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An Experiment in Teaching Calculus

What follows is an experiment in teaching calculus. This starts with computing derivatives and integrals, assuming the rules that are ordinarily proved as theorems, allowing earlier practice using the calculus. The reasonableness of the rules will be discussed in an informal way, to justify the reasonableness of the rules and to develop intuition about these techniques. Proofs will be supplied later.

Integration is the most challenging of the applications encountered, sometimes calling for creative ways to solve an integral. Specific integrals may not have great theoretical interest, but solving them might be part of solving a larger engineering or scientific problem. After a few preliminaries, the student will be able to practice working integrals almost immediately.

Organization of the Material

Getting to problems quickly means that topics will initially be partially introduced, with more detail, and importantly, more problems in later sections. While helpful for learning the material, such an organization is not ideal for a reference. To meet that need a reference section will be added.