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.

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.

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 friends4.7 Comparison tests 4.8 Alternating series and absolute convergence 4.9 More tests for convergence 4.10 Power series4.11 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 Cupid5.1 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 product5.6 Lines in space 5.7 Planes in space Parametric Curves in Space: Riding the Roller Coaster6.1 Parametric curves6.2 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 rule8.8 The gradient and directional derivatives 8.9 Lagrange multipliers 8.10 Second derivative test Multiple Integrals9.1 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 moments9.8 Change of coordinatesVector 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 JargonIndex Just the Facts: A Quick Reference Guide