Best Calculus Textbooks - Top 12 Choices in 2021!

Jamey Muller
February 23, 2021

Calculus is not an easy subject to most students who are just beginning to appreciate math. Some would even argue that calculus has no practical real-life applications. Those who know better are quick to argue the opposite. Calculus is everywhere. People, objects, concepts, and life itself are in constant and continuous motion, and this truth alone makes calculus relevant to man and society. Calculus is the mathematical study of continuous change, complementing geometry, as the study of shapes, and algebra, the study of generalizations of arithmetic operations. Man, without knowing it, has been employing principles of calculus in early Greece, China, India, Persia, and Japan. It was later fully developed in the late 17th century by no less than Sir Isaac Newton and Gottfried Wilhelm Leibniz. Calculus, today, has very specific and helpful functions in science, engineering, and economics. People today have a better understanding of the patterns and changes present in the natural world. Some of the practical applications of calculus includes a better understanding of velocity, acceleration, and slopes of a curve, as well as mass, pressure, and work. Through math and its many areas of study, including calculus and precalculus, man now has a better understanding of the nature of space, time, and motion.

Best Calculus Textbooks

If you wish to better appreciate calculus, below are the Top 12 titles that tackle this mathematical discipline. These books are perfect for students who are about to tackle calculus as one of their college majors.

1. Essential Calculus Skills Practice Workbook with Full Solutions by Chris McMullen

Learning calculus and perfecting it requires practice, and this is what Essential Calculus Skills Practice Workbook with Full Solutions offers. The author, Chris Mullen, has been teaching math to physics students for more than 20 years. He has developed strategies in mastering calculus and openly shares his techniques in this workbook. Essential Calculus Skills Practice Workbook with Full Solutions covers a number of important calculus skills and provides full solutions to every problem presented. The problems and skills are in the areas of derivatives of polynomials, trig functions, exponentials, logarithms, second derivatives, antiderivatives of polynomials, definite and indefinite integrals, and multiple integrals. In the workbook, Chris Mullen teaches how to find the extreme values of a function limits, including l’Hopital’s rule, and the techniques of integration, including substitution, trig sub, and integration by parts. The goal is not simply to tackle every possible topic from calculus, but more importantly to focus on the most essential skills.

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2. Calculus: An Intuitive and Physical Approach (Second Edition) (Dover Books on Mathematics) by Morris Kline

Calculus: An Intuitive and Physical Approach (Second Edition) (Dover Books on Mathematics) by Morris Kline is an introduction to calculus that focuses on its application to the real world. The best books on calculus can only be written by the best authors. Morris Kline was a professor of mathematics and a popularizer of math. In this book, he relates calculus as closely as possible to science and other applications, by providing in-depth explorations of the derivative, differentiating and integrating the powers of x, highlighting theorems on differentiation and antidifferentiation lead to a definition of the chain rule and examinations of relevant functions such as trigonometric, logarithmic and exponential. Calculus: An Intuitive and Physical Approach also tackles the techniques of integration and polar coordinates, among others, with very clear explanations, illustrative examples, and a variety of drills. The book is accompanied by a workbook that provides a solution guide, which is available upon request.

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3. The Humongous Book of Calculus Problems (Humongous Books) by W. Michael Kelley

Calculus may be a daunting subject to many, but the only real way to learn it is to do calculus problems, a lot of them. The Humongous Book of Calculus Problems (Humongous Books) by W. Michael Kelley provides students, readers, and mathematics enthusiasts the chance to do just that – practice, solve, and master calculus. As its name says, this book presents an enormous among to calculus problems, more than any student’s worst nightmare, but with notes and solutions that will truly help the leaner. W. Michael Kelley is a well-known and award-winning teacher in calculus. In this humongous book, he reveals his own notes and solutions to over 1,000 calculus problems, with really detailed step-by-step answers. He also provides clarifications, extra explanations, and special pointers to some problems. The Humongous Book of Calculus Problems tackles the essentials of calculus, which are derivatives, integrals, limits, continuity, tangent lines, infinite series, velocity, acceleration, area, and volume, as well as the more difficult areas of calculus, such as epsilon-delta proofs and formal Riemann sums.

