Introduction
Indeterminate Forms and Improper Integrals
2.1 Indeterminate forms
2.2 Improper integrals
Polar Coordinates
3.1 Introduction to polar coordinates
3.2 Area in polar coordinates
Infinite Series
4.1 Sequences
4.2 Limits of sequences
4.3 Series: The basic idea
4.4 Geometric series: The extroverts
4.5 The nth-term test
4.6 Integral test and p-series: More friends
4.7 Comparison tests
4.8 Alternating series and absolute convergence
4.9 More tests for convergence
4.10 Power series
4.11 Which test to apply when?
4.12 Taylor series
4.13 Taylor's formula with remainder
4.14 Some famous Taylor series
Vectors: From Euclid to Cupid
5.1 Vectors in the plane
5.2 Space: The final (exam) frontier
5.3 Vectors in space
5.4 The dot product
5.5 The cross product
5.6 Lines in space
5.7 Planes in space
Parametric Curves in Space: Riding the Roller Coaster
6.1 Parametric curves
6.2 Curvature
6.3 Velocity and acceleration
Surfaces and Graphing
7.1 Curves in the plane: A retrospective
7.2 Graphs of equations in 3-D space
7.3 Surfaces of revolution
7.4 Quadric surfaces (the -oid surfaces)
Functions of Several Variables and Their Partial Derivatives
8.1 Functions of several variables
8.2 Contour curves
8.3 Limits
8.4 Continuity
8.5 Partial derivatives
8.6 Max-min problems
cf08.7 The chain rule
8.8 The gradient and directional derivatives
8.9 Lagrange multipliers
8.10 Second derivative test
Multiple Integrals
9.1 Double integrals and limits-the technical stuff
9.2 Calculating double integrals
9.3 Double integrals and volumes under a graph
9.4 Double integrals in polar coordinates
9.5 Triple integrals
9.6 Cylindrical and spherical coordinates
9.7 Mass, center of mass, and moments
9.8 Change of coordinates
Vector Fields and the Green-Stokes Gang
10.1 Vector fields
10.2 Getting acquainted with div and curl
10.3 Line up for line integrals
10.4 Line integrals of vector fields
10.5 Conservative vector fields
10.6 Green's theorem
10.7 Integrating the divergence; the divergence theorem
10.8 Surface integrals
10.9 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
