Table of Contents

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CHAPTER ONE: PREREQUISITES FOR CALCULUS

* 1.1 Lines
* 1.2 Functions and Graphs
* 1.3 Exponential Functions
* 1.4 Parametric Equations
* 1.5 Functions and Logarithms
* 1.6 Trigonometric Functions
* Chapter 1 Key Terms
* Chapter 1 Review Exercises

CHAPTER TWO: LIMITS AND CONTINUITY

* 2.1 Rates of Change and Limits
* 2.2 Limits Involving Infinity
* 2.3 Continuity
* 2.4 Rates of Change and Tangent Lines
* Chapter 2 Key Terms
* Chapter 2 Review Exercises

CHAPTER THREE: DERIVATIVES

* 3.1 Derivative of a Function
* 3.2 Differentiability
* 3.3 Rules for Differentiation
* 3.4 Velocity and Other Rates of Change
* 3.5 Derivatives of Trigonometric Functions
* 3.6 Chain Rule
* 3.7 Implicit Differentiation
* 3.8 Derivatives of Inverse Trigonometric Functions
* 3.9 Derivatives of Exponential and Logarithmic Functions
* Chapter 3 Key Terms
* Chapter 3 Review Exercises

CHAPTER FOUR: APPLICATIONS OF DERIVATIVES

* 4.1 Extreme Values of Functions
* 4.2 Mean Value Theorem
* 4.3 Connecting and with the Graph of
* 4.4 Modeling and Optimization
* 4.5 Linearization and Newton's Method
* 4.6 Related Rates
* Chapter 4 Key Terms
* Chapter 4 Review Exercises

CHAPTER FIVE: THE DEFINITE INTEGRAL
* 5.1 Estimating with Finite Sums
* 5.2 Definite Integrals
* 5.3 Definite Integrals and Antiderivatives
* 5.4 Fundamental Theorem of Calculus
* 5.5 Trapezoidal Rule
* Chapter 5 Key Terms
* Chapter 5 Review Exercises

CHAPTER SIX: DIFFERENTIAL EQUATIONS AND MATHEMATICAL MODELING

* 6.1 Slope Fields and Euler's Method
* 6.2 Antidifferentiation by Substitution
* 6.3 Antidifferentiation by Parts
* 6.4 Exponential Growth and Decay
* 6.5 Logistic Growth
* Chapter 6 Key Terms
* Chapter 6 Review Exercises

CHAPTER SEVEN: APPLICATIONS OF DEFINITE INTEGRALS

* 7.1 Integral as Net Change
* 7.2 Areas in the Plane
* 7.3 Volumes
* 7.4 Lengths of Curves
* 7.5 Applications from Science and Statistics
* Chapter 7 Key Terms
* Chapter 7 Review Exercises

CHAPTER EIGHT: SEQUENCES, L'HÔPITAL'S RULE, AND IMPROPER INTEGRALS

* 8.1 Sequences
* 8.2 L'Hôpital's Rule
* 8.3 Relative Rates of Growth
* 8.4 Improper Integrals
* Chapter 8 Key Terms
* Chapter 8 Review Exercises

CHAPTER NINE: INFINITE SERIES

    * 9.1 Power Series
    * 9.2 Taylor Series
    * 9.3 Taylor's Theorem
    * 9.4 Radius of Convergence
    * 9.5 Testing Convergence at Endpoints
    * Chapter 9 Key Terms
    * Chapter 9 Review Exercises

CHAPTER TEN: PARAMETRIC, VECTOR, AND POLAR FUNCTIONS

    * 10.1 Parametric Functions
    * 10.2 Vectors in the Plane
    * 10.3 Polar Functions
    * Chapter 10 Key Terms
    * Chapter 10 Review Exercises