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Note: Each chapter includes Review Exercises and Problem Solving.
P. Preparation for Calculus
P.1 Graphs and Models
P.2 Linear Models and Rates of Change
P.3 Functions and Their Graphs
P.4 Fitting Models to Data
1. Limits and Their Properties
1.1 A Preview of Calculus
1.2 Finding Limits Graphically and Numerically
1.3 Evaluating Limits Analytically
1.4 Continuity and One-Sided Limits
1.5 Infinite Limits
Section Project: Graphs and Limits of Trigonometric Functions
2. Differentiation
2.1 The Derivative and the Tangent Line Problem
2.2 Basic Differentiation Rules and Rates of Change
2.3 The Product and Quotient Rules and Higher-Order Derivatives
2.4 The Chain Rule
2.5 Implicit Differentiation
Section Project: Optical Illusions
2.6 Related Rates
3. Applications of Differentiation
3.1 Extrema on an Interval
3.2 Rolle's Theorem and the Mean Value Theorem
3.3 Increasing and Decreasing Functions and the First Derivative Test
Section Project: Rainbows
3.4 Concavity and the Second Derivative Test
3.5 Limits at Infinity
3.6 A Summary of Curve Sketching
3.7 Optimization Problems
Section Project: Connecticut River
3.8 Newton's Method
3.9 Differentials
4. Integration
4.1 Antiderivatives and Indefinite Integration
4.2 Area
4.3 Riemann Sums and Definite Integrals
4.4 The Fundamental Theorem of Calculus
Section Project: Demonstrating the Fundamental Theorem
4.5 Integration by Substitution
4.6 Numerical Integration
5. Logarithmic, Exponential, and Other Transcendental Functions
5.1 The Natural Logarithmic Function: Differentiation
5.2 The Natural Logarithmic Function: Integration
5.3 Inverse Functions
5.4 Exponential Functions: Differentiation and Integration
5.5 Bases Other than e and Applications
Section Project: Using Graphing Utilities to Estimate Slope
5.6 Inverse Trigonometric Functions: Differentiation
5.7 Inverse Trigonometric Functions: Integration
5.8 Hyperbolic Functions
Section Project: St. Louis Arch
6. Differential Equations
6.1 Slope Fields and Euler's Method
6.2 Differential Equations: Growth and Decay
6.3 Separation of Variables and the Logistic Equation
6.4 First-Order Linear Differential Equations
Section Project: Weight Loss
7. Applications of Integration
7.1 Area of a Region Between Two Curves
7.2 Volume: The Disk Method
7.3 Volume: The Shell Method
Section Project: Saturn
7.4 Arc Length and Surfaces of Revolution
7.5 Work
Section Project: Tidal Energy
7.6 Moments, Centers of Mass, and Centroids
7.7 Fluid Pressure and Fluid Force
8. Integration Techniques, L'Hopital's Rule, and Improper Integrals
8.1 Basic Integration Rules
8.2 Integration by Parts
8.3 Trigonometric Integrals
Section Project: Power Lines
8.4 Trigonometric Substitution
8.5 Partial Fractions
8.6 Integration by Tables and Other Integration Techniques
8.7 Indeterminate Forms and L'Hopital's Rule
8.8 Improper Integrals
9. Infinite Series
9.1 Sequences
9.2 Series and Convergence
Section Project: Cantor's Disappearing Table
9.3 The Integral Test and p-Series
Section Project: The Harmonic Series
9.4 Comparisons of Series
Section Project: Solera Method
9.5 Alternating Series
9.6 The Ratio and Root Tests
9.7 Taylor Polynomials and Approximations
9.8 Power Series
9.9 Representation of Functions by Power Series
9.10 Taylor and Maclaurin Series
10. Conics, Parametric Equations, and Polar Coordinates
10.1 Conics and Calculus
10.2 Plane Curves and Parametric Equations
Section Project: Cycloids
10.3 Parametric Equations and Calculus
10.4 Polar Coordinates and Polar Graphs
Section Project: Anamorphic Art
10.5 Area and Arc Length in Polar Coordinates
10.6 Polar Equations of Conics and Kepler's Laws
11. Vectors and the Geometry of Space
11.1 Vectors in the Plane
11.2 Space Coordinates and Vectors in Space
11.3 The Dot Product of Two Vectors
11.4 The Cross Product of Two Vectors in Space
11.5 Lines and Planes in Space
Section Project: Distances in Space
11.6 Surfaces in Space
11.7 Cylindrical and Spherical Coordinates
12. Vector-Valued Functions
12.1 Vector-Valued Functions
Section Project: Witch of Agnesi
12.2 Differentiation and Integration of Vector-Valued Functions
