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Classroom Notes: Symbolic Integration and Asymptotic Expansions
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| Organization: | Center for Wave Phenomena, Colorado School of Mines |
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Elementary Symbolic Integration, by Jack K. Cohen; Convergent vs. Asymptotic Representations by John W. Stockwell, Jr.
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In the new calculus curriculum, finding antiderivatives by exotic substitutions and other tricks is replaced by investigating classes of integrals that succumb to systematic approaches. It is easy to design Mathematica exercises based on the built-in fuction Integrate. However, an additional lecture and assignment explaining how packages such as Mathematica handle symbolic integration is useful in dispelling the impression that these tools are magic "black boxes." It isn't difficult to build a small prototype symbolic integration package. Indeed, the discussion in section 2.3.13 of the Mathematica Book provides a good start and is the basis for this article. On the other hand, it should be emphasized that the function developed here is, indeed, only a prototype and is not part of the built-in Mathematica fuction Integrate.
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http://www.mathematica-journal.com/issue/v5i4/columns/cohen/52-56cohen.54.mj.pdf
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