Calculus is fundamentally different from the mathematics that you have studied previously: calculus is less static and more dynamic. It is concerned with change and motion; it deals with quantities that approach other quantities. For that reason, it may be useful to have an overview of the subject before beginning its intensive study.
The invention of calculus brought a new dimension to mathematics. Basically, mathematics was only able to calculate objects that were completely static. So there was no answer to a lot of dynamic mathematical questions.
Calculus potentially solved this problem by helping calculate objects in constant motion. It is crucial that you can study calculus yourself with the help of the following best calculus books for self study.
Best Calculus Books for Self Study
Book Name & Author | Image | Rating | Price |
Essential Calculus Skills Practice Workbook with Full Solutions by Chris McMullen |
9.3 | View on Amazon | |
Calculus: An Intuitive and Physical Approach (Dover Books on Mathematics) by Morris Kline | 9.2 | View on Amazon | |
Quick Calculus: A Self-Teaching Guide by Daniel Kleppner & Norman Ramsey | 9.0 | View on Amazon | |
Calculus For Dummies by Mark Ryan | 9.0 | View on Amazon | |
Calculus: Early Transcendentals by James Stewart | 9.0 | View on Amazon | |
The Humongous Book of Calculus Problems by W. Michael Kelley | 9.2 | View on Amazon | |
Calculus: Concepts and Applications by Paul A. Foerster | 9.2 | View on Amazon |
1. Essential Calculus Skills Practice Workbook with Full Solutions
This is an essential calculus book for self-study that each chapter begins with a concise review of the pertinent concepts and math. It is fully solved examples that help to serve as a guide, and practice exercises that help you to build fluency.
The author, Chris McMullen, Ph.D., has over twenty years of experience teaching math skills to physics students. He prepared this comprehensive workbook with full solutions to every problem to share his strategies for mastering calculus. This workbook covers a variety of essential calculus skills, including:
- Derivatives of polynomials, trig functions, exponentials, and logarithms.
- The chain rule, product rule, and quotient rule.
- Second derivatives.
- How to find the extreme values of a function.
- Limits, including l’Hopital’s rule.
- Antiderivatives of polynomials, trig functions, exponentials, and logarithms.
- Definite and indefinite integrals.
- Techniques of integration, including substitution, trig sub, and integration by parts
- Multiple integrals.
The goal of this workbook isn’t to cover every possible topic from calculus, but to focus on the most essential skills needed to apply calculus to other subjects, such as physics or engineering.
2. Calculus: An Intuitive and Physical Approach (Dover Books on Mathematics)
This is an application-oriented introduction that relates the subject as closely as possible to science. In-depth explorations of the derivative, the differentiation and integration of the powers of x, and theorems on differentiation and antidifferentiation lead to a definition of the chain rule and examinations of trigonometric functions, logarithmic and exponential functions, techniques of integration, polar coordinates, much more. Clear-cut explanations, numerous drills, and illustrative examples.
It is very satisfying to share the vision, thoughts, and conclusions of the author and this calculus book take a new dimension, a dimension beyond the symbols and the equations. It becomes alive as a language that is relating to a story much more clear and structured of the things around, and of the different phenomena like motion, time, constants, initial conditions, relations, rates of change, limits, and even more.
This book contains all the topics typically covered in three semesters of calculus and in that sense is similar to any number of other good books. The most important thing that makes this book unique is the intuitive approach through geometry taken to explain topics that would otherwise just be abstract mathematics. If you are struggling with understanding what a derivative or integral of a function really means, or especially functions of multiple variables and partial derivatives, this book may be highly useful to you.
3. Quick Calculus: A Self-Teaching Guide
A self-instructional guide for students who need additional help with calculus, or working professionals who need to brush up on the fundamentals. The book uses a unique insured learning format that lets readers work at their own pace, with frequent reviews, quizzes, examples, exercises, and problems with answers. It treats the elementary techniques of differential and integral calculus with a preliminary review of algebra and trigonometry. It emphasizes technique and application that includes many numerical exercises on the pocket calculator and microcomputer.
This book provides a strong foundation for people who haven’t learned and people who lost track of the subject. It includes reviews of mandatory concepts like trig, and logs, in the first chapter. The content is organized perfectly into numbered sections, making it very easy to refer to other sections and keep track of your progress. What you will like the most about this book is its appendix because it contains derivations that prove to be a great way to build a strong knowledge foundation, and provides a thorough view of calculus.
Quick Calculus: A Self-Teaching Guide is essential for understanding subjects ranging from physics and chemistry to economics and ecology. Nevertheless, countless students and others who need quantitative skills limit their futures by avoiding this subject like the plague. Maybe that’s why the first edition of this self-teaching guide sold over 250,000 copies.
Quick Calculus, Second Edition continues to teach the elementary techniques of differential and integral calculus quickly and painlessly. Your “calculus anxiety” will rapidly disappear as you work at your own pace on a series of carefully selected work problems. Each correct answer to a work problem leads to new material, while an incorrect response is followed by additional explanations and reviews. This updated edition incorporates the use of calculators and features more applications and examples.
4. Calculus For Dummies
Calculus For Dummies makes calculus manageable even if you’re one of the many students who sweat at the thought of it. By breaking down differentiation and integration into digestible concepts, this guide helps you build a stronger foundation with a solid understanding of the big ideas at work.
