
2005TextSLinearizeItAll
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...

7011TextSCoupledSystemLaplace
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...

1003STextIntroNumericalMethods
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.