Fresh into Calculus? Are you looking for the best calculus books that you should start with? Well, when I was your age I had tried several books from library, borrowed books from friends and purchased over a dozen from Amazon. But not all books were effective and most of these only wasted my time. Going over too many books can be harmful. So , you should sticky only to a fix number of resources.
Combined by own experience and latest trends in Calculus study, I have collected and listed 20 of the best calculus books that you can start with.
These books are available on Amazon and can be categorized into 6 sections. The first 4 books (1-4) are essential calculus textbooks. These are essential because every college or university syllabus can be covered by these books.
The next 5 calculus books (5-9) are best for students who are just starting with Calculus. Book #10 to #12 are related to the history and applications of calculus to general life. These are great if you are willing to become a calculus teacher someday or just want to surprise your classmates with some random facts.
Other books are self-help guides with pedagogical approach and practice problems, followed by books on applied calculus.
The last 2 of the best calculus books are for students with entrepreneurial mindsets. Read these books to know and understand how you could use calculus in business and marketing.
Most of these books have Kindle® versions available as well. Some of the books are available in audible format, which can be used for free with this 30 days trial with 2 free audiobooks.
So, let’s start with the list of the best calculus books in 2021.
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Most Essential Calculus Textbooks
Calculus: Early Transcendentals
Author – James Stewart
The late James Stewart is one of the most renowned names in the field of mathematics. He did extensive research in the field of harmonic analysis and was the Professor of Mathematics at the McMaster University. Calculus: Early Transcendentals, with its accurate and precise writing supplemented by real-world examples, is a worldwide bestseller.
In this book, Stewart helps you develop a solid understanding of calculus and also allows you to appreciate the intrinsic beauty of the subject. With the help of the relevant examples and inbuilt learning aids in this text, you will gain confidence in this field of mathematics and achieve success in your goals.
Thomas’ Calculus: Early Transcendentals
Author – George Thomas Jr., Maurice Weir, and Joel Hass
Thomas’ Calculus: Early Transcendentals has been one of the most popular books on calculus for more than half a century. It is well-known for its crystal clear explanations, superior figures, meticulously selected explanations, and reliable exercise sets. The book aims to introduce readers to the intrinsic beauty of calculus and the scope of its applications.
This new edition presents a more refined and expanded version of these exercises, aiming to help readers develop technical competence. Co-authors Maurice Weir and Joel Hass have done an admirable job in improving the text, keeping in mind the ambitions and preparations of contemporary students.
Calculus by Larson and Edwards
Author – Ron Larson and Bruce Edwards
Authors Ron Larson and Bruce Edwards have earned a reputation for their teaching style. Even this book’s solid and effective pedagogy, successfully addressing the requirements of a wide range of teaching and learning styles, has received widespread praise from a generation of students and professors alike.
The book is loaded with excellent explanations and exercises, presented comprehensively and professionally. You can view detailed solutions to the odd exercises on the book’s companion website as well.
Calculus by Ron Larson and Bruce Edwards is well worth the rather high price and is an ideal accompaniment to various professional calculus courses in universities.
Calculus: An Intuitive and Physical Approach
Author – Morris Kline
Calculus: An Intuitive and Physical Approach is widely considered to be one of the best texts on calculus available today. Morris Kline takes an intuitive approach through geometry to explain topics that would otherwise appear to be just abstract mathematics. Parallel to the development of the “how-to” of the mathematical tools, it promptly shows you the “why” as well. The book encourages you to think mathematically and form connections between the new content and what you already know.
The author presents detailed explorations of the derivative, theorems on differentiation and antidifferentiation, the differentiation and integration of the powers of x, the chain rule and examinations of trigonometric functions, polar coordinates, and much more. He encourages the student to solve problems without resorting to memorizing formulas. He also makes a lot of effort to show how every mathematical technique is relevant in real life as well.
This book is a highly recommended and invaluable resource for every student of calculus.
Best Calculus Books for Beginners
The Calculus Lifesaver: All the Tools you Need to Excel at Calculus
Author – Adrian Banner
Calculus is often considered to be one of the most frustrating and challenging courses ever taken by students. However, this impression is quite misleading. The Calculus Lifesaver offers a wide range of helpful tools for students to not only learn calculus but to perform exceptionally well at it. It is a user-friendly guide with quality study notes that are proven to yield good results. It is an excellent supplement to any single-variable calculus textbook or course and can also be used as a textbook in its own right.
