Fourier and Other Orthogonal Function Expansions in Maple - Recorded Webinar - Maplesoft

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Fourier and Other Orthogonal Function Expansions in Maple

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Dr. Robert Lopez

Fourier and Other Orthogonal Function Expansions in Maple

The built-in Maple commands for integration, summing, and graphing suffice for generating and manipulating Fourier series. Why, then, did at least four different authors construct packages for use in teaching, learning, and using Fourier series (and other orthogonal function expansions)? Convenience may not be the only reason.

Maple commands like solve, or int (for integrate) free the user from the many steps that would have to be performed to obtain the results these commands provide. They allow the user to operate at a more conceptual level than prescribed by the typical textbook where manipulations are learned first, in the expectation that eventually, concepts will be absorbed.

So too with a Fourier series. To obtain one, it should not be necessary to create its coefficients by integrating; to visualize one, it should not be necessary to form partial sums and invoke graphing and animation commands. There should be higher-level commands for this, just as tools are provided for calculus, linear algebra, and so many other fields of mathematics.

This video will explore two external packages from the Maple Application Center, packages that provide tools for obtaining and manipulating Fourier and orthogonal-function expansions without the burden of computational micro-management. Once again, we will see tools that allow a resequencing of skills and concepts, tools that make for a more conceptual approach to mathematics.

Language: English
Duration: 55 Minutes
Related Terms: Fourier-series

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