Chapter 11. Calculus: Continuous and Discrete
Time may change me But I can’t trace time I said that time may change me But I can’t trace time
—David Bowie, “Changes”
This chapter primarily focuses on the types of problems students and teachers will cover in college-level mathematics courses and how Mathematica can be used as a calculator (tool for getting an answer) and a teacher (tool for gaining insight into a mathematical problem). However, this focus was largely pragmatic and does not imply that Mathematica is limited to introductory calculus. Quite the contrary. Mathematica has been leading the charge among computer algebra systems since its inception, and with each new release the depth and breadth of its abilities in symbolic calculus improve. My goal in most of these recipes is to provide a starting point for the inexperienced user. Experts will probably find little that is new or highly original. This was a conscious choice based on space limitations. I am quite certain one could write a small cookbook by turning each recipe here into an entire chapter! Such is the depth of Mathematica’s abilities.
Most of the recipes in this chapter address what is commonly known as infinitesimal or continuous calculus. These problems deal with limits (11.1 Computing Limits), series (11.3 Using Power Series Representations), derivatives (11.4 Differentiating Functions), integrals (11.5 Integration), and differential equations (11.6 Solving Differential Equations). A common ...