• Before Starting Integral Calculus

Table of Contents

1. Functions and Models

1.1 Four Ways to Represent a Function
1.2 Mathematical Models: A Catalog of Essential Functions
1.3 New Functions from Old Functions
1.4 Graphing Calculators and Computers
1.5 Exponential Functions
1.6 Inverse Functions and Logarithms

2. Limits and Derivatives

2.1 The Tangent and Velocity Problems
2.2 The Limit of a Function
2.3 Calculating Limits Using the Limit Laws
2.4 The Precise Definition of a Limit
2.5 Continuity
2.6 Limits at Infinity; Horizontal Asymptotes
2.7 Derivatives and Rates of Change
2.8 The Derivative as a Function

3. Differentiation Rules

3.1 Derivatives of Polynomials and Exponential Functions
3.2 The Product and Quotient Rules
3.3 Derivatives of Trigonometric Functions
3.4 The Chain Rule
3.5 Implicit Differentiation
3.6 Derivatives of Logarithmic Functions
3.7 Rates of Change in the Natural and Social Sciences
3.8 Exponential Growth and Decay
3.9 Related Rates
3.10 Linear Approximations and Differentials
3.11 Hyperbolic Functions

4. Applications of Differentiation

4.1 Maximum and Minimum Values
4.2 The Mean Value Theorem
4.3 How Derivatives Affect the Shape of a Graph
4.4 Indeterminate Forms and L’Hôpital’s Rule
4.5 Summary of Curve Sketching
4.6 Graphing with Calculus and Calculators
4.7 Optimization Problems
4.8 Newton’s Method
4.9 Antiderivatives