Adrian Banner’s writing style is friendly and informal while being comprehensive at the same time. He elaborates standard course material with several relevant examples that help students develop problem-solving skills. These examples are of varying difficulty levels and illustrate the profound presentation of theoretical concepts. This book is highly recommended for anyone who wishes to master the fundamentals of calculus.
Calculus Made Easy
Author – Silvanus P. Thompson and Martin Gardner
First published in 1910 in England, Calculus Made Easy has long been one of the most popular publications on calculus in existence. It has now been transformed into a contemporary masterpiece that ably explains the beautiful concepts of calculus in a user-friendly manner. Silvanus P. Thompson expressed nearly 90 years ago that once a reader has grasped the fundamentals of differentiation and integration, the rest of calculus will follow naturally. His triumphant success is testified by the continuing popularity of Calculus Made Easy over the years.
In the first major revision of this book, Martin Gardner updated the text following recent developments in terminology and method. He added a comprehensive preface, three new introductory chapters, and 20 additional problems for practice. This book, which has sold over a million copies worldwide, will replace your apprehension of calculus with curiosity, levity, and delight. It is especially recommended to students of calculus with an interest in the history of the subject.
Pre-Calculus for Dummies
Author – Mary Jane Sterling
Calculus is a compulsory course for a lot of college majors. Unfortunately, students who don’t have a strong foundation in mathematics can find it quite challenging. In order to solve this issue, one needs to recognize calculus for what it is – just a tool for studying how variables interact with each other. Pre-Calculus for Dummies is a user-friendly book that has been written to make calculus manageable for such students.
This book simplifies differentiation and integration into easier concepts and helps the reader build a stronger foundation with a thorough understanding of the core ideas involved. It includes foundations in trigonometry, algebra, and pre-calculus and explores series, sequences, and graphing common functions in detail. It also shows you how to approximate an area using integration.
After going through the appropriate instructions and practical examples in the text, you will gain the confidence and skills needed to master this subject. Pre-Calculus for Dummies shows you the path to success and provides the resources needed to embark on your journey.
Calculus in 5 Hours: Concepts Revealed, so You Don’t Have to Sit Through a Semester of Lectures
Author – Dennis Jarecke
A lot of students struggle to get through their first calculus course. Most popular introductory textbooks reach up to 1,000 pages, making it even harder for them to get a grasp on the subject. Calculus in 5 Hours, on the other hand, can help you develop confidence in calculus in just about 124 pages. What most people don’t realize is that an excess of details can impair learning for beginners. This book serves as a straightforward guide that helps you understand the basic concepts thoroughly.
You will find Calculus in 5 Hours to be a worthy companion regardless of the calculus course you are enrolled in. It is a great resource for refreshing your knowledge of the subject. With the help of simple examples and drawings, it helps you organize your understanding of calculus for assignments and tests. It covers nearly 75% of a first-semester course and omits material that isn’t strictly necessary.
Calculus in 5 Hours is an excellent book for strengthening your concepts and achieving your goals as fast as possible.
The Textbook of Higher Mathematics: Learning Calculus, Integration and Differentiation in A Simple Way
Author – S.P Thompson
The Textbook of Higher Mathematics is an invaluable resource for students seeking to learn the fundamentals of calculus. It presents every aspect of calculus simply and engagingly. It encourages the reader to see and understand the subject in ways that they may never have appreciated as students before. It covers all the basic concepts of calculus, including some solid examples of physical and technical applications. It also lays the groundwork for the fundamentals of advanced courses in calculus. This text clears up all your queries related to differentiation and integration and helps you develop an ability to solve various mathematical problems by yourself.
This updated edition features an all-new table of contents, along with handy symbols and formulae for differentiation, integration, and trigonometrical functions. Kindle version, available and priced at $2.99, is one of the most economically priced e-books on calculus currently available.
Best Recreational Books on Calculus
Infinite Powers: How Calculus Reveals the Secrets of the Universe
Author – Steven Strogatz
Calculus is the miraculous force behind many of humanity’s greatest inventions and discoveries. Unfortunately, a lot of people have been intimidated by this crucial subject in high school and college. Infinite Powers: How Calculus Reveals the Secrets of the Universe is dedicated to the history of the calculus and reveals that the subject is all about simplicity rather than complexity. It aims to solve real-world problems with the help of an unreal number – infinity.
