Section 1 . Four Ways to Represent a Function
Section 2 . Mathematical Models: A Catalog of Essential Functions
Section 3 . New Functions from Old Functions
Section 4 . Graphing Calculators and Computers
Section 5 . Exponential Functions
Section 6 . Inverse Functions and Logarithms

Section 1 . The Tangent and Velocity Problems
Section 2 . The Limit of a Function
Section 3 . Calculating Limits Using the Limit Laws
Section 4 . The Precise Definition of a Limit
Section 5 . Continuity
Section 6 . Limits at Infinity: Horizontal Asymptotes
Section 7 . Tangents, Velocities, and Other Rates of Change
Section 8 . Derivatives
Section 9 . The Derivative as a Function

Section 1 . Derivatives of Polynomials and Exponential Functions
Section 2 . The Product and Quotient Rules
Section 3 . Rates of Change in the Natural and Social Sciences
Section 4 . Derivatives of Trigonometric Functions
Section 5 . The Chain Rule
Section 6 . Implicit Differentiation
Section 7 . Higher Derivatives
Section 8 . Derivatives of Logarithmic Functions
Section 9 . Hyperbolic Functions
Section 10 . Related Rates
Section 11 . Linear Approximations and Differentials

Section 1 . Maximum and Minimum Values
Section 2 . The Mean Value Theorem
Section 3 . How Derivatives Affect the Shape of a Graph
Section 4 . Indeterminate Forms and L'Hospital's Rule
Section 5 . Summary of Curve Sketching
Section 6 . Graphing with Calculus and Calculators
Section 7 . Optimization Problems
Section 8 . Applications to Business and Economics
Section 9 . Newton's Method
Section 10 . Antiderivatives

Section 1 . Areas and Distances
Section 2 . The Definite Integral
Section 3 . The Fundamental Theorem of Calculus
Section 4 . Indefinite Integrals and the Net Change Theorem
Section 5 . The Substitution Rule
Section 6 . The Logarithm Defined as an Integral

Section 1 . Areas between Curves
Section 2 . Volume
Section 3 . Volumes by Cylindrical Shells
Section 4 . Work
Section 5 . Average Value of a Function

Section 1 . Integration by Parts
Section 2 . Trigonometric Integrals
Section 3 . Trigonometric Substitution
Section 4 . Integration of Rational Functions by Partial Fractions
Section 5 . Strategy for Integration
Section 6 . Integration Using Tables and Computer Algebra Systems
Section 7 . Approximate Integration
Section 8 . Improper Integrals

Section 1 . Arc Length
Section 2 . Area of a Surface of Revolution
Section 3 . Applications to Physics and Engineering
Section 4 . Applications to Economics and Biology
Section 5 . Probability

Section 1 . Modeling with Differential Equations
Section 2 . Direction Fields and Euler's Method
Section 3 . Separable Equations
Section 4 . Exponential Growth and Decay
Section 5 . The Logistic Equation
Section 6 . Linear Equations
Section 7 . Predator-Prey Systems

Section 1 . Curves Defined by Parametric Equations
Section 2 . Calculus with Parametric Curves
Section 3 . Polar Coordinates
Section 4 . Areas and Lengths in Polar Coordinates
Section 5 . Conic Sections
Section 6 . Conic Sections in Polar Coordinates

Section 1 . Sequences
Section 2 . Series
Section 3 . The Integral Test and Estimates of Sums
Section 4 . The Comparison Tests
Section 5 . Alternating Series
Section 6 . Absolute Convergence and the Ratio and Root Tests
Section 7 . Strategy for Testing Series
Section 8 . Power Series
Section 9 . Representation of Functions as Power Series
Section 10 . Taylor and Maclaurin Series
Section 11 . The Binomial Series
Section 12 . Applications of Taylor Polynomials

Section 1 . Three-Dimensional Coordinate Systems
Section 2 . Vectors
Section 3 . The Dot Product
Section 4 . The Cross Product
Section 5 . Equations of Lines and Planes
Section 6 . Cylinders and Quadric Surfaces
Section 7 . Cylindrical and Spherical Coordinates

Section 1 . Vector Functions and Space Curves
Section 2 . Derivatives and Integrals of Vector Functions
Section 3 . Arc Length and Curvature
Section 4 . Motion in Space: Velocity and Acceleration

Section 1 . Functions of Several Variables
Section 2 . Limits and Continuity
Section 3 . Partial Derivatives
Section 4 . Tangent Planes and Linear Approximations
Section 5 . The Chain Rule
Section 6 . Directional Derivatives and the Gradient Vector
Section 7 . Maximum and Minimum Values
Section 8 . Lagrange Multipliers

Section 1 . Double Integrals over Rectangles
Section 2 . Iterated Integrals
Section 3 . Double Integrals over General Regions
Section 4 . Double Integrals in Polar Coordinates
Section 5 . Applications of Double Integrals
Section 6 . Surface Area
Section 7 . Triple Integrals
Section 8 . Triple Integrals in Cylindrical and Spherical Coordinates
Section 9 . Change of Variables in Multiple Integrals

Section 1 . Vector Fields
Section 2 . Line Integrals
Section 3 . The Fundamental Theorem for Line Integrals
Section 4 . Green's Theorem
Section 5 . Curl and Divergence
Section 6 . Parametric Surfaces and Their Areas
Section 7 . Surface Integrals
Section 8 . Stokes' Theorem
Section 9 . The Divergence Theorem

Section 1 . Second-Order Linear Equations
Section 2 . Nonhomogeneous Linear Equations
Section 3 . Applications of Second-Order Differential Equations
Section 4 . Series Solutions