Cover
Title
Copyright
Contents
Preface
1. Preparation for Calculus
1.1 Graphs and Models
1.2 Linear Models and Rates of Change
1.3 Functions and Their Graphs
1.4 Review of Trigonometric Functions
1.5 Inverse Functions
1.6 Exponential and Logarithmic Functions
Review Exercises
P.S. Problem Solving
2. Limits and Their Properties
2.1 A Preview of Calculus
2.2 Finding Limits Graphically and Numerically
2.3 Evaluating Limits Analytically
2.4 Continuity and One-Sided Limits
2.5 Infinite Limits
Review Exercises
P.S. Problem Solving
3. Differentiation
3.1 The Derivative and the Tangent Line Problem
3.2 Basic Differentiation Rules and Rates of Change
3.3 Product and Quotient Rules and Higher-Order Derivatives
3.4 The Chain Rule
3.5 Implicit Differentiation
3.6 Derivatives of Inverse Functions
3.7 Related Rates
3.8 Newton's Method
Review Exercises
P.S. Problem Solving
4. Applications of Differentiation
4.1 Extrema on an Interval
4.2 Rolle's Theorem and the Mean Value Theorem
4.3 Increasing and Decreasing Functions and the First Derivative Test
4.4 Concavity and the Second Derivative Test
4.5 Limits at Infinity
4.6 A Summary of Curve Sketching
4.7 Optimization Problems
4.8 Differentials
Review Exercises
P.S. Problem Solving
5. Integration
5.1 Antiderivatives and Indefinite Integration
5.2 Area
5.3 Riemann Sums and Definite Integrals
5.4 The Fundamental Theorem of Calculus
5.5 Integration by Substitution
5.6 Indeterminate Forms and L'Hopital's Rule
5.7 The Natural Logarithmic Function: Integration
5.8 Inverse Trigonometric Functions: Integration
5.9 Hyperbolic Functions
Review Exercises
P.S. Problem Solving
6. Differential Equations
6.1 Slope Fields and Euler's Method
6.2 Growth and Decay
6.3 Separation of Variables
6.4 The Logistic Equation
6.5 First-Order Linear Differential Equations
6.6 Predator-Prey Differential Equations
Review Exercises
P.S. Problem Solving
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
7.4 Arc Length and Surfaces of Revolution
7.5 Work
7.6 Moments, Centers of Mass, and Centroids
7.7 Fluid Pressure and Fluid Force
Review Exercises
P.S. Problem Solving
8. Integration Techniques and Improper Integrals
8.1 Basic Integration Rules
8.2 Integration by Parts
8.3 Trigonometric Integrals
8.4 Trigonometric Substitution
8.5 Partial Fractions
8.6 Numerical Integration
8.7 Integration by Tables and Other Integration Techniques
8.8 Improper Integrals
Review Exercises
P.S. Problem Solving
9. Infinite Series
9.1 Sequences
9.2 Series and Convergence
9.3 The Integral Test and p-Series
9.4 Comparisons of Series
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
Review Exercises
P.S. Problem Solving
10. Conics, Parametric Equations, and Polar Coordinates
10.1 Conics and Calculus
10.2 Plane Curves and Parametric Equations
10.3 Parametric Equations and Calculus
10.4 Polar Coordinates and Polar Graphs
10.5 Area and Arc Length in Polar Coordinates
10.6 Polar Equations of Conics and Kepler's Laws
Review Exercises
P.S. Problem Solving
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
11.6 Surfaces in Space
11.7 Cylindrical and Spherical Coordinates
Review Exercises
P.S. Problem Solving
12. Vector-Valued Functions
12.1 Vector-Valued Functions
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
Review Exercises
P.S. Problem Solving
13. Functions of Several Variables
13.1 Introduction to Functions of Several Variables
13.2 Limits and Continuity
13.3 Partial Derivatives
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
13.8 Extrema of Functions of Two Variables
13.9 Applications of Extrema
13.10 Lagrange Multipliers
Review Exercises
P.S. Problem Solving
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
14.5 Surface Area
14.6 Triple Integrals and Applications
14.7 Triple Integrals in Other Coordinates
14.8 Change of Variables: Jacobians
Review Exercises
P.S. Problem Solving
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
15.5 Parametric Surfaces
15.6 Surface Integrals
15.7 Divergence Theorem
15.8 Stokes's Theorem
Review Exercises
P.S. Problem Solving
Appendixes
A: Proofs of Selected Theorems
B: Integration Tables
C: Precalculus Review
Answers to Odd-Numbered Exercises
1.
1.1
1.2
1.3
1.4
1.5
1.6
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2.
2.1
2.2
2.3
2.4
2.5
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3.
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
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4.
4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8
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5.
5.1
5.2
5.3
5.4
5.5
5.6
5.7
5.8
5.9
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6.
6.1
6.2
6.3
6.4
6.5
6.6
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7.
7.1
7.2
7.3
7.4
7.5
7.6
7.7
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8.
8.1
8.2
8.3
8.4
8.5
8.6
8.7
8.8
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9.
9.1
9.2
9.3
9.4
9.5
9.6
9.7
9.8
9.9
9.10
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10.
10.1
10.2
10.3
10.4
10.5
10.6
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11.
11.1
11.2
11.3
11.4
11.5
11.6
11.7
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12.
12.1
12.2
12.3
12.4
12.5
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13.
13.1
13.2
13.3
13.4
13.5
13.6
13.7
13.8
13.9
13.10
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14.
14.1
14.2
14.3
14.4
14.5
14.6
14.7
14.8
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15.
15.1
15.2
15.3
15.4
15.5
15.6
15.7
15.8
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C.
C.1
C.2
Index
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
Index of Applications
Index of Applications (continued)
DERIVATIVES AND INTEGRALS
TRIGONOMETRY
ALGEBRA