Have you just gotten into calculus? Are you looking for the best calculus books that you should start with? well, when i was your age, i tried out various books from the library, borrowed books from friends, and bought over a dozen on amazon. but not all the books were effective and most of these just wasted my time. reviewing too many books can be detrimental. therefore, you should stick to only a fixed amount of resources.
Combined with my own experience and the latest trends in the study of calculus, I have compiled and listed 20 of the best calculus books to get you started.
You are reading: Best books on calculus
These books are available on amazon and can be classified into 6 sections. the first 4 books (1-4) are essential calculus textbooks. these are essential because all college or university study programs can be covered by these books.
The following 5 calculus books (5-9) are best for students just starting out with calculus. books #10 to #12 are related to the history and applications of calculus to life in general. these are great if you’re up for becoming a calculus teacher one day or just want to surprise your classmates with some random facts.
Other books are self-help guides with a pedagogical approach and practical problems, followed by books on applied calculus.
The last two of the best calculus books are for students with an entrepreneurial mindset. read these books to learn and understand how you could use calculus in business and marketing.
Most of these books also have kindle® versions available. some of the books are available in audible format, which can be used for free with this 30-day trial with 2 free audiobooks.
So, let’s start with the list of the best calculus books in 2022.
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 a professor of mathematics at mcmaster university. Calculus: Transcendental Firsts, with its exact and precise writing supplemented with real-world examples, is a worldwide bestseller.
In this book, Stewart helps you develop a strong understanding of calculus while also allowing you to appreciate the intrinsic beauty of the subject. With the help of the relevant examples and learning aids incorporated in this text, he will gain confidence in this field of mathematics and achieve success in his goals.
thomas calculus: first transcendentals
author: george thomas jr., maurice weir and joel hass
Thomas Calculus: Transcendental Firsts has been one of the most popular books on calculus for more than half a century. 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, with the goal of helping readers develop technical proficiency. Co-authors Maurice Weir and Joel Hass have done an admirable job of improving the text, keeping in mind the ambitions and readiness of contemporary students.
calculus of 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 strong and effective pedagogy, which successfully addresses the requirements of a wide range of teaching and learning styles, has received widespread praise from a generation of students and teachers alike.
The book is packed with excellent explanations and exercises, presented in a comprehensive and professional manner. you can also see detailed solutions for the strange exercises on the book’s companion website.
Calculus by Ron Larson and Bruce Edwards is worth the fairly high price tag and is an ideal addition to various professional calculus courses at universities.
calculus: an intuitive and physical approach
author – morris kline
Calculus: An Intuitive and Physical Approach is widely regarded as one of the best calculus texts available today. Morris Kline takes an intuitive approach through geometry to explain topics that would otherwise appear to be abstract mathematics. parallel to the development of the “how” of the mathematical tools, it also quickly shows you the “why”. the book encourages him to think mathematically and to make connections between new content and what he already knows.
The author presents detailed explorations of the derivative, theorems on differentiation and antidifferentiation, the differentiation and integration of powers of x, the chain rule, and tests of trigonometric functions, polar coordinates, and much more. encourages the student to solve problems without resorting to memorizing formulas. he also goes to great lengths to show how each mathematical technique is also relevant in real life.
This book is a highly recommended and invaluable resource for all calculus students.
the 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 students have ever taken. however, this impression is quite misleading. Calculus Lifesaver offers a wide range of useful tools for students to not only learn calculus, but also perform exceptionally well at it. is an easy-to-use guide with quality study notes that have been shown to work. is an excellent addition 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 and, at the same time, complete. develops standard course material with several relevant examples that help students develop problem-solving skills. These examples are of various levels of difficulty and illustrate the in-depth presentation of theoretical concepts. This book is highly recommended for anyone who wants to master the fundamentals of calculus.
simplified calculation
author – silvanus p. thompson and martin gardner
First published in 1910 in England, calculus made easy has long been one of the most popular calculus publications around. now it has been transformed into a contemporary masterpiece that deftly explains the beautiful concepts of calculus in a user-friendly way. Silvano P. Thompson stated almost 90 years ago that once the reader has understood the basics of differentiation and integration, the rest of the calculus will follow naturally. his triumphant success is attested to by the continued popularity of the simplified calculus over the years.
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In the first major revision of this book, Martin Gardner updated the text following recent developments in terminology and method. she added a full preface, three new introductory chapters, and 20 additional practice problems. This book, which has sold more than a million copies worldwide, will replace her apprehension of calculation with curiosity, levity, and delight. It is especially recommended for students of calculus with an interest in the history of the subject.
precalculus for beginners
author – mary jane sterling
Calculus is a required course for many college majors. Unfortunately, students who do not have a strong foundation in math may find it quite challenging. To solve this problem, one needs to recognize calculus for what it is: just a tool for studying how variables interact with each other. Precalculus For Dummies is an easy-to-use book that has been written to make calculus manageable for these students.
