Calculus

Cover
Contents
Preface
A Tribute to James Stewart
About the Authors
Technology in the Ninth Edition
To the Student
Diagnostic Tests
A Preview of Calculus
Chapter 1: Functions and Limits
	1.1 Four Ways to Represent a Function
	1.2 Mathematical Models: A Catalog of Essential Functions
	1.3 New Functions from Old Functions
	1.4 The Tangent and Velocity Problems
	1.5 The Limit of a Function
	1.6 Calculating Limits Using the Limit Laws
	1.7 The Precise Definition of a Limit
	1.8 Continuity
	1 Review
	Principles of Problem Solving
Chapter 2: Derivatives
	2.1 Derivatives and Rates of Change
	2.2 The Derivative as a Function
	2.3 Differentiation Formulas
	2.4 Derivatives of Trigonometric Functions
	2.5 The Chain Rule
	2.6 Implicit Differentiation
	2.7 Rates of Change in the Natural and Social Sciences
	2.8 Related Rates
	2.9 Linear Approximations and Differentials
	2 Review
	Problems Plus
Chapter 3: Applications of Differentiation
	3.1 Maximum and Minimum Values
	3.2 The Mean Value Theorem
	3.3 What Derivatives Tell Us about the Shape of a Graph
	3.4 Limits at Infinity; Horizontal Asymptotes
	3.5 Summary of Curve Sketching
	3.6 Graphing with Calculus and Technology
	3.7 Optimization Problems
	3.8 Newton's Method
	3.9 Antiderivatives
	3 Review
	Problems Plus
Chapter 4: Integrals
	4.1 The Area and Distance Problems
	4.2 The Definite Integral
	4.3 The Fundamental Theorem of Calculus
	4.4 Indefinite Integrals and the Net Change Theorem
	4.5 The Substitution Rule
	4 Review
	Problems Plus
Chapter 5: Applications of Integration
	5.1 Areas between Curves
	5.2 Volumes
	5.3 Volumes by Cylindrical Shells
	5.4 Work
	5.5 Average Value of a Function
	5 Review
	Problems Plus
Chapter 6: Inverse Functions: Exponential, Logarithmic, and Inverse Trigonometric Functions
	6.1 Inverse Functions and Their Derivatives
	6.2 Exponential Functions and Their Derivatives
	6.3 Logarithmic Functions
	6.4 Derivatives of Logarithmic Functions
	6.2* The Natural Logarithmic Function
	6.3* The Natural Exponential Function
	6.4* General Logarithmic and Exponential Functions
	6.5 Exponential Growth and Decay
	6.6 Inverse Trigonometric Functions
	6.7 Hyperbolic Functions
	6.8 Indeterminate Forms and l’Hospital's Rule
	6 Review
	Problems Plus
Chapter 7: Techniques of Integration
	7.1 Integration by Parts
	7.2 Trigonometric Integrals
	7.3 Trigonometric Substitution
	7.4 Integration of Rational Functions by Partial Fractions
	7.5 Strategy for Integration
	7.6 Integration Using Tables and Technology
	7.7 Approximate Integration
	7.8 Improper Integrals
	7 Review
	Problems Plus
Chapter 8: Further Applications of Integration
	8.1 Arc Length
	8.2 Area of a Surface of Revolution
	8.3 Applications to Physics and Engineering
	8.4 Applications to Economics and Biology
	8.5 Probability
	8 Review
	Problems Plus
Chapter 9: Differential Equations
	9.1 Modeling with Differential Equations
	9.2 Direction Fields and Euler's Method
	9.3 Separable Equations
	9.4 Models for Population Growth
	9.5 Linear Equations
	9.6 Predator-Prey Systems
	9 Review
	Problems Plus
Chapter 10: Parametric Equations and Polar Coordinates
	10.1 Curves Defined by Parametric Equations
	10.2 Calculus with Parametric Curves
	10.3 Polar Coordinates
	10.4 Calculus in Polar Coordinates
	10.5 Conic Sections
	10.6 Conic Sections in Polar Coordinates
	10 Review
	Problems Plus
Chapter 11: Sequences, Series, and Power Series
	11.1 Sequences
	11.2 Series
	11.3 The Integral Test and Estimates of Sums
	11.4 The Comparison Tests
	11.5 Alternating Series and Absolute Convergence
	11.6 The Ratio and Root Tests
	11.7 Strategy for Testing Series
	11.8 Power Series
	11.9 Representations of Functions as Power Series
	11.10 Taylor and Maclaurin Series
	11.11 Applications of Taylor Polynomials
	11 Review
	Problems Plus
Chapter 12: Vectors and the Geometry of Space
	12.1 Three-Dimensional Coordinate Systems
	12.2 Vectors
	12.3 The Dot Product
	12.4 The Cross Product
	12.5 Equations of Lines and Planes
	12.6 Cylinders and Quadric Surfaces
	12 Review
	Problems Plus
Chapter 13: Vector Functions
	13.1 Vector Functions and Space Curves
	13.2 Derivatives and Integrals of Vector Functions
	13.3 Arc Length and Curvature
	13.4 Motion in Space: Velocity and Acceleration
	13 Review
	Problems Plus
Chapter 14: Partial Derivatives
	14.1 Functions of Several Variables
	14.2 Limits and Continuity
	14.3 Partial Derivatives
	14.4 Tangent Planes and Linear Approximations
	14.5 The Chain Rule
	14.6 Directional Derivatives and the Gradient Vector
	14.7 Maximum and Minimum Values
	14.8 Lagrange Multipliers
	14 Review
	Problems Plus
Chapter 15: Multiple Integrals
	15.1 Double Integrals over Rectangles
	15.2 Double Integrals over General Regions
	15.3 Double Integrals in Polar Coordinates
	15.4 Applications of Double Integrals
	15.5 Surface Area
	15.6 Triple Integrals
	15.7 Triple Integrals in Cylindrical Coordinates
	15.8 Triple Integrals in Spherical Coordinates
	15.9 Change of Variables in Multiple Integrals
	15 Review
	Problems Plus
Chapter 16: Vector Calculus
	16.1 Vector Fields
	16.2 Line Integrals
	16.3 The Fundamental Theorem for Line Integrals
	16.4 Green's Theorem
	16.5 Curl and Divergence
	16.6 Parametric Surfaces and Their Areas
	16.7 Surface Integrals
	16.8 Stokes' Theorem
	16.9 The Divergence Theorem
	16.10 Summary
	16 Review
	Problems Plus
Appendixes
	Appendix A: Numbers, Inequalities, and Absolute Values
	Appendix B: Coordinate Geometry and Lines
	Appendix C: Graphs of Second-Degree Equations
	Appendix D: Trigonometry
	Appendix E: Sigma Notation
	Appendix F: Proofs of Theorems
	Appendix G: Answers to Odd-Numbered Exercises