Rest of Calculus: The Streetwise Guide - Including Multi-Variable Calculus

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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.

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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.

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Editorial Reviews

From the Publisher

"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

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Product Details

  • ISBN-13: 9780716741749
  • Publisher: Holt, Henry & Company, Inc.
  • Publication date: 5/28/2001
  • Edition description: New Edition
  • Pages: 304
  • Sales rank: 297,598
  • Product dimensions: 7.22 (w) x 9.14 (h) x 0.81 (d)

Meet 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.

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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

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Customer Reviews

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Sort by: Showing all of 4 Customer Reviews
  • Posted October 9, 2011

    Highly recommended - Explains in detail

    Does a good job of explaining the most complicated concepts.

    1 out of 1 people found this review helpful.

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  • Posted September 28, 2010

    This is a MUST for any student SERIOUS about passing Calculus !!!!!!

    I am an engineering student who is nearing the end of my calculus sequence. I had been searching for a help book, and when i saw this in the store i thought id give it a shot. This has been the single most helpful utility i have come across, and i have tried everything. Not only is this book hysterical, it is extremely clear and explains things in a way that makes it stick. If i didnt have this, passing Calculus 1 and 2 would have been alot harder. This book will even help you select the right teacher !!! it is truly a mathematical godsend, and recommend it to any person who is serious about not just passing, but really understanding Calculus ! Dont bother looking any further, this book is the BEST !

    1 out of 1 people found this review helpful.

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  • Anonymous

    Posted March 30, 2004

    Read what my daughter wrote:

    Here's an actual email from my daughter, who was struggling with freshman calculus: 'OK, folks, I sat down tonight with my NEW 'How To Ace Calculus Book' and REALLY dug in. And I found it humorous, yet educational. It caught me up to what we're doing in class. I wish I had this book all semester. Sad, but true. I'm still meeting with Dr. (prof¿s name) tomorrow, and I still have questions, but this book lays out the basic principles of calculus in an excellent manner, helping me to understand why things need to be done the way we're doing them. Know what I mean? I spent the last three hours reading, laughing, highlighting- really BONDING with my calc. book. awwwww, how special. Love, (daughter¿s name) P.S. Yes, Dad, you were right. Thanks for the book. P.P.S. My roommate is dropping HER calc. class. Maybe she needs a helpful book?' How can you top a review like that?

    1 out of 1 people found this review helpful.

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  • Anonymous

    Posted August 4, 2013

    I have read where Albert Einstein when very young was introduced

    I have read where Albert Einstein when very young was introduced to Algebra by his uncle, an engineer. His uncle explained that doing Algebra is like hunting an animal; until it is found we shall call it "X.."  To a  child this must have engaged an imaginative , adventurous  and fun way of learning. I think that is what  the three illustrious Authors of this book have attempted to do. Concepts are simply explained without  using big, confusing words and introducing clauses of exceptions  to the simple  explanation. This  (temporary perhaps) "solidity" gives the student something on which  at least to stand and feel secure, and then enables  the reader to try to tackle  the meaning and solution of one of the  "situation"  examples, such as the work  done by "Fifi" the  poodle , in Chapter 5. As we  use the concepts we have been given so clearly,  making a  diagram  of the vectors  and the angle  of 45 degrees from X axis, we worry about how much  work little Fifi  actually did!  Chapter 10 is wonderful!  So many interesting concepts and  practical uses of Calculus   begin to grow out  of all  we have learned before!  Line Integrals are made fun by way of the "Hot Tub"  example. In studying this example, I wondered what would  happen if the cooler were placed at (0,0) .  Another  excellent example is the  "Bee Flux"  on page 246-247.  I was a little confused by the  incorrect  y Spherical  Coordinate  stated there at the top of page 247, but  the correct  trig. functions are used in working  through the problem. below.  In referring to  Section 9.6, we see that   "Cos phi and Cos theta have   mistakenly  taken the place of Sin phi and Sin theta.I am sure that Mathematics is profound and deep and that what we have in this book  are glittering , beautiful "shells" washed up onto the shore of an infinitely deep ocean of wondrous theorems , but what we have in our hands are as beautiful and mysterious  and  as   satisfying  as what may lie beyond- at least for many  people who cannot venture further  into the depths.  Sincere thanks to the Authors and Publishers  and all who have given the thankful readers  of this book  a veritable treasure  to delight us for the rest of our lives!

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