This book simplifies differentiation and integration into easier concepts and helps the reader build a stronger foundation with a deep understanding of the core ideas involved. includes foundations in trigonometry, algebra, and precalculus, and explores series, sequences, and common graphing functions in detail. also shows you how to approximate an area using integration.
After following the appropriate instructions and practical examples in the text, you will gain the confidence and skills to master this topic. precalculus for dummies shows you the path to success and provides the resources you need to embark on your journey.
calculus in 5 hours: concepts revealed, so you don’t have to spend a semester of lectures
author – dennis jarecke
many students struggle to finish their first calculus course. the most popular introductory textbooks reach up to 1,000 pages, making it even more difficult for them to grasp the subject. Calculus in 5 hours, on the other hand, can help you build confidence in calculus in about 124 pages. What most people don’t realize is that too much detail can hurt beginners’ learning. This book serves as a simple guide to help you understand the basics thoroughly.
You will find Calculus in 5 Hours to be a worthy companion no matter what calculus course you are enrolled in. is a great resource to refresh your knowledge on the subject. With the help of simple examples and drawings, it helps you organize your understanding of calculus for homework and exams. it covers almost 75% of a first semester course and omits material that is not strictly necessary.
calculus in 5 hours is an excellent book to reinforce your concepts and achieve your goals as quickly as possible.
The Higher Mathematics Textbook: Learning Calculus, Integration, and Differentiation the Easy Way
author – s.p thompson
The Higher Mathematics Textbook is an invaluable resource for students looking to learn the fundamentals of calculus. presents all aspects of calculus in a simple and attractive way. it encourages the reader to see and understand the subject in ways they may never have appreciated before as a student. covers all the basics of calculus, including some solid examples of physical and technical applications. it also lays the groundwork for the foundations of advanced calculus courses. this text clarifies all your queries related to differentiation and integration and helps you develop the ability to solve various mathematical problems by yourself.
This updated edition features a completely new table of contents, along with useful symbols and formulas for differentiation, integration, and trigonometric functions. The Kindle version, available for $2.99, is one of the cheapest calculus e-books available today.
best recreational books on calculus
infinite powers: how calculation reveals the secrets of the universe
author – steven strogatz
Calculus is the miraculous force behind many of mankind’s greatest inventions and discoveries. Unfortunately, many people have been intimidated by this crucial topic in high school and college. Infinite Powers: How Calculus Reveals the Secrets of the Universe is dedicated to the history of calculus and reveals that the theme is all about simplicity rather than complexity. your goal is to solve real-world problems with the help of an unreal number: infinity.
Infinite Powers offers a comprehensive account of the history of calculus, beginning with its modest beginnings in ancient Greece and continuing to the successful prediction and discovery of gravitational waves. the author also reveals how the calculus accepted the challenges posed by each era. for example, he showed us how to:
- calculate the area of a circle using nothing more than sand and a stick.
- produce electricity using magnets.
- explain the phenomenon of mars occasionally going “towards back” .
- make sure a rocket doesn’t miss the moon.
- tilt 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.
reordered calculus: a history of great 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 the 17th-century figures Isaac Newton and Gottfried Leibniz and how 19th-century developments gave rise to its current structure.
Bressoud continues to explore the birth of calculus in the Hellenistic Eastern Mediterranean and considers how the field developed in response to questions raised by astronomy and engineering. he also reveals problems with the standard ordering of the calculus curriculum: limits, differentiation, integration, and series. he expresses that the historical order makes much more sense in the classroom setting.
Calculus Reordered explores the motivations behind the discovery of calculus and is a must-read for all enthusiasts of this fundamental tool of mathematics.
change is the only constant: the wisdom of calculation in a crazy world
author – ben orlin
ben orlin is a well known math blogger and author of the underground bestseller math with bad pictures. In this book, Ben Orlin explores the relevance of calculus to our daily lives. With the help of 28 engaging math stories, his trademark witty humor, and his charmingly mean drawings, Orlin proves that calculus is just another language for expressing various aspects of human life, including the most important one: change.
The book consists of two sections: “moments” and “eternities”, and invokes various personalities such as david foster wallace, mark twain and even sherlock holmes. Change is the only constant is full of interesting math fables, riddles, and paradoxes that make for a truly engaging and compelling read. the way he discovers the connections between literature, art, calculus, and a beloved dog named elvis is just too good.
This is an excellent book for both math lovers and people who are intimidated by math. in the case of the latter, it can help them appreciate the subject in a whole new light. is a great piece of work that beautifully shows how calculus and mathematics in general relate to our world.
best self-help guides on calculus
quick calculus: a self-study guide
author – daniel kleppner
Calculus is an important subject that plays a key role in the concepts of several other subjects, ranging from physics and chemistry to ecology and economics. Quick Calculus: A Self-Study Guide is a self-study guide for students and professionals who want to strengthen their understanding of the fundamentals of calculus. teaches the elementary principles of differential and integral calculus in a fluent and concise manner.
