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Preface

Introduction

1 Introduction

1.1 Review of Functions

1.2 Basic Classes of Functions

1.3 Trigonometric Functions

1.4 Inverse Functions

1.5 Exponential and Logarithmic Functions

Chapter 1 Review Exercises

2 Introduction

2.1 A Preview of Calculus

2.2 The Limit of a Function

2.3 The Limit Laws

2.4 Continuity

2.5 The Precise Definition of a Limit

2.6 Limits at Infinity and Asymptotes

Chapter 2 Review Exercises

3 Introduction

3.1 Defining the Derivative

3.2 The Derivative as a Function

3.3 Differentiation Rules

3.4 Derivatives as Rates of Change

3.5 Derivatives of Trigonometric Functions

3.6 The Chain Rule

3.7 Derivatives of Inverse Functions

3.8 Implicit Differentiation

3.9 Derivatives of Exponential and Logarithmic Functions

Chapter 3 Review Exercises

4 Introduction

4.1 Related Rates

4.2 Linear Approximations and Differentials

4.3 Maxima and Minima

4.4 The Mean Value Theorem

4.5 Derivatives and the Shape of a Graph

4.6 Curve Sketching

4.7 Applied Optimization Problems

4.8 L’Hôpital’s Rule

4.9 Newton’s Method

4.10 Antiderivatives

Chapter 4 Review Exercises

5 Introduction

5.1 Approximating Areas

5.2 The Definite Integral

5.3 The Fundamental Theorem of Calculus

5.4 Integration Formulas and the Net Change Theorem

5.5 Substitution

5.6 Integrals Involving Exponential and Logarithmic Functions

5.7 Integrals Resulting in Inverse Trigonometric Functions

Chapter 5 Review Exercises

Appendix

Table of Integrals

Table of Derivatives

Review of Pre-Calculus

This is where you can write your introduction.

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Calculus Volume 1 by OSCRiceUniversity is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, except where otherwise noted.