• 1.1 Functions and Their Graphs
• 1.2 Combining Functions; Shifting and Scaling Graphs
• 1.3 Trigonometric Functions
• 1.4 Graphing with Software

• 2.1 Rates of Change and Tangent Lines to Curves
• 2.2 Limit of a Function and Limit Laws
• 2.3 The Precise Definition of a Limit
• 2.4 One-Sided Limits
• 2.5 Continuity
• 2.6 Limits Involving Infinity; Asymptotes of Graphs

• 3.1 Tangent Lines and the Derivative at a Point
• 3.2 The Derivative as a Function
• 3.3 Differentiation Rules
• 3.4 The Derivative as a Rate of Change
• 3.5 Derivatives of Trigonometric Functions
• 3.6 The Chain Rule
• 3.7 Implicit Differentiation
• 3.8 Derivatives of Inverse Functions and Logarithms
• 3.9 Related Rates
• 3.10 Linearization and Differentials

• 4.1 Extreme Values of Functions on Closed Intervals
• 4.2 The Mean Value Theorem
• 4.3 Monotonic Functions and the First Derivative Test
• 4.4 Concavity and Curve Sketching
• 4.5 Applied Optimization
• 4.6 Newton's Method
• 4.7 Antiderivatives

• 5.1 Area and Estimating with Finite Sums
• 5.2 Sigma Notation and Limits of Finite Sums
• 5.3 The Definite Integral
• 5.4 The Fundamental Theorem of Calculus
• 5.5 Indefinite Integrals and the Substitution Method
• 5.6 Definite Integral Substitutions and the Area Between Curves

• 6.1 Volumes Using Cross-Sections
• 6.2 Volumes Using Cylindrical Shells
• 6.3 Arc Length
• 6.4 Areas of Surfaces of Revolution
• 6.5 Work and Fluid Forces
• 6.6 Moments and Centers of Mass

• 7.1 Inverse Functions and Their Derivatives
• 7.2 Natural Logarithms
• 7.3 Exponential Functions
• 7.4 Exponential Change and Separable Differential Equations
• 7.5 Indeterminate Forms and L'Hpital's Rule
• 7.6 Inverse Trigonometric Functions
• 7.7 Hyperbolic Functions
• 7.8 Relative Rates of Growth

• 8.1 Using Basic Integration Formulas
• 8.2 Integration by Parts
• 8.3 Trigonometric Integrals
• 8.4 Trigonometric Substitutions
• 8.5 Integration of Rational Functions by Partial Fractions
• 8.6 Integral Tables and Computer Algebra Systems
• 8.7 Numerical Integration
• 8.8 Improper Integrals
• 8.9 Probability

• 9.1 Solutions, Slope Fields, and Euler's Method
• 9.2 First-Order Linear Equations
• 9.3 Applications
• 9.4 Graphical Solutions of Autonomous Equations
• 9.5 Systems of Equations and Phase Planes

• 10.1 Sequences
• 10.2 Infinite Series
• 10.3 The Integral Test
• 10.4 Comparison Tests
• 10.5 Absolute Convergence; The Ratio and Root Tests
• 10.6 Alternating Series and Conditional Convergence
• 10.7 Power Series
• 10.8 Taylor and Maclaurin Series
• 10.9 Convergence of Taylor Series
• 10.10 Applications of Taylor Series

• 11.1 Parametrizations of Plane Curves
• 11.2 Calculus with Parametric Curves
• 11.3 Polar Coordinates
• 11.4 Graphing Polar Coordinate Equations
• 11.5 Areas and Lengths in Polar Coordinates
• 11.6 Conic Sections
• 11.7 Conics in Polar Coordinates

• A.1 Real Numbers and the Real Line
• A.2 Mathematical Induction
• A.3 Lines, Circles, and Parabolas
• A.4 Proofs of Limit Theorems
• A.5 Commonly Occurring Limits
• A.6 Theory of the Real Numbers
• A.7 The Distributive Law for Vector Cross Products
• A.8 The Mixed Derivative Theorem and the Increment Theorem

• B.1 Determinants
• B.2 Extreme Values and Saddle Points for Functions of More than Two Variables
• B.3 The Method of Gradient Descent

Answers to Odd-Numbered Exercises

Applications Index

Subject Index

A Brief Table of Integrals

Credits