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Introductory Explorations of the Fourier Series

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Abstract

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.

Figure 1. Fourier series of three terms fitted to a step function.

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Version	Download
Mathcad 11	fourier11.mcd

Version	Download
Mathcad 11	fourier11.pdf

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Keywords

Audience: Upper-Division Undergraduate;

Domain: Physical Chemistry;

Pedagogy: Computer-Based Learning;

Topics: Chemometrics; Mathematics / Symbolic Mathematics; Quantum Chemistry;

JCE Citation