How to Ace the Rest of Calculus: The Streetwise Guide, Including MultiVariable Calculus

by Colin Adams, Abigail Thompson, Joel Hass

Overview

The sequel to How to Ace Calculus, How to Ace the Rest of Calculus provides humorous and highly readable explanations of the key topics of second and third semester calculus—such as sequences and series, polor coordinates, and multivariable calculus—without the technical details and fine print that would be found in a formal text.

Product Details

ISBN-13:	9780716741749
Publisher:	Holt, Henry & Company, Inc.
Publication date:	05/01/2001
Series:	How to Ace S
Pages:	312
Sales rank:	948,477
Product dimensions:	7.20(w) x 9.33(h) x 0.63(d)

About the Author

Colin Adams is Professor of Mathematics at Williams College. He is the author of The Knot Book and winner of the Mathematical Association of America Distinguished Teaching Award for 1998. Joel Hass is Professor of Mathematics at the University of California at Davis, and Abigail Thompson is also Professor of Mathematics at the University of California at Davis. Adams, Hass, and Thompson are co-authors of How to Ace Calculus.

Table of Contents

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

Editorial Reviews

What a great book! It's short, it's funny, and it reveals the secrets of the calculus guild. What more could you want?” —Fernando Gouvea, Editor, MAA Online

“Congratulations! You made it through the first term of calculus. Now the fun really begins. This wonderful book will take you on a fantastic journey.” —Mikhail Chkhenkeli, Williams College

From the Publisher