- Chapter 1: Functions
- Section 1.1: Functions and Their Graphs
- Section 1.2: Combining Functions; Shifting and Scaling Graphs
- Section 1.3: Trigonometric Functions
- Section 1.4: Graphing with Software
- Section 1.5: Exponential Functions
- Section 1.6: Inverse Functions and Logarithms

- Chapter 2: Limits and Continuity
- Section 2.1: Rates of Change and Tangent Lines to Curves
- Section 2.2: Limit of a Function and Limit Laws
- Section 2.3: The Precise Definition of a Limit
- Section 2.4: One-Sided Limits
- Section 2.5: Continuity
- Section 2.6: Limits Involving Infinity; Asymptotes of Graphs

- Chapter 3: Derivatives
- Section 3.1: Tangent Lines and the Derivative at a Point
- Section 3.2: The Derivative as a Function
- Section 3.3: Differentiation Rules
- Section 3.4: The Derivative as a Rate of Change
- Section 3.5: Derivatives of Trigonometric Functions
- Section 3.6: The Chain Rule
- Section 3.7: Implicit Differentiation
- Section 3.8: Derivatives of Inverse Functions and Logarithms
- Section 3.9: Inverse Trigonometric Functions
- Section 3.10: Related Rates
- Section 3.11: Linearization and Differentials

- Chapter 4: Applications of Derivatives
- Section 4.1: Extreme Values of Functions on Closed Intervals
- Section 4.2: The Mean Value Theorem
- Section 4.3: Monotonic Functions and the First Derivative Test
- Section 4.4: Concavity and Curve Sketching
- Section 4.5: Indeterminate Forms and L'Hopital's Rule
- Section 4.6: Applied Optimization
- Section 4.7: Newton's Method
- Section 4.8: Antiderivatives

- Chapter 5: Integrals
- Section 5.1: Area and Estimating with Finite Sums
- Section 5.2: Sigma Notation and Limits of Finite Sums
- Section 5.3: The Definite Integral
- Section 5.4: The Fundamental Theorem of Calculus
- Section 5.5: Indefinite Integrals and the Substitution Method
- Section 5.6: Definite Integral Substitutions and the Area Between Curves

- Chapter 6: Applications of Definite Integrals
- Section 6.1: Volumes Using Cross-Sections
- Section 6.2: Volumes Using Cylindrical Shells
- Section 6.3: Arc Length
- Section 6.4: Areas of Surfaces of Revolution
- Section 6.5: Work and Fluid Forces
- Section 6.6: Moments and Centers of Mass

- Chapter 7: Integrals and Transcendental Functions
- Section 7.1: The Logarithm Defined as an Integral
- Section 7.2: Exponential Change and Separable Differential Equations
- Section 7.3: Hyperbolic Functions
- Section 7.4: Relative Rates of Growth

- Chapter 8: Techniques of Integration
- Section 8.1: Using Basic Integration Formulas
- Section 8.2: Integration by Parts
- Section 8.3: Trigonometric Integrals
- Section 8.4: Trigonometric Substitutions
- Section 8.5: Integration of Rational Functions by Partial Fractions
- Section 8.6: Integral Tables and Computer Algebra Systems
- Section 8.7: Numerical Integration
- Section 8.8: Improper Integrals
- Section 8.9: Probability

- Chapter 9: First-Order Differential Equations
- Section 9.1: Solutions, Slope Fields, and Euler's Method
- Section 9.2: First-Order Differential Equations
- Section 9.3: Applications
- Section 9.4: Graphical Solutions of Autonomous Equations
- Section 9.5: Systems of Equations and Phase Planes

- Chapter 10: Infinite Sequences and Series
- Section 10.1: Sequences
- Section 10.2: Infinite Series
- Section 10.3: The Integral Test
- Section 10.4: Comparison Tests
- Section 10.5: Absolute Convergence; The Ratio and Root Tests
- Section 10.6: Alternating Series and Conditional Convergence
- Section 10.7: Power Series
- Section 10.8: Taylor and Maclaurin Series
- Section 10.9: Convergence of Taylor Series
- Section 10.10: Applications of Taylor Series

