Doing Calculus

Fancy-pants calculus books are easy to find. There are so many it's a wonder that we aren't drowning under the crush. There are three times as many "math" listing on Amazon as there are "sex" listings. This may be because nearly a million American college students are expected to shell out some $200 annually to purchase these doorstops that they never even crack open.

"Doing Calculus” is a giant step backwards in publishing. It doesn't have any bells and whistles. Unlike those those other calculus books, the ones with gee-whiz animations that rattle your teeth and on-line assessment tools that blink and flash and pop your cerebellar networks into a seemingly catatonic overload, it's just ink on paper. Or you can go for the DRM-free PDF file. With lots of snarky comments hidden between the lines. And cool pictures.

Sure, it comes with a web page (in fact you're looking at it right now), but there's virtually nothing useful on the web page, so it is unlikely to drive you nuts. And equally unlikely to crash your computer. Calculus might drive you bonkers, but the web page is unlikely to do more than mildly amuse you.

"Doing Calculus" is not just another doorstop. It's a cheaper doorstop. It's a better looking doorstop. Though the paperback is thin enough that you might actually be able to cram it under some doors. Depends on the door. If you go for the PDF, you'll have to print out a lot of pages and use really big staples to turn it into a door stop.
Contents
Quantifying Change
1 Slope and Rate of Change
2 Limits
3 Limit Laws
4 Trigonometric Limits
5 Asymptotes
6 Formal Theory of Limits
7 Continuity
8 Calculus Without Limits

Differential Calculus
9 Basic Formulas for Derivatives
10 Product and Quotient Rules
11 The Chain Rule
12 Implicit Differentiation
13 Related Rates
14 Inverse Functions
15 Exponentials and Logarithms
16 Indeterminate Limits
17 Extreme Values
18 Mean Value Theorem
19 Curve Shape
20 Optimization
21 Newton’s Method

Integral Calculus
22 Antiderivatives
23 Area Under a Curve
24 The Definite Integral
25 Substitution Methods
26 Area Between Curves
27 Volumes of Rotation
28 Average Values
29 Integration by Parts
30 Improper Integrals
31 Trigonometric Integrals
32 Trigonometric Substitutions
33 Integrating Rational Functions
34 Numerical Integration
35 Arc Length


Applications
36 Parametric Equations
37 Polar Coordinates
38 Sequences
39 Series
40 Power Series
41 Differential Equations

 Appendices
Algebraic Formulas

Table of Derivatives

Table of Integrals


Index

download pdf of table of contents    download pdf of chapter 1
PDF of appendices: algebra, derivative, integral tables

Doing Calculus was written with partial support provided by the EText initiative at the California State University, Northridge. Currently enrolled students at CSUN may obtain PDF copies by clicking on the button below.

List of known errata

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Don't waste your money on expensive calculus books.
If you feel a compulsive need to throw your money away, give it to me instead.