Chapter 0: Preliminaries
0.1 Polynomials and Rational Functions
0.2 Graphing Calculators and Computer Algebra Systems
0.3 Inverse Functions
0.4 Trigonometric and Inverse Trigonometric Functions
0.5 Exponential and Logarithmic Functions
0.6 Transformations of Functions
Chapter 1: Limits and Continuity
1.1 A Brief Preview of Calculus: Tangent Lines and the Length of a Curve
1.2 The Concept of Limit
1.3 Computation of Limits
1.4 Continuity and Its Consequences
1.5 Limits Involving Infinity; Asymptotes
1.6 Formal Definition of the Limit
1.7 Limits and Loss-of-Significance Errors
Chapter 2: Differentiation
2.1 Tangent Lines and Velocity
2.2 The Derivative
2.3 Computation of Derivatives: The Power Rule
2.4 The Product and Quotient Rules
2.5 The Chain Rule
2.6 Derivatives of Trigonometric Functions
2.7 Derivatives of Exponential and Logarithmic Functions
2.8 Implicit Differentiation and Inverse Trigonometric Functions
2.9 The Hyperbolic Functions
2.10 The Mean Value Theorem
Chapter 3: Applications of the Derivative
3.1 Linear Approximations and Newton's Method
3.2 Indeterminate Forms and L'Hôpital's Rule
3.3 Maximum and Minimum Values
3.4 Increasing and Decreasing Functions
3.5 Concavity and the Second Derivative Test
3.6 Overview of Curve Sketching
3.7 Optimization
3.8 Related Rates
3.9 Rates of Change in Economics and the Sciences
Chapter 4: Integration
4.1 Antiderivatives
4.2 Sums and Sigma Notation
4.3 Area
4.4 The Definite Integral
4.5 The Fundamental Theorem of Calculus
4.6 Integration by Substitution
4.7 Numerical Integration
4.8 The Natural Logarithm as an Integral
Chapter 5: Applications of the Definite Integral
5.1 Area Between Curves
5.2 Volume: Slicing, Disks and Washers
5.3 Volumes by Cylindrical Shells
5.4 Arc Length and Surface Area
5.5 Projectile Motion
5.6 Applications of Integration to Physics and Engineering
5.7 Probability
Chapter 6: Integration Techniques
6.1 Review of Formulas and Techniques
6.2 Integration by Parts
6.3 Trigonometric Techniques of Integration
6.4 Integration of Rational Functions Using Partial Fractions
6.5 Integration Tables and Computer Algebra Systems
6.6 Improper Integrals
Chapter 7: First-Order Differential Equations
7.1 Modeling with Differential Equations
7.2 Separable Differential Equations
7.3 Direction Fields and Euler's Method
7.4 Systems of First-Order Differential Equations
Chapter 8: Infinite Series
8.1 Sequences of Real Numbers
8.2 Infinite Series
8.3 The Integral and Comparison Tests
8.4 Alternating Series
8.5 Absolute Convergence and the Ratio Test
8.6 Power Series
8.7 Taylor Series
8.8 Applications of Taylor Series
8.9 Fourier Series
Chapter 9: Parametric Equations and Polar Coordinates
9.1 Plane Curves and Parametric Equations
9.2 Calculus and Parametric Equations
9.3 Arc Length and Surface Area in Parametric Equations
9.4 Polar Coordinates
9.5 Calculus and Polar Coordinates
9.6 Conic Sections
9.7 Conic Sections in Polar Coordinates
Chapter 10: Vectors and the Geometry of Space
10.1 Vectors in the Plane
10.2 Vectors in Space
10.3 The Dot Product
10.4 The Cross Product
10.5 Lines and Planes in Space
10.6 Surfaces in Space
Chapter 11: Vector-Valued Functions
11.1 Vector-Valued Functions
11.2 The Calculus of Vector-Valued Functions
11.3 Motion in Space
11.4 Curvature
11.5 Tangent and Normal Vectors
11.6 Parametric Surfaces
Chapter 12: Functions of Several Variables and Partial Differentiation
12.1 Functions of Several Variables
12.2 Limits and Continuity
12.3 Partial Derivatives
12.4 Tangent Planes and Linear Approximations
12.5 The Chain Rule
12.6 The Gradient and Directional Derivatives
12.7 Extrema of Functions of Several Variables
12.8 Constrained Optimization and and Lagrange Multipliers
Chapter 13: Multiple Integrals
13.1 Double Integrals
13.2 Area, Volume and Center of Mass
13.3 Double Integrals in Polar Coordinates
13.4 Surface Area
13.5 Triple Integrals
13.6 Cylindrical Coordinates
13.7 Spherical Coordinates
13.8 Change of Variables in Multiple Integrals
Chapter 14: Vector Calculus
14.1 Vector Fields
14.2 Line Integrals
14.3 Independence of Path and Conservative Vector Fields
14.4 Green's Theorem
14.5 Curl and Divergence
14.6 Surface Integrals
14.7 The Divergence Theorem
14.8 Stokes' Theorem
14.9 Applications of Vector Calculus
Chapter 15: Second Order Differential Equations
15.1 Second-Order Equations With Constant Coefficients
15.2 Nonhomogeneous Equations: Undetermined Coefficients
15.3 Applications of Second-Order Equations
15.4 Power Series Solutions of Differential Equations
Appendix A: Proofs of Selected Theorems
Appendix B: Answers to Odd-Numbered Exercises