This user-friendly calculus book leads you step-by-step through each concept, operation, and solution, explaining the “how” and “why” in plain English instead of math-speak. Through relevant instruction and practical examples, you’ll soon learn that real-life calculus isn’t nearly the monster it’s made out to be.
Calculus is a required course for many college majors, and for students without a strong math foundation, it can be a real barrier to graduation. Breaking that barrier down means recognizing calculus for what it is simply a tool for studying the ways in which variables interact. It’s the logical extension of the algebra, geometry, and trigonometry you’ve already taken, and Calculus For Dummies, 2nd Edition proves that if you can master those classes, you can tackle calculus and win.
- Includes foundations in algebra, trigonometry, and pre-calculus concepts.
- Explores sequences, series, and graphing common functions.
- Instructs you how to approximate area with integration.
- Features things to remember, things to forget, and things you can’t get away with.
Stop fearing calculus, and learn to embrace the challenge. With this comprehensive study guide, you’ll gain the skills and confidence that make all the difference. Calculus For Dummies, 2nd Edition provides a roadmap for success, and the backup you need to get there.
5. Calculus: Early Transcendentals
The text is very comprehensive and covers all topics in a typical three-semester calculus sequence. The writing is very concise, but on the other hand, does not provide a lot of context or applications interwoven throughout the sections. The exercise sections could be a bit more robust.
To practice and develop an understanding of topics, this text offers a range of problems, from routine to challenging, with selected solutions. As this is an open text, instructors and students are encouraged to interact with the textbook by annotating, revising, and reusing it to their advantage.
Stewart conveys not only the utility of calculus to help you develop technical competence, but also gives you an appreciation for the intrinsic beauty of the subject. His patient examples and built-in learning aids will help you build your mathematical confidence and achieve your goals in the course.
Here are some of the changes for the sixth edition of Calculus: Early Transcendentals.
At the beginning of the book, there are four diagnostic tests, Basic Algebra, Analytic Geometry, Functions, and Trigonometry. Answers are given and students who don’t do well are referred to where they should seek help (Appendixes, review sections of Chapter 1, and the website).
In response to requests of several users, the material motivating the derivative is briefer: Sections 2.7 and 2.8 are combined into a single section called derivatives and rates of change. The section on Higher Derivatives in Chapter 3 has disappeared and that material is integrated into various sections in Chapters 2 and 3.
Instructors who do not cover the chapter on differential equations have commented that the section on Exponential Growth and Decay was inconveniently located there. Accordingly, it is moved earlier in the book, to Chapter 3. This move precipitates a reorganization of Chapters 3 and 9. Sections 4.7 and 4.8 are merged into a single section, with a briefer treatment of optimization problems in business and economics.
6. The Humongous Book of Calculus Problems
W. Michael Kelly has put together here a wonderful book of 1000 calculus problems including solutions. I think that including solutions is important for the student, because even if you manage to find the answer to a problem, by studying the solution, you may learn a different approach to solving the problem. Plus, having the solutions is important if you are learning this outside of a classroom, and don’t have an instructor to consult with. Kelly has done a great job of providing easy-to-follow solutions to the problems. He even has call-outs in the margins to provide additional information.
The book is light on theory, so I recommend the book: The Calculus Lifesaver by Adrian Banner for the theory part The Calculus Lifesaver: All the Tools You Need to Excel at Calculus (Princeton Lifesaver Study Guides). This book can also be used as an adjunct to a school text to provide additional problems for practice. If you decide to use Banner’s book for theory, I have put together a table to cross-reference the chapters in the books. Just read the theory part in the Lifesaver book, and then follow up with more problems in the Humongous Book.
This book is a great resource, but understand that you are getting pages of SOLVED calculus problems; this is not a workbook (where you solve the problem and then check the solution in the back). Of course, you could choose to cover up the solution steps on the page while you work on the solution yourself. Working and understanding problems are the path to success in math, the more you are exposed to the better chance you have to do well on tests.
The benefit of this particular book is that it shows the steps of a solution in more detail than most other guides I’ve used. The author has also “doodled” additional helpful tips in the margins of the problems. The skull icon on certain problems indicates they are especially challenging.
7. Calculus: Concepts and Applications
In Calculus: Concepts and Applications, students start off with calculus! A review of precalculus occurs at various points when it’s needed. The text combines graphing-calculator technology with a unique, real-world application approach, and presents calculus as a study of just four fundamental concepts: limits, derivatives, definite integrals, and indefinite integrals. Students learn these concepts using algebraic, numerical, graphical, and verbal approaches.
As a result, students with a wider range of abilities can be successful in calculus, not just those who are strong in algebra. The accompanying set of Explorations in the Instructor’s Resource Book, designed for cooperative group work, gives students hands-on experience with new topics before they are formally introduced.
The book is presented in an easily understood fashion with ample technology-based examples and exercises. The applications are intimately connected with the topic and amplify the key elements in the section. The textbook is a wealth of both fresh items and ancient insights that have stood the test of time. For example, alongside Escalante’s “crosshatch” method of repeated integration by parts, you’ll find Heaviside’s thumb trick for solving partial fractions. Later still, the author presents the logistic curve and slope fields in differential equations. All of these are beautiful examples of how computing technology has changed the calculus course.
The changes and additions found in this second edition exhibit the timeliness of the text. Exponentials and logarithms have been given an even more prominent role that reflects their greater emphasis in today’s calculus instruction.