The Laplace Transform: Motivating the Definition | Zendy

Howard Dwyer | Zendy

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The Laplace Transform: Motivating the Definition

Author(s) -

Howard Dwyer

Publication year - 2011

Publication title -

codee journal

Language(s) - English

Resource type - Journals

ISSN - 2160-5211

DOI - 10.5642/codee.201108.01.05

Subject(s) - laplace transform , two sided laplace transform , laplace transform applied to differential equations , ode , wonder , integral transform , laplace–stieltjes transform , mathematics , mellin transform , inverse laplace transform , calculus (dental) , ordinary differential equation , sequence (biology) , mathematical analysis , epistemology , fractional fourier transform , fourier transform , differential equation , philosophy , medicine , fourier analysis , dentistry , biology , genetics

Most undergraduate texts in ordinary differential equations (ODE) contain a chapter covering the Laplace transform which begins with the definition of the transform, followed by a sequence of theorems which establish the properties of the transform, followed by a number of examples. Many students accept the transform as a Gift From The Gods, but the better students will wonder how anyone could possibly have discovered/developed it. This article outlines a presentation, which offers a plausible (hopefully) progression of thoughts, which leads to integral transforms in general, and the Laplace transform in particular.

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