12.3 Velocity and Acceleration
12.4 Tangent Vectors and Normal Vectors
12.5 Arc Length and Curvature
13. Functions of Several Variables
13.1 Introduction to Functions of Several Variables
13.2 Limits and Continuity
13.3 Partial Derivatives
Section Project: Moiré Fringes
13.4 Differentials
13.5 Chain Rules for Functions of Several Variables
13.6 Directional Derivatives and Gradients
13.7 Tangent Planes and Normal Lines
Section Project: Wildflowers
13.8 Extrema of Functions of Two Variables
13.9 Applications of Extrema of Functions of Two Variables
Section Project: Building a Pipeline
13.10 Lagrange Multipliers
14. Multiple Integration
14.1 Iterated Integrals and Area in the Plane
14.2 Double Integrals and Volume
14.3 Change of Variables: Polar Coordinates
14.4 Center of Mass and Moments of Inertia
Section Project: Center of Pressure on a Sail
14.5 Surface Area
Section Project: Capillary Action
14.6 Triple Integrals and Applications
14.7 Triple Integrals in Cylindrical and Spherical Coordinates
Section Project: Wrinkled and Bumpy Spheres
14.8 Change of Variables: Jacobians
15. Vector Analysis
15.1 Vector Fields
15.2 Line Integrals
15.3 Conservative Vector Fields and Independence of Path
15.4 Green's Theorem
Section Project: Hyperbolic and Trigonometric Functions
15.5 Parametric Surfaces
15.6 Surface Integrals
Section Project: Hyperboloid of One Sheet
15.7 Divergence Theorem
15.8 Stokes's Theorem
Section Project: The Planimeter
Appendix
A. Proofs of Selected Theorems
B. Integration Tables
C. Additional Topics in Differential Equations (Web Only)
C.1 Exact First-Order Equations
C.2 Second-Order Homogeneous Linear Equations
C.3 Second-Order Nonhomogeneous Linear Equations
C.4 Series Solutions of Differential Equations
D. Precalculus Review (Web Only)
D.1 Real Numbers and the Real Number Line
D.2 The Cartesian Plane
D.3 Review of Trigonometric Functions
E. Rotation and the General Second-Degree Equation (Web Only)
F. Complex Numbers (Web Only)
G. Business and Economic Applications (Web Only)
Other Editions for Calculus - Text Only
Table of Contents
Note: Each chapter includes Review Exercises and Problem Solving.
P. Preparation for Calculus
P.1 Graphs and Models
P.2 Linear Models and Rates of Change
P.3 Functions and Their Graphs
P.4 Fitting Models to Data
1. Limits and Their Properties
1.1 A Preview of Calculus
1.2 Finding Limits Graphically and Numerically
1.3 Evaluating Limits Analytically
1.4 Continuity and One-Sided Limits
1.5 Infinite Limits
Section Project: Graphs and Limits of Trigonometric Functions
2. Differentiation
2.1 The Derivative and the Tangent Line Problem
2.2 Basic Differentiation Rules and Rates of Change
2.3 The Product and Quotient Rules and Higher-Order Derivatives
2.4 The Chain Rule
2.5 Implicit Differentiation
Section Project: Optical Illusions
2.6 Related Rates
3. Applications of Differentiation
3.1 Extrema on an Interval
3.2 Rolle's Theorem and the Mean Value Theorem
3.3 Increasing and Decreasing Functions and the First Derivative Test
Section Project: Rainbows
3.4 Concavity and the Second Derivative Test
3.5 Limits at Infinity
3.6 A Summary of Curve Sketching
3.7 Optimization Problems
Section Project: Connecticut River
3.8 Newton's Method
3.9 Differentials
4. Integration
4.1 Antiderivatives and Indefinite Integration
4.2 Area
4.3 Riemann Sums and Definite Integrals
4.4 The Fundamental Theorem of Calculus
Section Project: Demonstrating the Fundamental Theorem
4.5 Integration by Substitution
4.6 Numerical Integration
5. Logarithmic, Exponential, and Other Transcendental Functions
5.1 The Natural Logarithmic Function: Differentiation
5.2 The Natural Logarithmic Function: Integration
5.3 Inverse Functions
5.4 Exponential Functions: Differentiation and Integration
5.5 Bases Other than e and Applications
Section Project: Using Graphing Utilities to Estimate Slope
5.6 Inverse Trigonometric Functions: Differentiation
5.7 Inverse Trigonometric Functions: Integration
5.8 Hyperbolic Functions
Section Project: St. Louis Arch
6. Differential Equations
6.1 Slope Fields and Euler's Method
6.2 Differential Equations: Growth and Decay
