Introduction to Calculus: A Computational Approach (Wolfram eTextbook Series)

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Introduction to Calculus provides a comprehensive introduction to fundamental concepts in calculus and their applications, covering all of Calculus 1 and some of Calculus 2. The book starts with functions and limits, followed by differential calculus, and then moves on to integral calculus and a brief discussion of differential equations. It ends with the complete solution for a sample exam based on the AP Calculus AB course. Students can access a free, interactive version of the text using a link provided inside the Kindle version. Further supplemental materials, including videos, practice problems, exercises and quizzes, are available online in the companion Wolfram U course.

From the Publisher

From the Foreword

"This book will give you a comprehensive introduction to the basic concepts of calculus along with their history and applications. It begins with functions and limits, followed by differential calculus and its applications, and then moves on to integral calculus and its applications. You will learn each concept in a traditional manner but you will also learn how to build intuition and solve real-world problems with blinding speed using the world-class functionality for doing calculus computations and visualizations in Mathematica.

Perhaps the most important feature of this approach is the ease with which you can vary any problem to gain insight into its essential features while Mathematica does the tedious calculations for you. Also, when you have finished studying this book, you will have acquired considerable expertise with using the powerful and versatile Mathematica system.

We recommend that you use this book along with the popular interactive Wolfram U course on 'Introduction to Calculus' which has already helped thousands of students all over the world including those preparing for the AP Calculus exam in the United States and others in seemingly distant places such as Nasarawa in Nigeria."

Contents

To the Student · What Is Calculus? · Functions · The Elementary Functions · The Limit of a Function · The Laws of Limits · Continuity · Derivatives and Rates of Change · The Derivative as a Function · Differentiation Formulas · Derivatives of Trigonometric Functions · The Chain Rule · Implicit Differentiation · Rates of Change in the Sciences · Related Rates · Linear Approximations · Maxima and Minima · The Mean Value Theorem · Derivatives and the Shape of Graphs · Asymptotes · Curve Sketching · Optimization · Antiderivatives · Riemann Sums · The Definite Integral · The Fundamental Theorem of Calculus · Indefinite Integrals · The Substitution Rule · Areas between Curves · Volumes of Solids · Volumes by Cylindrical Shells · Average Value of a Function · Approximate Integration · Exponential Functions · Logarithmic Functions · L'Hôpital's Rule · Slope Fields and Euler's Method · Separable Differential Equations · Calculus and Programming · Sample Calculus Exam, Part 1 · Sample Calculus Exam, Part 2

About the Authors

John Michael Clark is a mathematics PhD student at the University of Texas at Austin. He received his BSc in mathematics from the California Institute of Technology in 2016 and later his MSc from Oklahoma State University in 2020.

About the Authors

Devendra Kapadia is the Manager of Mathematical Computation at Wolfram. He has a BSc and an MSc in mathematics from the University of Mumbai, an MSc by Research in mathematics from the University of Oxford and a PhD in mathematics from the University of Pittsburgh. He is actively involved in algorithm development for Wolfram Language and in developing online mathematics courses for Wolfram U.

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Page Count
538 220 424 368 332 572

Publication Year
2024 2020 2021 2023 2020 2020

ASIN ‏ : ‎ B0DB9FC6SF
Publisher ‏ : ‎ Wolfram Media, Inc.
Accessibility ‏ : ‎ Learn more
Publication date ‏ : ‎ July 30, 2024
Edition ‏ : ‎ 1st
Language ‏ : ‎ English
File size ‏ : ‎ 12.6 MB
Enhanced typesetting ‏ : ‎ Not Enabled
X-Ray ‏ : ‎ Not Enabled
Word Wise ‏ : ‎ Not Enabled
Print length ‏ : ‎ 538 pages
Format ‏ : ‎ Print Replica
ISBN-13 ‏ : ‎ 978-1579550929
Page Flip ‏ : ‎ Not Enabled
Part of series ‏ : ‎ Wolfram eTextbook Series
Best Sellers Rank: #967,065 in Kindle Store (See Top 100 in Kindle Store) #55 in Advanced Placement Test Guides #142 in Mathematics Study & Teaching (Kindle Store) #153 in Calculus (Kindle Store)
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