James Stewart

Brooks/Cole

Chapter 1. Functions And Models

Section 1 . Four Ways to Represent a FunctionChapter 2. Limits And Derivatives

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 ProblemsChapter 3. Differentiation Rules

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 FunctionsChapter 4. Applications Of Differentiation

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 ValuesChapter 5. Integrals

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 DistancesChapter 6. Applications Of Integration

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 CurvesChapter 7. Techniques Of Integration

Section 2 . Volume

Section 3 . Volumes by Cylindrical Shells

Section 4 . Work

Section 5 . Average Value of a Function

Section 1 . Integration by PartsChapter 8. Further Applications Of Integration

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 LengthChapter 9. Differential Equations

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 EquationsChapter 10. Parametric Equations And Polar Coordinates

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 EquationsChapter 11. Infinite Sequences And Series

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 . SequencesChapter 12. Vectors And The Geometry Of Space

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 SystemsChapter 13. Vector Functions

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 CurvesChapter 14. Partial Derivatives

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 VariablesChapter 15. Multiple Integrals

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 RectanglesChapter 16. Vector Calculus

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 FieldsChapter 17. Second-Order Differential Equations

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