6.3 Separation of Variables and the Logistic Equation
6.4 First-Order Linear Differential Equations
Section Project: Weight Loss
7. Applications of Integration
7.1 Area of a Region Between Two Curves
7.2 Volume: The Disk Method
7.3 Volume: The Shell Method
Section Project: Saturn
7.4 Arc Length and Surfaces of Revolution
7.5 Work
Section Project: Tidal Energy
7.6 Moments, Centers of Mass, and Centroids
7.7 Fluid Pressure and Fluid Force
8. Integration Techniques, L'Hopital's Rule, and Improper Integrals
8.1 Basic Integration Rules
8.2 Integration by Parts
8.3 Trigonometric Integrals
Section Project: Power Lines
8.4 Trigonometric Substitution
8.5 Partial Fractions
8.6 Integration by Tables and Other Integration Techniques
8.7 Indeterminate Forms and L'Hopital's Rule
8.8 Improper Integrals
9. Infinite Series
9.1 Sequences
9.2 Series and Convergence
Section Project: Cantor's Disappearing Table
9.3 The Integral Test and p-Series
Section Project: The Harmonic Series
9.4 Comparisons of Series
Section Project: Solera Method
9.5 Alternating Series
9.6 The Ratio and Root Tests
9.7 Taylor Polynomials and Approximations
9.8 Power Series
9.9 Representation of Functions by Power Series
9.10 Taylor and Maclaurin Series
10. Conics, Parametric Equations, and Polar Coordinates
10.1 Conics and Calculus
10.2 Plane Curves and Parametric Equations
Section Project: Cycloids
10.3 Parametric Equations and Calculus
10.4 Polar Coordinates and Polar Graphs
Section Project: Anamorphic Art
10.5 Area and Arc Length in Polar Coordinates
10.6 Polar Equations of Conics and Kepler's Laws
11. Vectors and the Geometry of Space
11.1 Vectors in the Plane
11.2 Space Coordinates and Vectors in Space
11.3 The Dot Product of Two Vectors
11.4 The Cross Product of Two Vectors in Space
11.5 Lines and Planes in Space
Section Project: Distances in Space
11.6 Surfaces in Space
11.7 Cylindrical and Spherical Coordinates
12. Vector-Valued Functions
12.1 Vector-Valued Functions
Section Project: Witch of Agnesi
12.2 Differentiation and Integration of Vector-Valued Functions
12.3 Velocity and Acceleration
12.4 Tangent Vectors and Normal Vectors
12.5 Arc Length and Curvature
13. Functions of Several Variables
13.1 Introduction to Functions of Several Variables
13.2 Limits and Continuity
13.3 Partial Derivatives
Section Project: Moiré Fringes
13.4 Differentials
13.5 Chain Rules for Functions of Several Variables
13.6 Directional Derivatives and Gradients
13.7 Tangent Planes and Normal Lines
Section Project: Wildflowers
13.8 Extrema of Functions of Two Variables
13.9 Applications of Extrema of Functions of Two Variables
Section Project: Building a Pipeline
13.10 Lagrange Multipliers
14. Multiple Integration
14.1 Iterated Integrals and Area in the Plane
14.2 Double Integrals and Volume
14.3 Change of Variables: Polar Coordinates
14.4 Center of Mass and Moments of Inertia
Section Project: Center of Pressure on a Sail
14.5 Surface Area
Section Project: Capillary Action
14.6 Triple Integrals and Applications
14.7 Triple Integrals in Cylindrical and Spherical Coordinates
Section Project: Wrinkled and Bumpy Spheres
14.8 Change of Variables: Jacobians
15. Vector Analysis
15.1 Vector Fields
15.2 Line Integrals
15.3 Conservative Vector Fields and Independence of Path
15.4 Green's Theorem
Section Project: Hyperbolic and Trigonometric Functions
15.5 Parametric Surfaces
15.6 Surface Integrals
Section Project: Hyperboloid of One Sheet
15.7 Divergence Theorem
15.8 Stokes's Theorem
Section Project: The Planimeter
Appendix
A. Proofs of Selected Theorems
B. Integration Tables
C. Additional Topics in Differential Equations (Web Only)
C.1 Exact First-Order Equations
C.2 Second-Order Homogeneous Linear Equations
C.3 Second-Order Nonhomogeneous Linear Equations
C.4 Series Solutions of Differential Equations
D. Precalculus Review (Web Only)
D.1 Real Numbers and the Real Number Line
D.2 The Cartesian Plane
D.3 Review of Trigonometric Functions
E. Rotation and the General Second-Degree Equation (Web Only)
F. Complex Numbers (Web Only)
G. Business and Economic Applications (Web Only)
Other Editions for Calculus - Text Only