How to Ace the Rest of Calculus: The Streetwise Guide

Cover
Contents
1 Introduction
2 Indeterminate Forms and Improper Integrals
	2.1 Indeterminate forms
	2.2 Improper integrals
3 Polar Coordinates
	3.1 Introduction to polar coordinates
	3.2 Area in polar coordinates
4 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
5 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
6 Parametric Curves in Space: Riding the Roller Coaster
	6.1 Parametric curves
	6.2 Curvature
	6.3 Velocity and acceleration
7 Surfaces and Graphing
	7.1 Curves in the plane: A retrospective
	7.2 Graphs of equations in 3-space
	7.3 Surfaces of revolution
	7.4 Quadric surfaces (the -oid surfaces)
8 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
	8.7 The chain rule
	8.8 The gradient and directional derivatives
	8.9 Lagrange multipliers
	8.10 Second derivative test
9 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
10 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!
11 What’s Going to Be on the Final?
Glossary: A Quick Guide to the Mathematical Jargon
Index
Just the Facts: A Quick Reference Guide
About the Authors