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

P.S. Problem Solving
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
P.S. Problem Solving
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

P.S. Problem Solving
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

P.S. Problem Solving
4. Integration

4.1 Antiderivatives and Indefinite Integration
4.2 Area
4.3 Reimann 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

P.S. Problem Solving
5. Logarithmic, Exponential, and Other Transcendental Functions

5.1 The Natural Logarithmic Function and Differentiation
5.2 The Natural Logarithmic Function and 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 Differential Equations: Growth and Decay
5.7 Differential Equations: Separation of Variables
5.8 Inverse Trigonometric Functions and Differentiation
5.9 Inverse Trigonometric Functions and Integration
5.10 Hyperbolic Functions

Section Project: St. Louis Arch
P.S. Problem Solving
6. Applications of Integration

6.1 Area of a Region Between Two Curves
6.2 Volume: The Disc Method
6.3 Volume: The Shell Method

Section Project: Saturn's Oblateness

6.4 Arc Length and Surfaces of Revolution
6.5 Work

Section Project: Tidal Energy

6.6 Moments, Centers of Mass, and Centroids
6.7 Fluid Pressure and Fluid Force

P.S. Problem Solving
7. Integration Techniques, L'Hôpital's Rule, and Improper Integrals

7.1 Basic Integration Rules
7.2 Integration by Parts
7.3 Trigonometric Integrals

Section Project: Power Lines

7.4 Trigonometric Substitution
7.5 Partial Fractions
7.6 Integration by Tables and Other Integration Techniques
7.7 Indeterminant Forms and L'Hôpital's Rule
7.8 Improper Integrals

P.S. Problem Solving
8. Infinite Series

8.1 Sequences
8.2 Series and Convergence

Section Project: Cantor's Disappearing Table

8.3 The Integral Test and p-Series

Section Project: The Harmonic Series

8.4 Comparisons of Series

Section Project: Solera Method

8.5 Alternating Series
8.6 The Ratio and Root Tests
8.7 Taylor Polynomials and Approximations
8.8 Power Series
8.9 Representation of Functions by Power Series
8.10 Taylor and Maclaurin Series

P.S. Problem Solving
9. Conics, Parametric Equations, and Polar Coordinates

9.1 Conics and Calculus
9.2 Plane Curves and Parametric Equations

Section Project

9.3 Parametric Equations and Calculus
9.4 Polar Coordinates and Polar Graphs

Section Project

9.5 Area and Arc Length in Polar Coordinates
9.6 Polar Equations of Conics and Kepler's Laws

P.S. Problem Solving