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How to Ace the Rest of Calculus : The Streetwise Guide - Colin Adams

How to Ace the Rest of Calculus

The Streetwise Guide

Paperback Published: 1st May 2001
ISBN: 9780716741749
Number Of Pages: 240

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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.

"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 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"" "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

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
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780716741749
ISBN-10: 0716741741
Series: How to Ace S
Audience: Professional
Format: Paperback
Language: English
Number Of Pages: 240
Published: 1st May 2001
Publisher: W.H.Freeman & Co Ltd
Country of Publication: AU
Dimensions (cm): 19.4 x 23.6  x 2.0
Weight (kg): 0.54
Edition Number: 1