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4. Calculus For Dummies (For Dummies (Lifestyle) by Mark Ryan

Calculus For Dummies (For Dummies (Lifestyle)) by Mark Ryan is a user-friendly guide for students, novices, and anyone wanting to learn more about this otherwise difficult math discipline. Students can’t get away with calculus, since it is a required course for a number of college majors. The problem, however, is that math, let alone calculus, is not popular to many students, and so they could really  struggle with it. To some, the word “calculus” itself can be scary, but students need to understand and recognize that calculus is simply a tool to study the ways in which variables interact. Calculus is the logical extension of algebra, geometry, and trigonometry, which students have taken before being required to enroll in this class. Calculus For Dummies is here to help. The book talks about the foundations in algebra and trigonometry, as well as presents pre-calculus concepts. It explores sequences and series, graphs common functions, and teaches how to approximate area with integration.

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5. AP Calculus Premium: With 12 Practice Tests by David Bock M.S.

To learn calculus and get good grades in the exams, one doesn’t have to be a mathematics genius. A student simply needs to be willing to practice and do a lot of calculus problems. AP Calculus Premium: With 12 Practice Tests by David Bock M.S. presents a number of comprehensive reviews and practice tests that will help students ace any AP Calculus AB and BC exams. The subject reviews are detailed and clear to help learners master the test topics. Likewise, practice tests will allow students to get used to facing calculus problems so that they wouldn’t freeze during the actual exams. David Bock and experienced teachers wrote this book, highlighting six practice tests in Calculus AB (four in the book and two online) and six practice tests in Calculus BC (again four in the book and two online). AP Calculus Premium also provides comprehensive content review covering topics for both AB and BC exams, plus helpful bits of advice on how to efficiently use graphing calculators.

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6. Calculus Made Easy by Silvanus P. Thompson

Everybody loves a book that makes difficult subjects easy to understand. This is what one gets from Calculus Made Easy by Silvanus P. Thompson. Students and teachers in calculus recognize this book and its author as it has long been the most popular calculus primer. Silvanus Phillips Thompson FRS was a professor of physics at the City and Guilds Technical College in Finsbury, England. He was a respected mathematicians in the late 1800s to the early 1900s. Elected to the Royal Society in 1891, Thompson was popular for his work as an electrical engineer and as an author, which made him an expert in calculus. Thompson is also a leading figure in physics and thus wrote Elementary Lessons in Electricity and Magnetism. He also authored the biographies of Lord Kelvin and Michael Faraday. In 1910, he wrote Calculus Made Easy, and the book has endured through the years, as a testament to its usability and helpfulness.

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7. Calculus Workbook For Dummies with Online Practic by Mark Ryan

Calculus Workbook For Dummies with Online Practice by Mark Ryan offers calculus students to study and master this math subject at their own convenience online. No doubt, calculus is a hard subject, even to those who have inclination in mathematics. But, as they say, practice makes perfect, and this applies to calculus, too. Calculus Workbook For Dummies with Online Practice provides an easy way for anyone to learn calculus. It can help students better understand and remember what they learned inside the classroom, as the book talks about key concepts, lays out concept reviews, and presents practice problems, using an easy-to-follow, practical approach. To complement the book, students will get free access to an online quiz provided in every chapter. This way, the learning becomes fun, immersive, and accessible to many. One of the book’s special features is the presentation of multiple examples of limits, vectors, differentiation, integration, continuity, curve-sketching, natural logarithms, and infinite series.

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8. Introduction to Probability, Statistics, and Random Processes by Hossein Pishro-Nik

Introduction to Probability, Statistics, and Random Processes by Hossein Pishro-Nik helps students to better and more easily grasp mathematical concepts that are otherwise difficult to master. Readers, learners, and any calculus enthusiasts will be introduced to probability, statistics, and stochastic processes. What makes this book special is that it is also helpful to professionals in the areas of finance, engineering, various sciences, and other related fields, with a clear and intuitive approach and mathematical accuracy. Students and practitioners could make use of the book’s several exercises and solutions to basic concepts such as random experiments, probability axioms, conditional probability, and counting methods. The book also tackles limit theorems and convergence, Bayesian and classical statistics, single and multiple random variables (discrete, continuous, and mixed), and random processes, including random signals, Poisson processes, discrete-time and continuous-time Markov chains, and Brownian motion. Hossein Pishro-Nik also included some online chapters that present simulations using MATLAB and R.

