To the Instructor
To the Student
P Preliminaries
1 Lines
2 Functions and Graphs
3 Exponential Functions
4 Inverse Functions and Logarithms
5 Trigonometric Functions and Their Inverses
6 Parametric Equations
7 Modeling Change
QUESTIONS TO GUIDE YOUR REVIEW
PRACTICE EXERCISES
ADDITIONAL EXERCISES: THEORY， EXAMPLES， APPLICATIONS

1 Limits and Continuity
1.1 Rates of Change and Limits _ _
1.2 Finding Limits and One-Sided Limits
1.3 Limits Involving Infinity
1.4 Continuity
1.5 Tangent Lines
QUESTIONS TO GUIDE YOUR REVIEW
PRACTICE EXERCISES
ADDITIONAL EXERCISES: THEORY， EXAMPLES， APPLICATIONS

2 Derivatives
2.1 The Derivative as a Function
2.2 The Derivative as a Rate of Change
2.3 Derivatives of Products， Quotients， and Negative Powers
2.4 Derivatives of Trigonometric Functions
2.5 The Chain Ruleand Parametric Equations
2.6 Implicit Differentiation
2.7 Related Rates
QUESTIONS TO GUIDE YOUR REVIEW
PRACTICE EXERCISES
ADDITIONAL EXERCISES: THEORY， EXAMPLES， APPLICATIONS

3 Applications of Derivatives
3.1 Extreme Values of Functions
3.2 The Mean Value Theorem and Differential Equations
3.3 The Shape of a Graph
3.4 Graphical Solutions of Autonomous Differential Equations
3.5 Modeling and Optimization
3.6 Linearization and Differentials
3.7 Newtons Method
QUESTIONS TO GUIDE YOUR REVIEW
PRACTICE EXERCISES
ADDITIONAL EXERCISES: THEORY， EXAMPLES， APPLICATIONS

4 Integration
4.1 Indefinite Integrals， Differential Equations， and Modeling
4.2 Integral Rules; Integration by Substitution
4.3 Estimating with Finite Sums
4.4 Riemann Sumsand Definite Integrals
4.5 The Mean Value and Fundamental Theorems
4.6 Substitution in Definite Integrals
4.7 Numerical Integration
QUESTIONS TO GUIDE YOUR REVIEW
PRACTICE EXERCISES
ADDITIONAL EXERCISES: THEORY， EXAMPLES， APPLICATIONS

5 Applications of Integrals
5.1 Volumes by Slicing and Rotation About an Axis
5.2 Modeling Volume Using Cylindrical Shells
5.3 Lengths of Plane Curves
5.4 Springs， Pumping， and Lifting
……

6 Transcendental Functions and Differential Equations
7 Integration Techniques， LHopitals Rule and Improper Integrals
8 Infinite Series
9 Vectors in the Plane and Polar Functions
10 Vectors and motion in Space
11 Multivariable Functions and Their Derivatives
12 Multiple Integrals
13 Integration in Vector Fields
Appendices
Answers
Index
A Brief Table of Integrals