Infinite Powers offers a comprehensive account of the history of calculus, starting with its modest inception in ancient Greece and leading up to the successful prediction and discovery of gravitational waves. The author also reveals how calculus accepted the challenges posed by every age. For example, it showed us how to:
- Calculate the area of a circle using nothing but sand and a stick.
- Produce electricity by using magnets.
- Explain the phenomenon of Mars occasionally going “backward”.
- Make sure that a rocket does not miss the moon.
- Tip the odds in our favor in the battle against HIV.
Strogatz beautifully explains why calculus is the language of the universe and helps readers appreciate our natural world in a fresh new light.
Calculus Reordered: A History of the Big Ideas
Author – David M. Bressoud
In this wonderful book, David Bressoud takes readers on an epic journey through the centuries to tell the story of the evolution of modern calculus. He explains why calculus has been credited to 17th-century figures Isaac Newton and Gottfried Leibniz and how developments in the 19th century gave rise to its present structure.
Bressoud goes on to explore calculus’s birth in the Hellenistic Eastern Mediterranean and considers how the field developed in response to questions posed by astronomy and engineering. He also reveals issues with the standard ordering of calculus’s curriculum – limits, differentiation, integration, and series. He expresses that the historical order makes much more sense in the classroom environment.
Calculus Reordered explores the motivations behind the discovery of calculus is a must-read for all enthusiasts of this critical tool of mathematics.
Change Is the Only Constant: The Wisdom of Calculus in a Madcap World
Author – Ben Orlin
Ben Orlin is a well-known math blogger and author of the underground bestseller Math With Bad Drawings. In this book, Ben Orlin explores the relevance of calculus in our daily lives. With the help of 28 interesting mathematical stories, his characteristic witty humor, and charmingly bad drawings, Orlin demonstrates that calculus is just another language to express various aspects of human life, including the most important thing – change.
The book consists of two sections – “Moments” and “Eternities”, and invokes various personalities like David Foster Wallace, Mark Twain, and even Sherlock Holmes. Change Is the Only Constant is filled with interesting mathematical fables, riddles, and paradoxes that make a truly engaging and compelling read. The way it unearths connections between literature, art, calculus, and a beloved dog named Elvis is simply too good.
This is an excellent book for both math lovers and people who find themselves intimidated by math. In the case of the latter, it can help them appreciate the subject in a whole new light. It is a great work that beautifully shows how calculus, and mathematics at large, relate to our world.
Best Self-help Guides on Calculus
Quick Calculus: A Self-Teaching Guide
Author – Daniel Kleppner
Calculus is an important subject that plays a key role in the concepts of various other subjects, ranging from physics and chemistry to ecology and economics. Quick Calculus: A Self-Teaching Guide is a self-instructional guide for both students and professionals who wish to strengthen their grasp on the fundamentals of calculus. It teaches the elementary principles of differential and integral calculus smoothly and concisely.
The book offers a series of carefully chosen work problems to help you overcome your fear of the subject. Every correct answer to one of these problems leads to new material. On the other hand, incorrect answers are followed by relevant explanations and reviews. This latest edition features the use of calculators and also presents more examples and examples.
Simply speaking, there is no better guide in the mystifying realm of calculus than Quick Calculus.
The Princeton Review: AP Calculus BC Prep, 2021
Since 1981, the experts at The Princeton Review have been helping teachers, students, and parents achieve the best possible results during the process of education. The Princeton Review has been helping millions of students by providing classroom courses, tutoring, standardized tests, and various other academic services. This comprehensive study guide contains everything you need to score a perfect 5 in the AP calculus AB exam, with five full-length practice tests, targeted strategies, and access to additional online content.
The book contains tried and tested techniques that have been proven to work in the exam. They will help you identify and avoid traps and critically assess your progress during preparation. With the help of your online Student Tools, you can get access to a comprehensive list of formulas, useful pre-college information, and much more. The book has been updated to align with the latest College Board standards.
The Humongous Book of Calculus Problems
Author – W. Michael Kelley
It is widely recognized that the only way to effectively learn calculus is to practice lots of problems. That is exactly what this wonderful book is meant for, but with a notable difference. Author W. Michael Kelley is an award-winning calculus teacher, recipient of numerous awards, and the founder of calculus-help.com. In The Humongous Book of Calculus Problems, he presents the reader with:
- 1,000 problems with detailed solutions.
- Annotated notes accompanying the text, explaining what is being asked.
- Highly comprehensive answers without any missing steps.
- Additional explanations to make all concepts crystal clear.
