Chapter 1 Functions
1.1 Functions and Graphs
1.2 Combining Functions
1.3 Polynomial and Rational Functions
1.4 Transcendental Functions
1.5 Inverse Functions
1.6 Exponential and Logarithmic Functions
1.7 From Words to Functions
Chapter 1 in Review
Chapter 2 Limit of a Function
2.1 Limits—An Informal Approach
2.2 Limit Theorems
2.3 Continuity
2.4 Trigonometric Limits
2.5 Limits That Involve Infinity
2.6 Limits—A Formal Approach
2.7 The Tangent Line Problem
Chapter 2 in Review
Chapter 3 The Derivative
3.1 The Derivative
3.2 Power and Sum Rules
3.3 Product and Quotient Rules
3.4 Trigonometric Functions
3.5 Chain Rule
3.6 Implicit Differentiation
3.7 Derivatives of Inverse Functions
3.8 Exponential Functions
3.9 Logarithmic Functions
3.10 Hyperbolic Functions
Chapter 3 in Review
Chapter 4 Applications of the Derivative
4.1 Rectilinear Motion
4.2 Related Rates
4.3 Extrema of Functions
4.4 Mean Value Theorem
4.5 Limits Revisited—L’Hôpital’s Rule
4.6 Graphing and the First Derivative
4.7 Graphing and the Second Derivative
4.8 Optimization
4.9 Linearization and Differentials
4.10 Newton’s Method
Chapter 4 in Review
Chapter 5 Integrals
5.1 The Indefinite Integral
5.2 Integration by the u-Substitution
5.3 The Area Problem
5.4 The Definite Integral
5.5 Fundamental Theorem of Calculus
Chapter 5 in Review
Chapter 6 Applications of the Integral
6.1 Rectilinear Motion Revisited
6.2 Area Revisited
6.3 Volumes of Solids: Slicing Method
6.4 Volumes of Solids: Shell Method
6.5 Length of a Graph
6.6 Area of a Surface of Revolution
6.7 Average Value of a Function
6.8 Work
6.9 Liquid Pressure and Force
6.10 Centers of Mass and Centroids
Chapter 6 in Review
Chapter 7 Techniques of Integration
7.1 Integration—Three Resources
7.2 Integration by Substitution
7.3 Integration by Parts
7.4 Powers of Trigonometric Functions
7.5 Trigonometric Substitutions
7.6 Partial Fractions
7.7 Improper Integrals
7.8 Approximate Integration
Chapter 7 in Review
Chapter 8 First-Order Differential Equations
8.1 Separable Equations
8.2 Linear Equations
8.3 Mathematical Models
8.4 Solution Curves without a Solution
8.5 Euler’s Method
Chapter 8 in Review
Chapter 9 Sequences and Series
9.1 Sequences
9.2 Monotonic Sequences
9.3 Series
9.4 Integral Test
9.5 Comparison Tests
9.6 Ratio and Root Tests
9.7 Alternating Series
9.8 Power Series
9.9 Representing Functions by Power Series
9.10 Taylor Series
9.11 Binomial Series
Chapter 9 in Review
Chapter 10 Conics and Polar Coordinates
10.1 Conic Sections
10.2 Parametric Equations
10.3 Calculus and Parametric Equations
10.4 Polar Coordinate System
10.5 Graphs of Polar Equations
10.6 Calculus in Polar Coordinates
10.7 Conic Sections in Polar Coordinates
Chapter 10 in Review
Appendix
Proofs of Selected Theorems
Answers to Test Yourself
Answers to Selected Odd-Numbered Problems
Index
Resource Pages:
Review of Algebra
Formulas from Geometry
Graphs and Functions
Review of Trigonometry
Exponential and Logarithmic Functions
Differentiation
Integration Formulas