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This article describes a laboratory module on Fourier series and Gibbs phenomenon which was undertaken by 32 Year 12 students. In…Įxploring Fourier Series and Gibbs Phenomenon Using Mathematica
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In the first module, the user is expected to learn how to use the unified method presented to obtain Laplace transforms, Fourier transforms, complex Fourier series, real Fourier series, and half-range sine series for given piecewise continuous functions. This document contains two units that examine integral transforms and series expansions. Modules and Monographs in Undergraduate Mathematics and Its Applications Project. Integral Transforms and Series Expansions. An Inversion Method for Laplace Transforms, Fourier Transforms, and Fourier Series. (Contains 1 note.)Ī Unified Method of Finding Laplace Transforms, Fourier Transforms, and Fourier Series. Particular cases are presented and two recent results involving numerical series are recovered. We discuss a class of trigonometric functions whose corresponding Fourier series, on a conveniently chosen interval, can be used to calculate several numerical series. On Sums of Numerical Series and Fourier Series Included is a historical development of Fourier series and Fourier transforms with their properties, importance and applications. This article deals with a brief biographical sketch of Joseph Fourier, his first celebrated work on analytical theory of heat, his first great discovery of Fourier series and Fourier transforms.
This is done through discovery learning and use of technology wherein students build the…Ī Short Biography of Joseph Fourier and Historical Development of Fourier Series and Fourier Transforms Specifically, it is shown how the study of Fourier series can be motivated to enrich a multivariable calculus class.
This note discusses the introduction of Fourier series as an immediate application of optimization of a function of more than one variable. ERIC Educational Resources Information Center
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