How to Ace the Rest of Calculus The Streetwise Guide, Including MultiVariable Calculus

by Adams, Colin; Thompson, Abigail; Hass, Joel

• ISBN13: 9780716741749
• ISBN10: 0716741741
• Format: Paperback
• Copyright: 2001-05-01
• Publisher: Times Books

Summary

The sequel toHow to Ace Calculus,How to Ace the Rest of Calculusprovides 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 Adamsis Professor of Mathematics at Williams College. He is the author ofThe Knot Bookand winner of the Mathematical Association of America Distinguished Teaching Award for 1998.Joel Hassis Professor of Mathematics at the University of California at Davis, andAbigail Thompsonis also Professor of Mathematics at the University of California at Davis. Adams, Hass, and Thompson are co-authors ofHow to Ace Calculus. The sequel toHow to Ace Calculus,How to Ace the Rest of Calculusprovides 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

Author Biography

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	1	(3)
Indeterminate Forms and Improper Integrals	4	(8)
Indeterminate forms	4	(4)
Improper integrals	8	(4)
Polar Coordinates	12	(12)
Introduction to polar coordinates	12	(6)
Area in polar coordinates	18	(6)
Infinite Series	24	(38)
Sequences	24	(2)
Limits of sequences	26	(1)
Series: The basic idea	26	(3)
Geometric series: The extroverts	29	(2)
The nth-term test	31	(1)
Integral test and p-series: More friends	32	(4)
Comparison tests	36	(5)
Alternating series and absolute convergence	41	(3)
More tests for convergence	44	(2)
Power series	46	(2)
Which test to apply when?	48	(2)
Taylor series	50	(7)
Taylor's formula with remainder	57	(3)
Some famous Taylor series	60	(2)
Vectors: From Euclid to Cupid	62	(32)
Vectors in the plane	62	(6)
Space: The final (exam) frontier	68	(2)
Vectors in space	70	(2)
The dot product	72	(6)
The cross product	78	(7)
Lines in space	85	(3)
Planes in space	88	(6)
Parametric Curves in Space: Riding the Roller Coaster	94	(15)
Parametric curves	94	(7)
Curvature	101	(4)
Velocity and acceleration	105	(4)
Surfaces and Graphing	109	(15)
Curves in the plane: A retrospective	109	(2)
Graphs of equations in 3-space	111	(4)
Surfaces of revolution	115	(2)
Quadric surfaces (the -oid surfaces)	117	(7)
Functions of Several Variables and Their Partial Derivatives	124	(47)
Functions of several variables	124	(5)
Contour curves	129	(3)
Limits	132	(4)
Continuity	136	(3)
Partial derivatives	139	(10)
Max-min problems	149	(6)
The chain rule	155	(3)
The gradient and directional derivatives	158	(6)
Lagrange multipliers	164	(3)
Second derivative test	167	(4)
Multiple Integrals	171	(45)
Double integrals and limits---the technical stuff	173	(1)
Calculating double integrals	174	(7)
Double integrals and volumes under a graph	181	(3)
Double integrals in polar coordinates	184	(4)
Triple integrals	188	(5)
Cylindrical and spherical coordinates	193	(12)
Mass, center of mass, and moments	205	(7)
Change of coordinates	212	(4)
Vector fields and the Green-Stokes gang	216	(36)
Vector fields	216	(3)
Getting acquainted with div and curl	219	(6)
Line up for line integrals	225	(1)
Line integrals of vector fields	226	(4)
Conservative vector fields	230	(5)
Green's theorem	235	(2)
Integrating the divergence; the divergence theorem	237	(4)
Surface integrals	241	(7)
Stoking!	248	(4)
What's Going to Be on the Final?	252	(6)
Glossary: A Quick Guide to the Mathematical Jargon	258	(11)
Index	269