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).

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