Has done four years of high school math
College calculus is next!
Life of Fred: Calculus Expanded Edition will offer a joyful romp through college freshman and sophomore calculus. Two years of college calculus—$49 and we pay the shipping.
All the traditional calculus topics are covered, including first and second order differential equations.
As with all of the Life of Fred books, things happen first in Fred's life, he needs a particular piece of math, and then we teach the math. Every part of calculus is motivated by real life.
To mention just one example, before we introduce the hyperbolic trig functions (sinh, cosh, and tanh) in Chapter 19, Fred and his three friends are at an all-you-can-eat buffet.
››› They are standing in a line between those ropes-on-poles.
››› One of Fred's friends (the 8'2" lion) is lassoed by some kid. The lion runs, and we look at the skid marks made by the kid.
››› The kid trips and ends up sinking in a 5000-gallon pot of cheese soup.
And suddenly, we have three uses of the hyperbolic trig functions.
In addition to the usual calculus topics, there is a "Further Ado" section at the end of the book (75+ pages) that includes many topics that are often not found in many lower division calculus books.
The proof of: If f:A –› B and g:B –› A are two 1-1 functions, then there exists a function h:A –› B that is both 1-1 and onto.
The formal defintion of limit.
Proofs of the Product Rule; the Quotient Rule; the Chain Rule; Rolle's Theorem; the Mean Value Theorem; and the Fundamental Theorem of Calculus.
The Parametric Form for Integrals.
An introduction to programming in BASIC.
Nine-dimensional vector spaces.
Green's theorem, Gauss's theorem, and Stokes's theorem.