Tags: ordinary

Technique Narratives (1-4 of 4)

  1. 5-010-S-MatrixExponential

    12 Sep 2019 | | Contributor(s):: Kurt Bryan

    The matrix exponential is a powerful computational and conceptual tool for analyzing systems of linear, constant coefficient, ordinary differential equations (ODE's). This narrative offers a quick introduction to the technique, with examples and exercises. It also includes an introduction to...

  2. 7-011-Text-S-CoupledSystemLaplace

    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. 2-001-Text-S-NumericalMethodsComparisons

    18 Aug 2018 | | Contributor(s):: Swarn Singh

    It is not always possible to solve a differential equation analytically.This material makes an effort to teach the basics of numerical methods for first order differential equations by following graphical and numerical approaches. Here we also discuss the order of accuracy of the methods and...

  4. 7-005-S-Text-LaplaceTransformOverview

    06 Jun 2015 | | Contributor(s):: Brian Winkel

    The Laplace Transform is a mathematical construct that has proven very useful in both solving and understanding differential equations. We introduce it and show its power here. This is done in a Mathematica notebook with pdf provided.