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  Home > JCE Print > Journal of Chemical Education > Issues > 2008  > December  >
On the Web
JCE SymMath: Symbolic Mathematics in Chemistry
Introductory Explorations of the Fourier Series
Theresa Julia Zielinski
Department of Chemistry, Medical Technology, and Physics, Monmouth University, West Long Branch, NJ 07764
Cover
December 2008
Vol. 85 No. 12
p. 1708
Full Text
The ability to use series expansions effectively is one of the important skills for students in quantum chemistry courses. This Mathcad template enables students to practice this skill using the Fourier series. Students start with the definition of orthonormal functions and then move on to the fundamental equations used in Fourier expansions. Using the Fourier series with odd and even trial functions is introduced by fitting the Fourier series to a simple step function. The study ends with a mastery problem for fitting the Fourier series to an even function. Some previous work with the Fourier series or other series in class or through outside readings would be useful as preparation for this exercise. Students also should have basic experience with Mathcad and know the difference between odd and even functions. This exercise serves as a foundation for future work in quantum mechanics where, for example, linear combinations of functions are used to express solutions to the Schrödinger Equation.

image

Fourier series of three terms fitted to a step function.
Supplement
Introductory Explorations of the Fourier Series summary and Mathcad document
More Information
*
Citation
Zielinski, Theresa Julia. J. Chem. Educ. 2008, 85, 1708.
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Keywords
Chemometrics; Computer-Based Learning; Mathematics / Symbolic Mathematics; Physical Chemistry; Quantum Chemistry; Upper-Division Undergraduate
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History
Created:
Last Updated:
10/24/2008
11/6/2008
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