
One Liner Laplace
28 Dec 2020  Contributor(s):: Brian Winkel
One liners, hey I got a million of 'em. Probably said by Henny Youngman, a famous 1950's TV Comedian!Another one is, "What's the use of happiness? It can't buy you money ."Henny Youngman Prepared by PROF Brian Winkel, Department of Mathematical...

Remote Teaching Module  Car Suspensions
28 Jul 2020   Contributor(s):: Therese Shelton
In this modeling activity, students examine the springmassdashpot that is part of a car suspension. We model a "quarter car'', meaning a single wheel, and compare effects of different masses, spring constants, damping coefficients, and the angle at which the assembly is installed....

3105SFrequencyResponse
22 Jul 2020   Contributor(s):: Brian Winkel
We describe the frequency response to a second order differential equation with a driving function as the maximum steady state solution amplitude and perform some analyses in this regard.

3034TCarSuspensions
14 Jul 2020   Contributor(s):: Therese Shelton, Brian Winkel
In this modeling activity, students examine the springmassdashpot that is part of a car suspension. We model a "quarter car'', meaning a single wheel, and compare effects of different masses, spring constants, damping coefficients, and the angle at which the assembly is...

3034SCarSuspensions
14 Jul 2020   Contributor(s):: Therese Shelton, Brian Winkel
We examine the springmassdashpot that is part of a car suspension, how the ride is related to parameter values, and the effect of changing the angle of installation. We model a "quarter car'', meaning a single wheel.

3027SBobbingDropping
10 Jul 2020   Contributor(s):: Brian Winkel
We present two exercises from a differential equations text in which we ask students to model (1) falling object experiencing terminal velocity and (2) bobbing block of wood in liquid. We model the motion using Newton's Second Law of Motion and Archimedes' Principle.

Laplace One Liner
04 Jul 2020   Contributor(s):: Brian Winkel
We offer a short Mathematica file in which we demonstrate the step by step commands for solving a second order, linear, constant coefficient, ordinary differential equation using Laplace Transforms and then we condense the entire set of instructions into one line of code  hence the name one liner.

Remote Teaching Module  Spring Design to Meet Specs at Minimum Costs
16 Jun 2020   Contributor(s):: Brian Winkel
We place here all the materials in support of the SIMIODE Remote Teaching Module  Spring Design to Meet Specs at Minimum Costs. This Module is about second order, linear, ordinary differential equations.The class lesson starts with building a model of a springmass using...

1088SRoomTemperature
15 Jun 2020   Contributor(s):: Tracy Weyand
Students will analyze temperature variations in a room using Newton's Cooling Law. In this model, the only influence on the indoor temperature is the (oscillating) outdoor temperature (as we assume the heating/cooling system is broken). The main goal of this project is for students to set up...

1136SMarriageAge
11 Jun 2020   Contributor(s):: Tracy Weyand
Students will build and analyze a model of the fraction of people who are married (for the first time) by a certain age. This model comes from a paper by Hernes and, in this project, is compared to another model used by Coale.These models are firstorder ordinary differential equations (which...

Remote Teaching Module  Modeling the Spread of Oil Slick
10 Jun 2020   Contributor(s):: Brian Winkel
We place here and in the Supporting Docs all the materials in support of the SIMIODE Remote Teaching Module  Modeling the Spread of Oil Slick.This module contains1) (Below and separate file in Supporting Docs) A brief Teaching Guide with an overview of the content and...

3031SSpringCost
28 May 2020   Contributor(s):: Brian Winkel
This is a situation where we are charged with analyzing costs for a spring to meet certain specifications.

9005SInvasiveSpeciesModel
08 Aug 2019   Contributor(s):: Eric Stachura
This scenario takes students through the development of an invasive species partial differential equation model. Basic models are discussed first, which lead students to eventually develop their own model which takes into account dispersion. Students will explore various Mathematica modules...

7011TextSCoupledSystemLaplace
31 Mar 2019   Contributor(s):: Mitaxi 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...

1062SBacterialGrowth
15 Sep 2018   Contributor(s):: Arati Nanda Pati
We offer students a simulation experience or data from a simulation and ask them to model the simulation using several approaches andusing EXCEL spreadsheet. In this particular modeling scenario, we know the exact solution and want to see how various models predict our expectations. We have used...

6070SBeerBubbles
24 Apr 2018   Contributor(s):: Michael Karls
The goal of this project is to set up and numerically solve a firstorder nonlinear ordinary differential equation (ODE) system of three equations in three unknowns that models beer bubbles that form at the bottom of a glass and rise to the top. The system solution is then used to verify...

Mike Karls  Incorporating a Modeling First Approach into a Traditional ODE Course
18 Jan 2018   Contributor(s):: Michael Karls
Incorporating a Modeling First Approach into a Traditional ODE Course by Mike Karls. Ball State University.A talk given at the AMS Special Session on Modeling in Differential Equations  High School, TwoYear College, FourYear Institution at Joint Mathematics Meetings, San Diego CA, 913 January...

2012KerckhoveMathematica Pop Dynamics Tutorial PDE
10 Sep 2017   Contributor(s):: Brian Winkel
Kerckhove, Michael. 2012. From Population Dynamics to Partial Differential Equations. The Mathematica Journal. 14: 118.Abstract: Differential equation models for population dynamics are now standard fare in singlevariable calculus. Building on these ordinary differential equation (ODE)...

2002FayThePendulumEquation
08 Sep 2017   Contributor(s):: Brian Winkel
Fay, T. 2001.The Pendulum Equation. Int. J. Math. Educ. Sci. Technology. 33(4): 505519.Abstract:We investigate the pendulum equation q’’(t) + l2 sin(q) = 0 and two approximations for it. On the one hand, we suggest that the third and fifthorder Taylor series...

1052SSaltWaterTanks
27 Nov 2016   Contributor(s):: Brian Winkel
We offer three mixing problems, of increasing order of difficulty, in which salt is coming into a tank of water and upon instantaneous mixing is leaving the tank.