A Preview of Calculus
Ch 1: Functions and Models
Ch 1: Introduction
1.1: Four Ways to Represent a Function
1.1: Exercises
1.2: Mathematical Models: A Catalog of Essential Functions
1.2: Exercises
1.3: New Functions from Old Functions
1.3: Exercises
1.4: Exponential Functions
1.4: Exercises
1.5: Inverse Functions and Logarithms
1.5: Exercises
Ch 1: Review
Principles of Problem Solving

Ch 2: Limits and Derivatives
Ch 2: Introduction
2.1: The Tangent and Velocity Problems
2.1: Exercises
2.2: The Limit of a Function
2.2: Exercises
2.3: Calculating Limits Using the Limit Laws
2.3: Exercises
2.4: The Precise Definition of a Limit
2.4: Exercises
2.5: Continuity
2.5: Exercises
2.6: Limits at Infinity; Horizontal Asymptotes
2.6: Exercises
2.7: Derivatives and Rates of Change
2.7: Exercises
2.8: The Derivative as a Function
2.8: Exercises
Ch 2: Review
Ch 2: Problems Plus

Ch 3: Differentiation Rules
Ch 3: Introduction
3.1: Derivatives of Polynomials and Exponential Functions
3.1: Exercises
3.2: The Product and Quotient Rules
3.2: Exercises
3.3: Derivatives of Trigonometric Functions
3.3: Exercises
3.4: The Chain Rule
3.4: Exercises
3.5: Implicit Differentiation
3.5: Exercises
3.6: Derivatives of Logarithmic Functions
3.6: Exercises
3.7: Rates of Change in the Natural and Social Sciences
3.7: Exercises
3.8: Exponential Growth and Decay
3.8: Exercises
3.9: Related Rates
3.9: Exercises
3.10: Linear Approximations and Differentials
3.10: Exercises
3.11: Hyperbolic Functions
3.11: Exercises
Ch 3: Review
Ch 3: Problems Plus

Ch 4: Applications of Differentiation
Ch 4: Introduction
4.1: Maximum and Minimum Values
4.1: Exercises
4.2: The Mean Value Theorem
4.2: Exercises
4.3: How Derivatives Affect the Shape of a Graph
4.3: Exercises
4.4: Indeterminate Forms and l’Hospital’s Rule
4.4: Exercises
4.5: Summary of Curve Sketching
4.5: Exercises
4.6: Graphing with Calculus and Calculators
4.6: Exercises
4.7: Optimization Problems
4.7: Exercises
4.8: Newton’s Method
4.8: Exercises
4.9: Antiderivatives
4.9: Exercises
Ch 4: Review
Ch 4: Problems Plus

Ch 5: Integrals
Ch 5: Introduction
5.1: Areas and Distances
5.1: Exercises
5.2: The Definite Integral
5.2: Exercises
5.3: The Fundamental Theorem of Calculus
5.3: Exercises
5.4: Indefinite Integrals and the Net Change Theorem
5.4: Exercises
5.5: The Substitution Rule
5.5: Exercises
Ch 5: Review
Ch 5: Problems Plus

Ch 6: Applications of Integration
Ch 6: Introduction
6.1: Areas Between Curves
6.1: Exercises
6.2: Volumes
6.2: Exercises
6.3: Volumes by Cylindrical Shells
6.3: Exercises
6.4 Work
6.4: Exercises
6.5: Average Value of a Function
6.5: Exercises
Ch 6: Review
Ch 6: Problems Plus

Ch 7: Techniques of Integration
Ch 7: Introduction
7.1: Integration by Parts
7.1: Exercises
7.2: Trigonometric Integrals
7.2: Exercises
7.3: Trigonometric Substitution
7.3: Exercises
7.4: Integration of Rational Functions by Partial Fractions
7.4: Exercises
7.5: Strategy for Integration
7.5: Exercises
7.6: Integration Using Tables and Computer Algebra Systems
7.6: Exercises
7.7: Approximate Integration
7.7: Exercises
7.8: Improper Integrals
7.8: Exercises
Ch 7: Review
Ch 7: Problems Plus

Ch 8: Further Applications of Integration
Ch 8: Introduction
8.1: Arc Length
8.1: Exercises
8.2: Area of a Surface of Revolution
8.2: Exercises
8.3: Applications to Physics and Engineering
8.3: Exercises
8.4: Applications to Economics and Biology
8.4: Exercises
8.5: Probability
8.5: Exercises
Ch 8: Review
Ch 8: Problems Plus

Ch 9: Differential Equations
Ch 9: Introduction
9.1: Modeling with Differential Equations
9.1: Exercises
9.2: Direction Fields and Euler’s Method
9.2: Exercises
9.3: Separable Equations
9.3: Exercises
9.4: Models for Population Growth
9.4: Exercises
9.5: Linear Equations
9.5: Exercises
9.6: Predator-Prey Systems
9.6: Exercises
Ch 9: Review
Ch 9: Problems Plus

Ch 10: Parametric Equations and Polar Coordinates
Ch 10: Introduction
10.1: Curves Defined by Parametric Equations
10.1: Exercises
10.2: Calculus with Parametric Curves
10.2: Exercises
10.3: Polar Coordinates
10.3: Exercises
10.4: Areas and Lengths in Polar Coordinates
10.4: Exercises
10.5: Conic Sections
10.5: Exercises
10.6: Conic Sections in Polar Coordinates
10.6: Exercises
Ch 10: Review
Ch 10: Problems Plus

Ch 11: Infinite Sequences and Series
Ch 11: Introduction
11.1: Sequences
11.1: Exercises
11.2: Series
11.2: Exercises
11.3: The Integral Test and Estimates of Sums
11.3: Exercises
11.4: The Comparison Tests
11.4: Exercises
11.5: Alternating Series
11.5: Exercises
11.6: Absolute Convergence and the Ratio and Root Tests
11.6: Exercises
11.7: Strategy for Testing Series
11.7: Exercises
11.8: Power Series
11.8: Exercises
11.9: Representations of Functions as Power Series
11.9: Exercises
11.10: Taylor and Maclaurin Series
11.10: Exercises
11.11: Applications of Taylor Polynomials
11.11: Exercises
Ch 11: Review
Ch 11: 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: The Logarithm Defined as an Integral
Appendix H: Complex Numbers
Appendix I: Answers to Odd-Numbered Exercises
Index