Synopses & Reviews
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 calculussuch as sequences and series, polor coordinates, and multivariable calculuswithout the technical details and fine print that would be found in a formal text.
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.
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 calculussuch as sequences and series, polor coordinates, and multivariable calculuswithout the technical details and fine print that would be found in a formal text.
"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
Synopsis
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.
Synopsis
Written by three gifted teachers, this book provides humorous and highly readable explanations of the key topics of second and third semester calculus--such as sequences and series, polar coordinates and multivariable calculus--without the technical details and fine print that would be found in a formal text. 80 illustrations.
Synopsis
The second book in the "How to Ace" series, "How to Ace the Rest of Calculus" is a witty, irreverent, and practical guide to mastering second and third semester calculus. Based on the premise that students learn best when presented with direct, concise, and informal information, the pedagogy captures the tone and content of students exchanging ideas among themselves. A supplement for any type of calculus text.
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