concepts are very readable. Section 2.1 gives a nice overview of calculus, providing scaffolding for students to see where the course is heading. Each chapter begins with an exploration of a real-world problem, which is tackled in more detail later in the chapter as the mathematical concepts for its solution develop.
Visually, I found the pdf version more appealing and easier to follow. The examples and section exercises are not numbered online in the same way as in the pdf format, making referencing difficult. That said, I appreciate the continuous numbering of section problems in the pdf version. For instance, having only one problem #450 in the entire text eliminates confusion. Links to helpful interactive applets and demonstrations through the Wolfram Demonstrations Project, GeoGebra, Khan Academy, as well as OpenStax are embedded in the text, although two of the links I tried were broken.
None that I found.
While particular emphasis on Newton and Leibniz is appropriate, this text could benefit from a wider span of historical features from other early contributors to calculus, including non-Europeans and women.
Overall, this is a solid reference text. Out of the partner resources that I was able to access with a guest login, no particular online software stood out from the crowd. Although the surface-type questions presented are sufficient for skill-building, I was unable to find more comprehensive, multi-step problems that require students to synthesize concepts while providing immediate feedback. Using one of these resources in tandem with some sort of paper-and-pencil assignments from the text is likely the best alternative but still requires hand grading. Nevertheless, seeing several software companies embrace the OER initiative is an encouraging first step.
The table of contents and material covered is very similar to most standard, traditional Calculus textbooks intended for the first semester of study. read more
The table of contents and material covered is very similar to most standard, traditional Calculus textbooks intended for the first semester of study. In that regard, this textbook is extremely comprehensive. I like the learning objectives clearly stated at the beginning of each section, and the chapter summary and review problems. The text follows the usual format of offering many instructive, detailed examples for students to mimic, but tends to emphasize computational skills over conceptual understanding. While the text does include some examples and exercises using graphical and tabular approaches, I would like to see more examples and exercises that emphasize conceptual understanding and that encourage the development of modeling skills. Many of the exercises are straightforward and simply computational. There are a reasonable number of problems that involve applications, but in most of these, students are given the formula to use as if it were “pulled out of a hat” rather than derived by the student’s reasoning from general principles. I would like to see more interesting problems that emphasize deep conceptual understanding, or that require students to creatively bring together pieces of knowledge that come from different sections of the course. The “Student Projects” are of this type, but I would like to see more of these. I would need to supplement this textbook more than I would need to supplement other commercial options.
The content is accurate and unbiased. I did not find any errors in the text.
The text follows the usual format of a standard Calculus course, which tends to change little over the decades. The links to web resources and online data are in many cases helpful and enticing, but will require updates over time, not only to maintain functioning URL’s, but also to continue to refer to up-to-date data and examples. The applets at CalculusApplets.com did not open, probably because of updated browser security requirements, and other applets seemed outdated or only partly functional. I like the idea of linking to external resources, but most commercial textbooks (in e-book form) would be more likely to have stable, functioning internal links to illustrations and applets.
The exposition is very clear, direct, succinct, and at an appropriate level of mathematical sophistication for my Calculus I students. That is, it addresses all important issues, but broken down into comprehensible steps, without being pedantic or overly technical. In several key sections, the text succeeds in pointing out and warning against common mistakes, such as incorrectly that assuming the converse of a conditional also holds, or using a delta that depends upon x. The clarity is one of the strongest features of this text.
The text is internally consistent in terms of terminology, notation, and framework.
The sections seem well-partitioned and well-paced (again, not varying much from the standard Calculus textbook). I would want to reorder my presentation of some of them, but it appears that would not cause any major problems.
The overall organization, structure, and flow is good. Personally, I would make the following changes: present Section 4.6: Limits at Infinity as part of Chapter 2 on limits. Present exponential derivatives earlier in Chapter 3. Present L’Hopital’s Rule earlier, when discussing using derivatives in graphing. But this is a matter of personal preference, and the modularity of the text makes all of these changes appear to be pretty easy for instructors to adapt to their preferred order of presentation.
Navigation in the PDF version of the text could be improved. For one thing, I could not find a table of contents to navigate between different sections. Links to future examples and exercises are somewhat helpful, but it was not obvious how to return to the previous point in reading with the pdf file. The online HTML version includes the table of contents and is easier to navigate, but was somewhat slow to reload with my internet connection.
I did not find any grammatical or typographical errors. That said, I’m much more likely to notice errors (or have them brought to my attention by students) when actually using the text for a course.
The text is not culturally insensitive or offensive in any way. However, I would prefer a text that contains more historical observations or side-notes than this one.
