- Chapter P: Preparation for Calculus
- Section P.1: Graphs and Models
- Section P.2: Linear Models and Rates of Change
- Section P.3: Functions and Their Graphs
- Section P.4: Review of Trigonometric Functions

- Chapter 1: Limits and Their Properties
- Section 1.1: A Preview of Calculus
- Section 1.2: Finding Limits Graphically and Numerically
- Section 1.3: Evaluating Limits Analytically
- Section 1.4: Continuity and One-Sided Limits
- Section 1.5: Infinite Limits

- Chapter 2: Differentiation
- Section 2.1: The Derivative and the Tangent Line Problem
- Section 2.2: Basic Differentiation Rules and Rates of Change
- Section 2.3: Product and Quotient Rules and Higher-Order Derivatives
- Section 2.4: The Chain Rule
- Section 2.5: Implicit Differentiation
- Section 2.6: Related Rates

- Chapter 3: Applications of Differentiation
- Section 3.1: Extrema on an Interval
- Section 3.2: Rolle's Theorem and the Mean Value Theorem
- Section 3.3: Increasing and Decreasing Functions and the First Derivative Test
- Section 3.4: Concavity and the Second Derivative Test
- Section 3.5: Limits at Infinity
- Section 3.6: A Summary of Curve Sketching
- Section 3.7: Optimization Problems
- Section 3.8: Newton's Method
- Section 3.9: Differentials

- Chapter 4: Integration
- Section 4.1: Antiderivatives and Indefinite Integration
- Section 4.2: Area
- Section 4.3: Riemann Sums and Definite Integrals
- Section 4.4: The Fundamental Theorem of Calculus
- Section 4.5: Integration by Substitution

- Chapter 5: Logarithmic, Exponential, and Other Transcendental Functions
- Section 5.1: The Natural Logarithmic Function: Differentiation
- Section 5.2: The Natural Logarithmic Function: Integration
- Section 5.3: Inverse Functions
- Section 5.4: Exponential Functions: Differentiation and Integration
- Section 5.5: Bases Other than
*e*and Applications - Section 5.6: Indeterminate Forms and L'Hopital's Rule
- Section 5.7: Inverse Trigonometric Functions: Differentiation
- Section 5.8: Inverse Trigonometric Functions: Integration
- Section 5.9: Hyperbolic Functions

- Chapter 6: Differential Equations
- Section 6.1: Slope Fields and Euler's Method
- Section 6.2: Growth and Decay
- Section 6.3: Separation of Variables and the Logistic Equation
- Section 6.4: First-Order Linear Differential Equations

- Chapter 7: Applications of Integration
- Section 7.1: Area of a Region Between Two Curves
- Section 7.2: Volume: The Disk Method
- Section 7.3: Volume: The Shell Method
- Section 7.4: Arc Length and Surfaces of Revolution
- Section 7.5: Work
- Section 7.6: Moments, Centers of Mass, and Centroids
- Section 7.7: Fluid Pressure and Fluid Force

- Chapter 8: Integration Techniques and Improper Integrals
- Section 8.1: Basic Integration Rules
- Section 8.2: Integration by Parts
- Section 8.3: Trigonometric Integrals
- Section 8.4: Trigonometric Substitution
- Section 8.5: Partial Fractions
- Section 8.6: Numerical Integration
- Section 8.7: Integration by Tables and Other Integration Techniques
- Section 8.8: Improper Integrals

- Chapter 9: Infinite Series
- Section 9.1: Sequences
- Section 9.2: Series and Convergence
- Section 9.3: The Integral Test and
*p*-Series - Section 9.4: Comparisons of Series
- Section 9.5: Alternating Series
- Section 9.6: The Ratio and Root Tests
- Section 9.7: Taylor Polynomials and Approximations
- Section 9.8: Power Series
- Section 9.9: Representation of Functions by Power Series
- Section 9.10: Taylor and Maclaurin Series

- Chapter 10: Conics, Parametric Equations, and Polar Coordinates
- Section 10.1: Conics and Calculus
- Section 10.2: Plane Curves and Parametric Equations
- Section 10.3: Parametric Equations and Calculus
- Section 10.4: Polar Coordinates and Polar Graphs
- Section 10.5: Area and Arc Length in Polar Coordinates
- Section 10.6: Polar Equations of Conics and Kepler's Laws

- Chapter 11: Vectors and the Geometry of Space
- Section 11.1: Vectors in the Plane
- Section 11.2: Space Coordinates and Vectors in Space
- Section 11.3: The Dot Product of Two Vectors
- Section 11.4: The Cross Product of Two Vectors in Space
- Section 11.5: Lines and Planes in Space
- Section 11.6: Surfaces in Space
- Section 11.7: Cylindrical and Spherical Coordinates

- Chapter 12: Vector-Valued Functions
- Section 12.1: Vector-Valued Functions
- Section 12.2: Differentiation and Integration of Vector-Valued Functions
- Section 12.3: Velocity and Acceleration
- Section 12.4: Tangent Vectors and Normal Vectors
- Section 12.5: Arc Length and Curvature

- Chapter 13: Functions of Several Variables
- Section 13.1: Introduction to Functions of Several Variables
- Section 13.2: Limits and Continuity
- Section 13.3: Partial Derivatives
- Section 13.4: Differentials
- Section 13.5: Chain Rules for Functions of Several Variables
- Section 13.6: Directional Derivatives and Gradients
- Section 13.7: Tangent Planes and Normal Lines
- Section 13.8: Extrema of Functions of Two Variables
- Section 13.9: Applications of Extrema
- Section 13.10: Lagrange Multipliers

- Chapter 14: Multiple Integration
- Section 14.1: Iterated Integrals and Area in the Plane
- Section 14.2: Double Integrals and Volume
- Section 14.3: Change of Variables: Polar Coordinates
- Section 14.4: Center of Mass and Moments of Inertia
- Section 14.5: Surface Area
- Section 14.6: Triple Integrals and Applications
- Section 14.7: Triple Integrals in Other Coordinates
- Section 14.8: Change of Variables: Jacobians

- Chapter 15: Vector Analysis
- Section 15.1: Vector Fields
- Section 15.2: Line Integrals
- Section 15.3: Conservative Vector Fields and Independence of Path
- Section 15.4: Green's Theorem
- Section 15.5: Parametric Surfaces
- Section 15.6: Surface Integrals
- Section 15.7: Divergence Theorem
- Section 15.8: Stokes's Theorem

- Chapter 16: Additional Topics in Differential Equations
- Section 16.1: Exact First-Order Equations
- Section 16.2: Second-Order Homogeneous Linear Equations
- Section 16.3: Second-Order Nonhomogeneous Linear Equations
- Section 16.4: Series Solutions of Differential Equations

Exercises P.1.1 -