| Parametric Equations And Polar Coordinates | |
| Curves Defined by Parametric Equations, Laboratory Project: Families of Hypocycloids | |
| Calculus with Parametric Curves, Laboratory Project: Bezier Curves | |
| Polar Coordinates | |
| Areas and Lengths in Polar Coordinates | |
| Conic Sections | |
| Conic Sections in Polar Coordinates | |
| Review | |
| Problems Plus | |
| Infinite Sequences And Series | |
| Sequences, Laboratory Project: Logistic Sequences | |
| Series | |
| The Integral Test and Estimates of Sums | |
| The Comparison Tests | |
| Alternating Series | |
| Absolute Convergence and the Ratio and Root Tests | |
| Strategy for Testing Series | |
| Power Series | |
| Representation of Functions as Power Series | |
| Taylor and Maclaurin Series | |
| Laboratory Project: An Ellusive Limit | |
| The Binomial Series, Writing Project: How Newton Discovered the Binomial Series | |
| Applications of Taylor Polynomials, Applied Project: Radiation from the Stars | |
| Review | |
| Problems Plus | |
| Vectors And The Geometry Of Space | |
| Three-Dimensional Coordinate Systems | |
| Vectors | |
| The Dot Product | |
| The Cross Product, Discovery Project: The Geometry of a Tetrahedron | |
| Equations of Lines and Planes | |
| Cylinders and Quadric Surfaces | |
| Cylindrical and Spherical Coordinates, Laboratory Project: Families of Surfaces | |
| Review | |
| Problems Plus | |
| Vector Functions | |
| Vector Functions and Space Curves | |
| Derivatives and Integrals of Vector Functions | |
| Arc Length and Curvature | |
| Motion in Space: Velocity and Acceleration, Applied Project: Kepler's Laws | |
| Review | |
| Problems Plus | |
| Partial Derivatives | |
| Functions of Several Variables | |
| Limits and Continuity | |
| Partial Derivatives | |
| Tangent Planes and Linear Approximations | |
| The Chain Rule | |
| Directional Derivatives and the Gradient Vector | |
| Maximum and Minimum Values, Applied Project: Designing a Dumpster, Discovery Project: Quadratic Approximations and Critical Points | |
| Lagrange Multipliers, Applied Project: Rocket Science, Applied Project: Hydro-Turbine Optimization | |
| Review | |
| Problems Plus | |
| Multiple Integrals | |
| Double Integrals over Rectangles | |
| Iterated Integrals | |
| Double Integrals over General Regions | |
| Double Integrals in Polar Coordinates | |
| Applications of Double Integrals | |
| Surface Area | |
| Triple Integrals, Discovery Project: Volumes of Hyperspheres | |
| Triple Integrals in Cylindrical and Spherical Coordinates, Applied Project: Roller Derby, Discovery Project: The Intersection of Three Cylinders | |
| Change of Variables in Multiple Integrals | |
| Review | |
| Problems Plus | |
| Vector Calculus | |
| Vector Fields | |
| Line Integrals | |
| The Fundamental Theorem for Line Integrals | |
| Green's Theorem | |
| Curl and Divergence | |
| Parametric Surfaces and Their Areas | |
| Surface Integrals | |
| Stokes' Theorem, Writing Project: Three Men and Two Theorems | |
| The Divergence Theorem | |
| Summary | |
| Review | |
| Problems Plus | |
| Second-Order Differential Equations | |
| Second-Order Linear Equations | |
| Nonhomogeneous Linear Equations | |
| Applications of Second-Order Differential Equations | |
| Series Solutions | |
| Review | |
| Problems Plus | |
| Appendixes | |
| Answers to Odd-Numbered Exercises | |
| Index | |
| Table of Contents provided by Publisher. All Rights Reserved. |