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Technique Narratives (1-3 of 3)

  1. 2-005-Text-S-LinearizeItAll

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    09 Dec 2019 | | Contributor(s):: Don Hickethier

    Linear approximations are often used to simplify nonlinear ordinary differential equations (ODEs) for ease in analysis. The resulting linear approximation produces an ODE where closed form solutions may be obtained. A simple model using Torricelli's Law will compare the exact solution to...

  2. 7-011-Text-S-CoupledSystemLaplace

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    31 Mar 2019 | | Contributor(s):: Mitaxi Pranlal Mehta

    Differential equations and Laplace transforms are an integral part of control problems in engineering systems. However a clear explanation of the relationship of Laplace transforms with the differential equation formalism is difficult to find for coupled differential equations. Here we describe...

  3. 1-003-S-Text-IntroNumericalMethods

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    10 Jan 2019 | | Contributor(s):: Brian Winkel

    We ask students to develop two numerical methods for solving first order differential equations  geometrically and to compute numeric solutions and compare them to the analytic solutions for a number of different step sizes.