Calculus : Early Transcendental Functions - 4th edition

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 Fitting Models to Data
1.5 Inverse Functions
1.6 Exponential and Logarithmic Functions

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
Section Project: Graphs and Limits of Trig Functions

3. Differentiation

3.1 The Derivative and the Tangent Line Problem
3.2 Basic Differentiation Rules and Rates of Change
3.3 The Product and Quotient Rules and Higher-Order Derivatives
3.4 The Chain Rule
3.5 Implicit Differentiation
Section Project: Optical Illusions
3.6 Derivatives of Inverse Functions
3.7 Related Rates
3.8 Newton's Method

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
Section Project: Rainbows
4.4 Concavity and the Second Derivative Test
4.5 Limits at Infinity
4.6 A Summary of Curve Sketching
4.7 Optimization Problems
Section Project: Connecticut River
4.8 Differentials

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
Section Project: Demonstrating the Fundamental Theorem
5.5 Integration by Substitution
5.6 Numerical Integration
5.7 The Natural Logarithmic Function: Integration
5.8 Inverse Trigonometric Functions: Integration
5.9 Hyperbolic Functions
Section Project: St. Louis Arch

6. Differential Equations

6.1 Slope Fields and Euler's Method
6.4 Differential Equations: Growth and Decay
6.5 Differential Equations: Separation of Variables
6.4 The Logistic Equation
6.5 First-Order Linear Differential Equations
Section Project: Weight Loss
6.6 Predator-Prey Differential Equations

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

8. Integration Techniques, L'Hôpital's Rule, 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 Integration by Tables and Other Integration Techniques
8.7 Indeterminate Forms and L'Hôpital's Rule
8.8 Improper Integrals

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

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

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

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

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 of Functions of Two Variables
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
14.5 Surface Area
14.6 Triple Integrals and Applications
14.7 Triple Integrals in Cylindrical and Spherical Coordinates
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
15.5 Parametric Surfaces
15.6 Surface Integrals
15.7 Divergence Theorem
15.8 Stoke's Theorem

Appendices

Appendix A Proofs of Selected Theorems
Appendix B Integration Tables
Appendix C Business and Economic Applications
Additional Appendices
The following appendices are available at the textbook website, on the HM mathSpace Student CD-ROM, and the HM ClassPrep with HM Testing CD-ROM:
Appendix D Precalculus Review
Appendix E Rotation and the General Second-Degree Equation
Appendix F Complex Numbers