The strong points of this text are clear, straightforward explanation and examples of the standard computational techniques of Calculus. Any instructor wanting to focus on computational skills would be completely happy with this text. There is some inclusion of the “rule of four” (graphical, tabular, and verbal approaches in addition to symbolic computations), but not as much as I personally would like to see. The text could be improved, in my opinion, by greater inclusion of conceptual examples and exercises, and more modeling.
The text covers the same material that is covered in Calculus 1 textbooks that I have used in the past and that other members of the department still read more
The text covers the same material that is covered in Calculus 1 textbooks that I have used in the past and that other members of the department still use. There is an index at the end of the text and there is a glossary at the end of each section. It would be helpful if there was also a comprehensive glossary, especially in the pdf of the book for when it is printed.
I used this textbook in Calculus 1 during fall semester 2016. We did many of the problems both in class and as assigned problems and found no errors. For some of the worked examples in the text the students sometimes had a difficult time understanding what was being done but this is not uncommon regardless of the textbook. They do make an effort to update any errors that might be found and sent to them, as is stated in the preface to the book "Since our books are web based, we can make updates periodically when deemed pedagogically necessary. If you have a correction to suggest, submit it through the link on your book page on openstax.org. Subject matter experts review all errata suggestions. OpenStax is committed to remaining transparent about all updates, so you will also find a list of past errata changes on your book page on openstax.org."
The text makes attempts to give examples and problems that are current and up-to-date. Given the subject matter the text will likely stay relevance for a long time.
The text is written in a way that is generally easy to read although as mentioned before some of the examples students had a difficult time following. Also if using the online text, it is important that one uses the full screen view of the text as some of the diagrams become clutter and difficult to decipher because labeling is placed very close together. There are some pages where even if looking at the print version the diagrams are hard to fully understand. For example in section 3.1, Defining the Derivative the diagrams cluttered and students who are being exposed to the idea of the derivative for the first time may not understand what label goes with what.
Terminology is used in a consistent manner.
Some of the sections cover quite a lot of material, sometime too much to be covered with in a 50 minute class period which is not terribly uncommon. It was an easy task to find a suitable stopping point to fit within the allotted time.
When using the book in class I changed the order of some of the sections. Most specifically, section 4.6 "Limits at Infinity and Asymptotes" was covered in chapter 1 and chapter 2 while talking about functions and limits. When we got to chapter 4 the class was reminded of our previous discussion and we moved on.
The online text is easy to navigate to the start of a particular section using the table of contents. Also in the online text the sample problems have the solutions hidden so that the problems can be done without being influenced by their presence. A positive change to the online version would be if it were possible to jump to the exercises that appear at the end of the section. Some of the tables and diagrams in the sections seemed larger than necessary and not as organized as they might be. It would have been a nice addition to the online text to have links to animations that might illustrate a particular concept, like the derivative. In the pdf version of the book, the problems at the end of the section are numbered, it would be nice if the online version used the same numbering. It is difficult to use the online version in class and call students attention to a problem in their printed pdf copy. Also it is not possible in the pdf version of the text to jump to a section once you have navigated to a chapter. Each of the sections should be clickable so that by doing so you are taken to the start of the section. Further there should be a way to navigate to the end of the section to access the exercises without having to scroll all the way through.
I don't recall any grammatical errors.
Cultural content is slight. There's the obligatory picture of Newton and Leibniz and a nod to Archimedes but little else.
As mentioned this book was used to teach Calculus 1 in the fall of 2016. I used the book in conjunction with MyOpenMath. Used together the students found the resources helpful. This text made a suitable replacement for the text that I had used previously.
This text was very comprehensive. It covered every section that our current book covers for 251 and 252. read more
This text was very comprehensive. It covered every section that our current book covers for 251 and 252.
I found no errors. Of course there are probably many considering it is a newer math book. No bias was present.
Examples given covered topics that should endure for a good amount of time. Relativity, rockets, swimmers and runners, windows... this book won't feel dated in 10 years.
All of the author's explanations were exceedingly clear. This was one of the features I most appreciated. Diagrams were not overly cluttered, each page was free of distracting margin comments and very to the point.
I found no inconsistencies.
This book follows the traditional layout of a calculus book. The sections lined up almost exactly with our current book. In fact, we currently cover 251 in 24 sections, and Open stax covers the material in 25 sections.
Very logical flow. Again, this book structured in a similar way to our current book. Switching to open stax would be nearly effortless.
The images and graphs appeared to be lower budget. I should also not that the images and graphs were also free of clutter and easily understood. Many of the tables were oversized and distracting.