- Chapter 11: Parametric Equations and Polar Coordinates
- Section 11.1: Parametrizations of Plane Curves
- Section 11.2: Calculus with Parametric Curves
- Section 11.3: Polar Coordinates
- Section 11.4: Graphing Polar Coordinate Equations
- Section 11.5: Areas and Lengths in Polar Coordinates
- Section 11.6: Conic Sections
- Section 11.7: Conics in Polar Coordinates

- Chapter 12: Vectors and the Geometry of Space
- Section 12.1: Three-Dimensional Coordinate Systems
- Section 12.2: Vectors
- Section 12.3: The Dot Product
- Section 12.4: The Cross Product
- Section 12.5: Lines and Planes in Space
- Section 12.6: Cylinders and Quadric Surfaces

- Chapter 13: Vector-Valued Functions and Motion in Space
- Section 13.1: Curves in Space and Their Tangents
- Section 13.2: Integrals of Vector Functions; Projectile Motion
- Section 13.3: Arc Length in Space
- Section 13.4: Curvature and Normal Vectors of a Curve
- Section 13.5: Tangential and Normal Components of Acceleration
- Section 13.6: Velocity and Acceleration in Polar Coordinates

- Chapter 14: Partial Derivatives
- Section 14.1: Functions of Several Variables
- Section 14.2: Limits and Continuity in Higher Dimensions
- Section 14.3: Partial Derivatives
- Section 14.4: The Chain Rule
- Section 14.5: Directional Derivatives and Gradient Vectors
- Section 14.6: Tangent Planes and Differentials
- Section 14.7: Extreme Values and Saddle Points
- Section 14.8: Lagrange Multipliers
- Section 14.9: Taylor's Formula for Two Variables
- Section 14.10: Partial Derivatives with Constrained Variables

- Chapter 15: Multiple Integrals
- Section 15.1: Double and Iterated Integrals over Rectangles
- Section 15.2: Double Integrals over General Regions
- Section 15.3: Area by Double Integration
- Section 15.4: Double Integrals in Polar Form
- Section 15.5: Triple Integrals in Rectangular Coordinates
- Section 15.6: Applications
- Section 15.7: Triple Integrals in Cylindrical and Spherical Coordinates
- Section 15.8: Substitutions in Multiple Integrals

- Chapter 16: Integrals and Vector Fields
- Section 16.1: Line Integrals of Scalar Functions
- Section 16.2: Vector Fields and Line Integrals: Work, Circulation, and Flux
- Section 16.3: Path Independence, Conservative Fields, and Potential Functions
- Section 16.4: Green's Theorem in the Plane
- Section 16.5: Surfaces and Area
- Section 16.6: Surface Integrals
- Section 16.7: Stokes' Theorem
- Section 16.8: The Divergence Theorem and a Unified Theory

- Chapter 17: Second-Order Differential Equations
- Section 17.1: Second-Order Linear Equations
- Section 17.2: Nonhomogeneous Linear Equations
- Section 17.3: Applications
- Section 17.4: Euler Equations
- Section 17.5: Power-Series Solutions

- Chapter 18: Complex Functions
- Section 18.1: Complex Numbers
- Section 18.2: Functions of a Complex Variable
- Section 18.3: Derivatives
- Section 18.4: The Cauchy-Riemann Equations
- Section 18.5: Complex Power Series
- Section 18.6: Some Complex Functions
- Section 18.7: Conformal Maps

- Chapter 19: Fourier Series and Wavelets
- Section 19.1: Periodic Functions
- Section 19.2: Summing Sines and Cosines
- Section 19.3: Vectors and Approximation in Three and More Dimensions
- Section 19.4: Approximation of Functions
- Section 19.5: Advanced Topic: The Haar System and Wavelets

Exercises 1.1.1 - 1.2.32