The book offers a series of carefully selected work problems to help you overcome your fear of the subject. each correct answer to one of these problems leads to new material. on the other hand, incorrect answers are followed by relevant explanations and revisions. this latest edition introduces the use of calculators and also introduces more examples and examples.
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In a nutshell, there is no better guide in the bewildering realm of calculus than quick calculus.
princeton review: calculus bc ap prep, 2021
since 1981, the experts at princeton review have been helping teachers, students, and parents achieve the best possible results during the educational process. The Princeton Review has been helping millions of students by providing face-to-face courses, tutoring, standardized tests, and various other academic services. This comprehensive study guide contains everything you need to earn a perfect 5 on the AP Calculus AB Exam, with five comprehensive practice tests, specific strategies, and access to additional online content.
The book contains tried and tested techniques that have proven effective on the exam. they will help you identify and avoid pitfalls and critically assess your progress during preparation. With the help of their online student tools, you can get access to a full list of formulas, helpful pre-college information, and much more. the book has been updated to align with the latest university board standards.
the gigantic book of calculus problems
author – w. miguel kelley
It is widely recognized that the only way to learn calculus effectively is to practice lots of problems. that is exactly what this wonderful book is intended for, but with one notable difference. author w. Michael Kelley is an award-winning calculus teacher and founder of calculus-help.com. in the gigantic book of calculus problems, he introduces the reader:
- 1000 problems with detailed solutions.
- annotated notes that accompany the text, explaining what is asked.
- very complete answers without missing any steps.
- additional explanations to clarify all concepts.
- pointers to other problems related to the skills you need.
The book covers all the 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. is an excellent resource for students hoping to strengthen their understanding of calculus as much as possible.
Essential Calculus: Skills Practice Workbook with Complete Solutions
author – chris mcmullen
chris mcmullen has been teaching math to physics students for over twenty years. She has written this detailed workbook to share her strategies for mastering calculus with students around the world. includes detailed solutions to each problem and covers a wide range of crucial calculus skills, such as:
- derivatives of polynomials
- trigonometric functions
- exponentials and logarithms
- chain rule, quotient rule and product rule
- second derivative
- finding the extreme values of the limits of a function
- integration techniques
- definite and indefinite integrals
- multiple integrals
This book does not claim to cover every topic in calculus, but instead focuses on the most crucial skills needed to apply calculus to other subjects such as 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 intended for readers with a basic understanding of calculus and probability. its goal is to help them understand the theory of stochastic calculus and its applications. is an excellent textbook for both graduate students and advanced undergraduates in engineering, financial mathematics, and stochastic processes. it is also an invaluable resource for researchers hoping to gain a deeper understanding of stochastic calculus.
The book contains numerous worked examples and exercises for the benefit of students. it introduces various concepts with the help of such examples and finally leads to a complete statement of the general result. provides mathematically literate readers with a quick introduction to the subject and its important applications. the authors cover most of the important models in engineering, math 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 complement to more advanced books on the subject.
brief calculus applied
author – geoffrey b. Berresford and Andrew M. rocket
Brief Applied Calculus introduces readers to the practical side of calculus through the use of relevant real-world applications. These applications range from business and finance to topics of general interest, such as the age of the Dead Sea Scrolls, learning curves in aircraft production, stock prices, lives saved by seat belts, distance toured by sports cars, etc.
The book is well known for its examples of accurate and effective use of technology, graphical spreadsheets, and calculator coverage along with explained examples, chapter summaries, and additional practice problems. the exercises at the end of each section are particularly helpful and often use actual data with citations to the original sources. These exercises are very diverse and come in various levels of difficulty.
calculation for companies 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 excels in offering much more in-depth guidance than any other book on this topic. comes with a range of easy-to-use features to help students develop a strong understanding of the topics on their own.
The book also places special emphasis on prior skills and applications. This latest edition, with a refreshing new design and updated applications and data, enhances the book’s goal of helping students “get the idea.”
business calculation demystified
author – rhonda huettenmueller
In Business Calculus Demystified, best-selling math author Rhonda Huettenmueller clarifies the processes and concepts of calculus and introduces its applications in real-world business. The book allows her to learn at her own pace and builds her confidence and skill with a plethora of practical problems and detailed solutions.
business calculation demystified also offers excellent explanations that make differentiation and integration much more interesting and understandable. At the end of each chapter, there are multiple-choice quizzes and a “final exam” to help you test your general understanding of business calculus.
This book is a great resource for mastering this essential math subject in an engaging and entertaining way.
before you leave
so these were the top 20 calculus books used and loved by thousands of students. as I said, you should buy only one set of books. but if you have a budget and want to give your career (or your children’s, if you are a tutor) a little boost, you can try to buy at least my favorite calculus books, which are:
combine them with princeton’s companion to math and voila.
wait, this is not all. I have also compiled a set of free e-books on calculus. These ebooks are legally free to download and use. while these free books may not be as effective as the paid ones, they are worth checking out.
Do you have any questions? I reply to each and every comment.
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