Calculus, 3rd edition

1. Functions

• 1.1 Review of Functions
• 1.2 Representing Functions
• 1.3 Trigonometric Functions
• Review Exercises

2. Limits

• 2.1 The Idea of Limits
• 2.2 Definitions of Limits
• 2.3 Techniques for Computing Limits
• 2.4 Infinite Limits
• 2.5 Limits at Infinity
• 2.6 Continuity
• 2.7 Precise Definitions of Limits
• Review Exercises

3. Derivatives

• 3.1 Introducing the Derivative
• 3.2 The Derivative as a Function
• 3.3 Rules of Differentiation
• 3.4 The Product and Quotient Rules
• 3.5 Derivatives of Trigonometric Functions
• 3.6 Derivatives as Rates of Change
• 3.7 The Chain Rule
• 3.8 Implicit Differentiation
• 3.9 Related Rates
• Review Exercises

4. Applications of the Derivative

• 4.1 Maxima and Minima
• 4.2 Mean Value Theorem
• 4.3 What Derivatives Tell Us
• 4.4 Graphing Functions
• 4.5 Optimization Problems
• 4.6 Linear Approximation and Differentials
• 4.7 L'Hôpital's Rule
• 4.8 Newton's Method
• 4.9 Antiderivatives
• Review Exercises

5. Integration

• 5.1 Approximating Areas under Curves
• 5.2 Definite Integrals
• 5.3 Fundamental Theorem of Calculus
• 5.4 Working with Integrals
• 5.5 Substitution Rule
• Review Exercises

6. Applications of Integration

• 6.1 Velocity and Net Change
• 6.2 Regions Between Curves
• 6.3 Volume by Slicing
• 6.4 Volume by Shells
• 6.5 Length of Curves
• 6.6 Surface Area
• 6.7 Physical Applications
• Review Exercises

7. Logarithmic and Exponential Functions

• 7.1 Inverse Functions
• 7.2 The Natural Logarithmic and Exponential Functions
• 7.3 Logarithmic and Exponential Functions with Other Bases
• 7.4 Exponential Models
• 7.5 Inverse Trigonometric Functions
• 7.6 L' Hôpital's Rule and Growth Rates of Functions
• 7.7 Hyperbolic Functions
• Review Exercises

8. Integration Techniques

• 8.1 Basic Approaches
• 8.2 Integration by Parts
• 8.3 Trigonometric Integrals
• 8.4 Trigonometric Substitutions
• 8.5 Partial Fractions
• 8.6 Integration Strategies
• 8.7 Other Methods of Integration
• 8.8 Numerical Integration
• 8.9 Improper Integrals
• Review Exercises

9. Differential Equations

• 9.1 Basic Ideas
• 9.2 Direction Fields and Euler's Method
• 9.3 Separable Differential Equations
• 9.4 Special First-Order Linear Differential Equations
• 9.5 Modeling with Differential Equations
• Review Exercises

10. Sequences and Infinite Series

• 10.1 An Overview
• 10.2 Sequences
• 10.3 Infinite Series
• 10.4 The Divergence and Integral Tests
• 10.5 Comparison Tests
• 10.6 Alternating Series
• 10.7 The Ratio and Root Tests
• 10.8 Choosing a Convergence Test
• Review Exercises

11. Power Series

• 11.1 Approximating Functions with Polynomials
• 11.2 Properties of Power Series
• 11.3 Taylor Series
• 11.4 Working with Taylor Series
• Review Exercises

12. Parametric and Polar Curves

• 12.1 Parametric Equations
• 12.2 Polar Coordinates
• 12.3 Calculus in Polar Coordinates
• 12.4 Conic Sections
• Review Exercises

13. Vectors and the Geometry of Space

• 13.1 Vectors in the Plane
• 13.2 Vectors in Three Dimensions
• 13.3 Dot Products
• 13.4 Cross Products
• 13.5 Lines and Planes in Space
• 13.6 Cylinders and Quadric Surfaces
• Review Exercises

14. Vector-Valued Functions

• 14.1 Vector-Valued Functions
• 14.2 Calculus of Vector-Valued Functions
• 14.3 Motion in Space
• 14.4 Length of Curves
• 14.5 Curvature and Normal Vectors
• Review Exercises

15. Functions of Several Variables

• 15.1 Graphs and Level Curves
• 15.2 Limits and Continuity
• 15.3 Partial Derivatives
• 15.4 The Chain Rule
• 15.5 Directional Derivatives and the Gradient
• 15.6 Tangent Planes and Linear Approximation
• 15.7 Maximum/Minimum Problems
• 15.8 Lagrange Multipliers
• Review Exercises

16. Multiple Integration

• 16.1 Double Integrals over Rectangular Regions
• 16.2 Double Integrals over General Regions
• 16.3 Double Integrals in Polar Coordinates
• 16.4 Triple Integrals
• 16.5 Triple Integrals in Cylindrical and Spherical Coordinates
• 16.6 Integrals for Mass Calculations
• 16.7 Change of Variables in Multiple Integrals
• Review Exercises

17. Vector Calculus

• 17.1 Vector Fields
• 17.2 Line Integrals
• 17.3 Conservative Vector Fields
• 17.4 Green's Theorem
• 17.5 Divergence and Curl
• 17.6 Surface Integrals
• 17.7 Stokes' Theorem
• 17.8 Divergence Theorem
• Review Exercises

D2 Second-Order Differential Equations ONLINE

• D2.1 Basic Ideas
• D2.2 Linear Homogeneous Equations
• D2.3 Linear Nonhomogeneous Equations
• D2.4 Applications
• D2.5 Complex Forcing Functions
• Review Exercises

APPENDICES

• A. Proofs of Selected Theorems
• B. Algebra Review ONLINE
• C. Complex Numbers ONLINE

Answers

Index

Table of Integrals