- Pointers to other problems that deal with skills you require.
The book covers all important concepts like derivatives, continuity, limits, tangent lines, integrals, velocity, acceleration, infinite series, volume, area, and even advanced topics like formal Riemann sums and epsilon-delta proofs. It is an excellent resource for students hoping to strengthen their grasp of calculus as much as possible.
Essential Calculus: Skills Practice Workbook with Full Solutions
Author – Chris McMullen
Chris McMullen has been imparting mathematical skills to physics students for more than twenty years now. He has written this detailed workbook to share his strategies for mastering calculus with students worldwide. It includes detailed solutions to every problem and covers a wide range of crucial calculus skills, such as:
- Derivatives of polynomials
- Trigonometrical functions
- Exponentials and logarithms
- The chain rule, quotient rule, and product rule
- Second derivatives
- Finding the extreme values of a function limits
- Techniques of integration
- Definite and indefinite integrals
- Multiple integrals
This book doesn’t aim to cover each and every topic from calculus but focuses on the most crucial skills required to apply calculus to other subjects like engineering and physics.
Best Books on Practical Applications of Calculus
Introduction to Stochastic Calculus with Applications
Author – Fima C Klebaner
Stochastic calculus finds important applications in engineering, biology, and finance. This excellent book by Fima C Klebaner is aimed at readers with only a basic knowledge of calculus and probability. It aims to help them understand the theory of stochastic calculus and its applications. It is a great textbook for both graduate and advanced undergraduate students in engineering, financial mathematics, and stochastic processes. It is also an invaluable resource for researchers hoping to gain a deeper knowledge of stochastic calculus.
The book contains numerous solved examples and exercises for the benefit of students. It introduces several concepts with the help of such examples and eventually leads to a wholesome statement of the general result. It offers mathematically literate readers a quick introduction to the subject and its important applications. The authors cover most of the important models in engineering, mathematical finance, and biology in beautiful detail.
This book is a highly recommended first text on stochastic calculus for mathematicians. It can also serve as a companion to more advanced books on the subject.
Brief Applied Calculus
Author – Geoffrey B. Berresford and Andrew M. Rockett
Brief Applied Calculus introduces readers to the practical side of calculus by using relevant real-world applications. These applications are range from business and finance to topics of general interest, such as the age of the Dead Sea Scrolls, learning curves in airplane production, stock prices, lives saved by seat belts, the distance traveled by sports cars, and so on.
The book is well-known for its examples to precise and effective use of technology, graphing spreadsheets and calculator coverages along with explained examples, chapter summaries, and extra practice problems. The exercises at the end of every section are especially helpful and often use real data with citations to the original sources. These exercises are highly diverse and come in various levels of difficulty.
Calculus for Businesses and Entrepreneurs
Calculus for Business, Economics, Life Sciences, and Social Sciences
Author – Raymond Barnett, Michael Ziegler, and Karl Byleen
Calculus for Business, Economics, Life Sciences, and Social Sciences is notable for offering much deeper guidance than any other book on this subject. It comes with a range of student-friendly features to help students develop a strong grasp of the topics by themselves.
The book also lays special emphasis on prerequisite skills and applications. This latest edition, with a refreshing new design and updated applications and data, enhances the book’s aim of helping students “get the idea”.
Business Calculus Demystified
Author – Rhonda Huettenmueller
In Business Calculus Demystified, bestselling math author Rhonda Huettenmueller clarifies the processes and concepts of calculus and presents their applications in real-world business. The book allows you to learn at your own pace and builds your confidence and skill with a plethora of practice problems and detailed solutions.
Business Calculus Demystified also offers excellent explanations that make differentiation and integration much more interesting and understandable. At the end of every chapter, there are multiple-choice quizzes and a “final exam” to help you test your overall understanding of business calculus.
This book is a great resource for mastering this essential math subject in an engaging and entertaining manner.
Before you go
So these were the 20 best calculus books used and loved by thousands of students. As I said, you should buy only a set of books. But if you have a budget and want to give your career (or your children’s careers, if you are a guardian) a little push, you can try buying at least my favorite books on calculus, which are:
Combine these with Princeton’s Companion to Mathematics and you are good to go.
Wait, this is not it. I have also collected a set of free ebooks on Calculus. These ebooks are legally free to download and use. While these free books may not be as effective as the paid ones, these are still worth checking out.
Have a question? I reply each and every comment.
Last update on 2021-09-20 using Amazon Product Advertising API