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Publisher:

Henry Holt

Publication Date:

2001

Number of Pages:

240

Format:

Paperback

Price:

17.00

ISBN:

978-0-7167-4174-9

Category:

Student Helps

[Reviewed by , on ]

Kevin Anderson

12/12/2002

This is the second book in the *How to Ace ________: A Streetwise Guide* series. This book is for students who have already taken at least one semester of calculus. This book doesn't repeat all of the advice of the first book on how to pick your instructor, how to study, etc. Instead this book is devoted to the specific topics of the rest of calculus.

*How to Ace the Rest* does a good job of explaining the basic concepts of Calculus II and III with humorous and understandable explanations, and examples such as:

Fifi drags her owner along a sidewalk that's 200 meters long. If Fifi (she's a poodle, although I guess that's obvious from the name) exerts a force of 2 newtons on the leash, and the leash is at an angle of 45 degrees from the ground, how much work does Fifi do?

Suppose you hurl a wedge of Gouda cheese from the corner of the roof of a building 50 feet above the ground. You launch the cheese with an initial velocity vector v

_{0}= <8,6,4> in feet per second. Your roommate is standing on the ground at a point 14 feet 4 inches in the x-direction and 10 feet 9 inches in the y-direction from the corner of the building. Determine if your cheese will hit him.

To Students: The bottom line is that this book explains the basic concepts and ideals of Calculus II and III very well; the examples are clear, understandable and funny! The book also points out common mistakes that students make, which your instructor may not point out in lecture.

Yet another nice feature of this book is the "Just the Facts" sheets at the end of the book. These sheets contain all the important formulas. You can cut the sheets out of the book and use them as a reference guide and study sheet, a useful tool for you slackers (you know who you are) who cram for the Calculus Exam the night before.

To Faculty: This book has many nice examples and entertaining explanations of the basic concepts in Calculus. It would be a good resource book to add a little spice and humor to your lectures. The only negative comment I have is that the book didn't cover volumes and surfaces of revolution.

Kevin Anderson (andersk@mwsc.edu) is assistant professor of mathematics at Missouri Western State College.

**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 *n*th-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

8.7 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**

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