This is the second book in the How to Ace ________: A Streetwise Guide series. This book is for students who have already taken at least one semester of calculus. This book doesn't repeat all of the advice of the first book on how to pick your instructor, how to study, etc. Instead this book is devoted to the specific topics of the rest of calculus.
How to Ace the Rest does a good job of explaining the basic concepts of Calculus II and III with humorous and understandable explanations, and examples such as:
Fifi drags her owner along a sidewalk that's 200 meters long. If Fifi (she's a poodle, although I guess that's obvious from the name) exerts a force of 2 newtons on the leash, and the leash is at an angle of 45 degrees from the ground, how much work does Fifi do?
Suppose you hurl a wedge of Gouda cheese from the corner of the roof of a building 50 feet above the ground. You launch the cheese with an initial velocity vector v0 = <8,6,4> in feet per second. Your roommate is standing on the ground at a point 14 feet 4 inches in the x-direction and 10 feet 9 inches in the y-direction from the corner of the building. Determine if your cheese will hit him.
To Students: The bottom line is that this book explains the basic concepts and ideals of Calculus II and III very well; the examples are clear, understandable and funny! The book also points out common mistakes that students make, which your instructor may not point out in lecture.
Yet another nice feature of this book is the "Just the Facts" sheets at the end of the book. These sheets contain all the important formulas. You can cut the sheets out of the book and use them as a reference guide and study sheet, a useful tool for you slackers (you know who you are) who cram for the Calculus Exam the night before.
To Faculty: This book has many nice examples and entertaining explanations of the basic concepts in Calculus. It would be a good resource book to add a little spice and humor to your lectures. The only negative comment I have is that the book didn't cover volumes and surfaces of revolution.
Kevin Anderson (firstname.lastname@example.org) is assistant professor of mathematics at Missouri Western State College.
Indeterminate Forms and Improper Integrals
2.1 Indeterminate forms
2.2 Improper integrals
3.1 Introduction to polar coordinates
3.2 Area in polar coordinates
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
6.3 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
8.5 Partial derivatives
8.6 Max-min problems
8.7 The chain rule
8.8 The gradient and directional derivatives
8.9 Lagrange multipliers
8.10 Second derivative test
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
What's Going to Be on the Final?
Glossary: A Quick Guide to the Mathematical Jargon
Just the Facts: A Quick Reference Guide