Pearson eText Calculus

Contents
Preface
Credits
Chapter 1 Functions
	Chapter Opener
	1.1 Review of Functions
	1.2 Representing Functions
	1.3 Trigonometric Functions
	Review Exercises
Chapter 2 Limits
	Chapter Opener
	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
Chapter 3 Derivatives
	Chapter Opener
	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
Chapter 4 Applications of the Derivative
	Chapter Opener
	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
Chapter 5 Integration
	Chapter Opener
	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
Chapter 6 Applications of Integration
	Chapter Opener
	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
Chapter 7 Logarithmic and Exponential Functions
	Chapter Opener
	7.1 Inverse Functions
	7.2 The Natural Logarithmic and Exponential Functions
	7.3 Logarithimic 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
Chapter 8 Integration Techniques
	Chapter Opener
	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
Chapter 9 Differential Equations
	Chapter Opener
	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
Chapter 10 Sequences and Infinite Series
	Chapter Opener
	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
Chapter 11 Power Series
	Chapter Opener
	11.1 Approximating Functions with Polynomials
	11.2 Properties of Power Series
	11.3 Taylor Series
	11.4 Working with Taylor Series
	Review Exercises
Chapter 12 Parametric and Polar Curves
	Chapter Opener
	12.1 Parametric Equations
	12.2 Polar Coordinates
	12.3 Calculus in Polar Coordinates
	12.4 Conic Sections
	Review Exercises
Chapter 13 Vectors and the Geometry of Space
	Chapter Opener
	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
Chapter 14 Vector-Valued Functions
	Chapter Opener
	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
Chapter 15 Functions of Several Variables
	Chapter Opener
	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
Chapter 16 Multiple Integration
	Chapter Opener
	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
Chapter 17 Vector Calculus
	Chapter Opener
	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
Chapter D2 Second-Order Differential Equations
	Chapter Opener
	D2.1 Basic Ideas
	D2.2 Linear Homogeneous Equations
	D2.3 Linear Nonhomogeneous Equations
	D2.4 Applications
	D2.5 Complex Forcing Functions
	Review Exercises
Appendix A  Proofs of Selected Theorems
Appendix B  Algebra Review
Appendix C  Complex Numbers
Answers
Index
Index of Applications
Table of Integrals