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9. An Advanced Introduction to Calculus-Based Physics (Mechanics) by Chris McMullen

An Advanced Introduction to Calculus-Based Physics (Mechanics) by Chris McMullen offers tons of exercises, concepts, and notes for independent learners. Students must be willing to truly learn calculus and develop a strong introduction to the fundamentals of physics. Chris McMullen designed his book so that it can also serve as a useful reference for physics and engineering. Students who wish to advance in the fields of physics will benefit from reviewing the fundamentals presented by McMullen. Basically, An Advanced Introduction to Calculus-Based Physics (Mechanics) is a textbook for student who are already familiar with the algebra, the basic techniques of differentiation and integration, and polynomials and trig functions. Such students will further learn important concepts, such as the differences between mass and weight, between average speed and average velocity, and between velocity and acceleration. The book further helps by providing equation tables, problem-solving strategies, conceptual examples, tips and answers, as well as helpful notes and footnotes on common mistakes, exceptions, and other helpful discussions.

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10. Precalculus: A Self-Teaching Guide (Wiley Self-Teaching Guides) by Steve Slavin

Precalculus: A Self-Teaching Guide (Wiley Self-Teaching Guides) by Steve Slavin convinces learners that the best way to learn precalculus is to face it head-on. There’s no way around learning math. Students must simply do it and be immersed in problems, equations, concepts, solutions, and answers. Stave Slavin includes in his book a review of algebra and helpful discussions on exponential functions, log functions, and trigonometry. As the title says, Precalculus: A Self-Teaching Guide will help learners understand precalculus on their own, using the book’s tips and explanations. People want to learn precalculus for a number of reasons – as a course in college, to review the fundamentals, or simply to better appreciate math. In all cases, this book will serve as an interactive primer that will provide learners the necessary precalculus skills. What makes this book unique is its self-teaching approach with self-tests and exercises, so that readers could study at their own pace.

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11. The Math Book: Big Ideas Simply Explained by DK

The Math Book: Big Ideas Simply Explained by DK makes math as easy as 1-2-3. This may seem hard to believe, but The Math Book makes learning this discipline easy, fun, and intriguing. The book tackles mind-blogging questions such as how can math help us predict the future? What is an imaginary number? Can two parallel lines ever meet? You don't need to be a math genius to enjoy this one. It is an encyclopedia of mathematics that brilliantly presents short, easy-to-understand explanations of math concepts, step-by-step diagrams, and interesting illustrations that will convince readers that numbers are exciting. Unlike other titles in calculus and other areas of mathematics, The Math Book tells a story. It charts the development of math around the world, from ancient times to the Middle Ages, the Renaissance, and to modern living. It talks about how math helped in important inventions, including the recent rise of game and group theory.

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12. Calculus Deconstructed: A Second Course in First-Year Calculus (Mathematical Association of America Textbooks) by Zbigniew H. Nitecki

Calculus Deconstructed: A Second Course in First-Year Calculus (Mathematical Association of America Textbooks) by Zbigniew H. Nitecki is for readers with some previous understanding of calculus and its techniques, but not necessarily about the methods of proof. Zbigniew H. Nitecki, a professor in the Mathematics department at Tufts University, provides a thorough and mathematically detailed exposition of single-variable calculus, making his book appropriate for a beginning Honors Calculus course after high school calculus. The book could also help as a "bridge course", as it presents basic analysis to motivate and illustrate mathematical rigor. To students and enthusiasts who wish to have a deeper understanding and appreciation of this math discipline, Calculus Deconstructed can serve as a textbook for reference book for one’s person self-study time. The book presents topics and techniques in single-variable calculus, and discussed in context of a coherent logical structure, building on familiar properties of real numbers and teaching methods of proof by example.

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Final Thoughts: Best Calculus Textbooks

Calculus may not be for everyone, but it is here for all to understand and use. It is mostly underappreciated considering that the fibers and sinews of life and the universe is made up of calculus concepts – mass, motion, slopes, and so on. The Top 12 books listed are here to help learners and practitioners to have a firmer grip of this branch of mathematics. Not everyone is a math genius, but people could develop a deeper sense of life with the help of calculus and all other areas of mathematical studies.

Jamey Muller
Jamey is a 24-year-old living in Houston, Texas. He's an aspiring financial analyst with a passion for anything finance related. Over the last few years, he has taken many digital courses and read books on anything finance related. In his freetime he likes to hang out with his friends and likes to play video games.

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