Mathematica Demystified
Simple enough for a beginner, but challenging enough for an advanced user, this hands-on guide takes you from your very first calculation all the way to plotting complex fractals in Mathematica.
TABLE OF CONTENTS Mathematica Demystified
Chapter 7: Calculus
If mathematics is the language of science, then calculus is a large part of the dictionary. Calculus is exactly what is needed to describe how things change, and describing how things change is an important way in which scientists use mathematics. The authors of the book Calculus in Context [1] looked at how scientists actually use calculus in their work and discovered (not surprisingly) that modeling with differential equations is one of the primary uses.
Mathematica can be used for all the usual computations involving calculus: taking limits, finding derivatives, and computing integrals. In this chapter we'll try to hit the highlights of these computations. Obviously, this chapter cannot substitute for a course in calculus. Our goal is to not to teach you calculus (we assume you already know some, or are currently taking a course), but rather to describe a handful of useful Mathematica functions.
7.1 Limits
The really big idea of calculus is that of the limit. Once this notion is defined and understood it leads to the development of both the derivative as well as the integral, the two pillars of calculus.
Suppose that f (x) is some function of x and we would like to know the behavior of f (x) as x approaches some specific point, say x 0. Of course, the value f (x 0 ) of f (x) at x 0 is important for our understanding of f, but the...
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