- Chapter 1: Functions
- Section 1.1: Review of Functions
- Section 1.2: Representing Functions
- Section 1.3: Inverse, Exponential, and Logarithmic Functions
- Section 1.4: Trigonometric Functions and Their Inverses

- Chapter 2: Limits
- Section 2.1: The Idea of Limits
- Section 2.2: Definitions of Limits
- Section 2.3: Techniques for Computing Limits
- Section 2.4: Infinite Limits
- Section 2.5: Limits at Infinity
- Section 2.6: Continuity
- Section 2.7: Precise Definitions of Limits

- Chapter 3: Derivatives
- Section 3.1: Introducing the Derivative
- Section 3.2: The Derivative as a Function
- Section 3.3: Rules of Differentiation
- Section 3.4: The Product and Quotient Rules
- Section 3.5: Derivatives of Trigonometric Functions
- Section 3.6: Derivatives as Rates of Change
- Section 3.7: The Chain Rule
- Section 3.8: Implicit Differentiation
- Section 3.9: Derivatives of Logarithmic and Exponential Functions
- Section 3.10: Derivatives of Inverse Trigonometric Functions
- Section 3.11: Related Rates

- Chapter 4: Applications of the Derivative
- Section 4.1: Maxima and Minima
- Section 4.2: Mean Value Theorem
- Section 4.3: What Derivatives Tell Us
- Section 4.4: Graphing Functions
- Section 4.5: Optimization Problems
- Section 4.6: Linear Approximation and Differentials
- Section 4.7: L'Hopital's Rule
- Section 4.8: Newton's Method
- Section 4.9: Antiderivatives

- Chapter 5: Integration
- Section 5.1: Approximating Areas under Curves
- Section 5.2: Definite Integrals
- Section 5.3: Fundamental Theorem of Calculus
- Section 5.4: Working with Integrals
- Section 5.5: Substitution Rule

- Chapter 6: Applications of Integration
- Section 6.1: Velocity and Net Change
- Section 6.2: Regions Between Curves
- Section 6.3: Volume by Slicing
- Section 6.4: Volume by Shells
- Section 6.5: Length of Curves
- Section 6.6: Surface Area
- Section 6.7: Physical Applications

- Chapter 7: Logarithmic, Exponential, and Hyperbolic Functions
- Section 7.1: Logarithmic and Exponential Functions Revisited
- Section 7.2: Exponential Models
- Section 7.3: Hyperbolic Functions

- Chapter 8: Integration Techniques
- Section 8.1: Basic Approaches
- Section 8.2: Integration by Parts
- Section 8.3: Trigonometric Integrals
- Section 8.4: Trigonometric Substitutions
- Section 8.5: Partial Fractions
- Section 8.6: Integration Strategies
- Section 8.7: Other Methods of Integration
- Section 8.8: Numerical Integration
- Section 8.9: Improper Integrals

- Chapter 9: Differential Equations
- Section 9.1: Basic Ideas
- Section 9.2: Direction Fields and Euler's Method
- Section 9.3: Separable Differential Equations
- Section 9.4: Special First-Order Linear Differential Equations
- Section 9.5: Modeling with Differential Equations

- Chapter 10: Sequences and Infinite Series
- Section 10.1: An Overview
- Section 10.2: Sequences
- Section 10.3: Infinite Series
- Section 10.4: The Divergence and Integral Tests
- Section 10.5: Comparison Tests
- Section 10.6: Alternating Series
- Section 10.7: The Ratio and Root Tests
- Section 10.8: Choosing a Convergence Test

- Chapter 11: Power Series
- Section 11.1: Approximating Functions with Polynomials
- Section 11.2: Properties of Power Series
- Section 11.3: Taylor Series
- Section 11.4: Working with Taylor Series

- Chapter 12: Parametric and Polar Curves
- Section 12.1: Parametric Equations
- Section 12.2: Polar Coordinates
- Section 12.3: Calculus in Polar Coordinates
- Section 12.4: Conic Sections

- Chapter 13: Vectors and the Geometry of Space
- Section 13.1: Vectors in the Plane
- Section 13.2: Vectors in Three Dimensions
- Section 13.3: Dot Products
- Section 13.4: Cross Products
- Section 13.5: Lines and Planes in Space
- Section 13.6: Cylinders and Quadric Surfaces

- Chapter 14: Vector-Valued Functions
- Section 14.1: Vector-Valued Functions
- Section 14.2: Calculus of Vector-Valued Functions
- Section 14.3: Motion in Space
- Section 14.4: Length of Curves
- Section 14.5: Curvature and Normal Vectors

- Chapter 15: Functions of Several Variables
- Section 15.1: Graphs and Level Curves
- Section 15.2: Limits and Continuity
- Section 15.3: Partial Derivatives
- Section 15.4: The Chain Rule
- Section 15.5: Directional Derivatives and the Gradient
- Section 15.6: Tangent Planes and Linear Approximation
- Section 15.7: Maximum/Minimum Problems
- Section 15.8: Lagrange Multipliers

- Chapter 16: Multiple Integration
- Section 16.1: Double Integrals over Rectangular Regions
- Section 16.2: Double Integrals over General Regions
- Section 16.3: Double Integrals in Polar Coordinates
- Section 16.4: Triple Integrals
- Section 16.5: Triple Integrals in Cylindrical and Spherical Coordinates
- Section 16.6: Integrals for Mass Calculations
- Section 16.7: Change of Variables in Multiple Integrals

- Chapter 17: Vector Calculus
- Section 17.1: Vector Fields
- Section 17.2: Line Integrals
- Section 17.3: Conservative Vector Fields
- Section 17.4: Green's Theorem
- Section 17.5: Divergence and Curl
- Section 17.6: Surface Integrals
- Section 17.7: Stokes' Theorem
- Section 17.8: Divergence Theorem

- Chapter D2: Second-Order Differential Equations
- Section D2.1: Basic Ideas
- Section D2.2: Linear Homogeneous Equations
- Section D2.3: Linear Nonhomogeneous Equations
- Section D2.4: Applications
- Section D2.5: Complex Forcing Functions

Exercises 1.1.1 -