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
Product dimensions:	7.20(w) x 9.33(h) x 0.62(d)

About the Author

Colin Adams is the Thomas T. Read Professor of Mathematics at Williams College, where he has taught since 1985. He has produced a number of books that make mathematics more accessible and relatable, including How to Ace Calculus and its sequel, How to Ace the Rest of Calculus; Riot at the Calc Exam and other Mathematically Bent Stories; and Zombies & Calculus. Colin co-wrote and appears in the videos "The Great Pi vs. E Debate" and "Derivative vs. Integral: the Final Smackdown."

Adams received his undergraduate degree from MIT and his Ph.D. from the University of Wisconsin. He had held various grants for research in the area of knot theory and low-dimensional topology and has published numerous research articles. He received the Haimo National Distinguished Teaching Award from the Mathematical Association of America (MAA) in 1998, and the Robert Foster Cherry Teaching Award in 2003. Adams also served as MAA Polya Lecturer (1998-2000), and as Sigma Xi Distinguished Lecturer (2000-2002).

Abigail Thompson is a Professor of Mathematics at the University of California at Davis. She has held fellowships from the Sloan Foundation and the National Science Foundation.

Joel Hass is Professor of Mathematics at the University of California at Davis. He has held fellowships from the Sloan Foundation and the National Science Foundation.

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