If there are grammar errors in the book, they did not distract from the content. Again this book is written in a simple clear manner.
The text is not culturally insensitive or offensive in any way. Examples and problems do not make reference to individuals race or ethnicity.
I found this book to be clear and logically laid out. There were nice pieces of history interjected. The layout was intuitive. Each section was well motivated with examples. I also appreciated that volume 1 only covered only differential and integral calculus.
This text covers the same material as other common Calculus I textbooks. I was unable to find any major topic that is covered in my classes currently read more
This text covers the same material as other common Calculus I textbooks. I was unable to find any major topic that is covered in my classes currently that wasn't covered in this book. There are helpful glossaries at the end of each chapter, but no universal glossary for the entire textbook. There is an index at the back.
I worked through a few examples and exercises and did not find any errors.
The nature of the subject makes it difficult to imagine a calculus book becoming out-of-date. The non-mathematical content of some textbooks (like historical notes) can become irrelevant or outdated, but this textbook has very little non-mathematical content and so it is not in danger of becoming out-of-date quickly.
The text is written in an accessible way and the prose is easy to read. Most figures were well-designed, but a few were cluttered. In particular, the critical diagrams showing the construction of the derivative were difficult to decipher due to the labels being nearly on top of one another.
The textbook is very consistent in its visual presentation. I did not notice any inconsistencies in terminology.
This textbook easily divides into small sections and subsections, as most math textbooks do. The sections are often too long for an hour-long lesson but the divisibility of the book allows the instructor to shorten or lengthen a lesson to fit the time allowed.
This book has a similar structure to that of Stewart or Briggs. The content is broken up into 6 chapters covering essentially the same topics as those popular textbooks. One major difference: Limits at Infinity are not covered until just before Optimization, after the students have already been graphing functions using the derivative. The section on Limits at Infinity does not appear to rely on derivatives at all, so it could easily be taught with the rest of the material on limits if the instructor chooses.
The online interface is nearly identical to the static PDF file available for download. The online version hides solutions for the example problems by default, allowing the reader to attempt the problem without being influenced by a visible solution. Some of the diagrams were larger and easier to read in the online version. It is simple to navigate to a particular section using the Table of Contents in the online interface. However I could not find a way to navigate to a particular page by the page number.
I did not find any grammatical errors.
Cultural content is very thin in this book, so there isn't much to critique here. I did notice that Newton, Leibniz, and other European mathematicians are mentioned, while there is no mention of the contributions and discoveries of non-European mathematicians.
This book would make a suitable replacement for other popular calculus textbooks such as Stewart or Briggs. As a part of this review, I was not able to use the accompanying online homework system, WeBWorK. In my experience, students spend more time interacting with the online homework system than they do the textbook. An online homework system that is easy to use for both the instructor and the student is essential.
Table of Contents
Functions and Graphs
Applications of Derivatives
Applications of Integration
Table of Integrals
Table of Derivatives
Review of Pre-Calculus
About the Book
Calculus is designed for the typical two- or three-semester general calculus course, incorporating innovative features to enhance student learning. The book guides students through the core concepts of calculus and helps them understand how those concepts apply to their lives and the world around them. Due to the comprehensive nature of the material, we are offering the book in three volumes for flexibility and efficiency. Volume 1 covers functions, limits, derivatives, and integration.
OpenStax College has compiled many resources for faculty and students, from faculty-only content to interactive homework and study guides.
About the Contributors
Gilbert Strang was an undergraduate at MIT and a Rhodes Scholar at Balliol College, Oxford. His Ph.D. was from UCLA and since then he has taught at MIT. He has been a Sloan Fellow and a Fairchild Scholar and is a Fellow of the American Academy of Arts and Sciences. He is a Professor of Mathematics at MIT, an Honorary Fellow of Balliol College, and a member of the National Academy of Sciences. Professor Strang has published eleven books.
He was the President of SIAM during 1999 and 2000, and Chair of the Joint Policy Board for Mathematics. He received the von Neumann Medal of the US Association for Computational Mechanics, and the Henrici Prize for applied analysis. The first Su Buchin Prize from the International Congress of Industrial and Applied Mathematics, and the Haimo Prize from the Mathematical Association of America, were awarded for his contributions to teaching around the world. His home page is math.mit.edu/~gs/ and his video lectures on linear algebra and on computational science and engineering are on ocw.mit.edu
Edwin "Jed" Herman, Professor, Department of Mathematical Sciences, University of Wisconsin-Stevens Point. Ph.D., Mathematics, University of Oregon?.?