## Introduction to Calculus

This ebook 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. Videos for the topics covered in the ebook, along with practice problems, exercises and quizzes, are available in the interactive Wolfram U course Introduction to Calculus.

### Contents

- 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

- Title: Introduction to Calculus
- Authors: John Clark and Devendra Kapadia
- Paperback: forthcoming
- Kindle: forthcoming
- Digital online: download free
- Publisher: Wolfram Media, Inc.
- Publication Date: April 22, 2024
- ISBN-13: 978-1-57955-091-2 (paperback)
- ISBN-13: 978-1-57955-092-9 (Kindle)
- ISBN-13: 978-1-57955-080-6 (digital online)