| |
| |
| Introduction | |
| |
| |
| Indeterminate | |
| |
| |
| Forms and Improper Integrals | |
| |
| |
| |
| Indeterminate forms | |
| |
| |
| |
| Improper integrals | |
| |
| |
| Polar Coordinates | |
| |
| |
| |
| Introduction to polar coordinates | |
| |
| |
| |
| Area in polar coordinates | |
| |
| |
| Infinite Series | |
| |
| |
| |
| Sequences | |
| |
| |
| |
| Limits of sequences | |
| |
| |
| |
| Series: The basic idea | |
| |
| |
| |
| Geometric series: The extroverts | |
| |
| |
| |
| Thenth-term test | |
| |
| |
| |
| Integral test andp-series: More friends | |
| |
| |
| |
| Comparison tests | |
| |
| |
| |
| Alternating series and absolute convergence | |
| |
| |
| |
| More tests for convergence | |
| |
| |
| |
| Power series | |
| |
| |
| |
| Which test to apply when? | |
| |
| |
| |
| Taylor series | |
| |
| |
| |
| Taylor's formula with remainder | |
| |
| |
| |
| Some famous Taylor series | |
| |
| |
| Vectors: From Euclid to Cupid | |
| |
| |
| |
| Vectors in the plane | |
| |
| |
| |
| Space: The final (exam) frontier | |
| |
| |
| |
| Vectors in space | |
| |
| |
| |
| The dot product | |
| |
| |
| |
| The cross product | |
| |
| |
| |
| Lines in space | |
| |
| |
| |
| Planes in space | |
| |
| |
| Parametric Curves in Space: Riding the Roller Coaster | |
| |
| |
| |
| Parametric curves | |
| |
| |
| |
| Curvature | |
| |
| |
| |
| Velocity and acceleration | |
| |
| |
| Surfaces and Graphing | |
| |
| |
| |
| Curves in the plane: A retrospective | |
| |
| |
| |
| Graphs of equations in 3-D space | |
| |
| |
| |
| Surfaces of revolution | |
| |
| |
| |
| Quadric surfaces (the -oid surfaces) | |
| |
| |
| Functions of Several Variables and Their Partial Derivatives | |
| |
| |
| |
| Functions of several variables | |
| |
| |
| |
| Contour curves | |
| |
| |
| |
| Limits | |
| |
| |
| |
| Continuity | |
| |
| |
| |
| Partial derivatives | |
| |
| |
| |
| Max-min problems cf 0 | |
| |
| |
| |
| The chain rule | |
| |
| |
| |
| The gradient and directional derivatives | |
| |
| |
| |
| Lagrange multipliers | |
| |
| |
| |
| Second derivative test | |
| |
| |
| Multiple Integrals | |
| |
| |
| |
| Double integrals and limits—the technical stuff | |
| |
| |
| |
| Calculating double integrals | |
| |
| |
| |
| Double integrals and volumes under a graph | |
| |
| |
| |
| Double integrals in polar coordinates | |
| |
| |
| |
| Triple integrals | |
| |
| |
| |
| Cylindrical and spherical coordinates | |
| |
| |
| |
| Mass, center of mass, and moments | |
| |
| |
| |
| Change of coordinates | |
| |
| |
| Vector Fields and the Green-Stokes Gang | |
| |
| |
| |
| Vector fields | |
| |
| |
| |
| Getting acquainted with div and curl | |
| |
| |
| |
| Line up for line integrals | |
| |
| |
| |
| Line integrals of vector fields | |
| |
| |
| |
| Conservative vector fields | |
| |
| |
| |
| Green's theorem | |
| |
| |
| |
| Integrating the divergence; the divergence theorem | |
| |
| |
| |
| Surface integrals | |
| |
| |
| |
| Stoking! What's Going to Be on the Final? | |
| |
| |
| Glossary: A Quick Guide to the Mathematical Jargon | |
| |
| |
| Index | |
| |
| |
| Just the Facts: A Quick Reference Guide | |