I am an applied mathematics instructor with a background in mathematical biology and operations research. I am quite interested in mathematics education and have released many open-access...
2021-Bryan, Kurt - SIMIODE Textbook Code Materials Arranged by Software
04 Jul 2021 | Contributor(s):: Kurt Bryan
SIMIODE Textbook ResourcesPreambleThe various scripts and routines below are preliminary versions that support the exercises and projects throughout the book, especially those that involve data or large symbolic or numerical computations (they will be "official" in late August...
2020-Winkel, Brian - 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...
2020-Shelton, Therese - Remote Teaching Module - Car Suspensions
28 Jul 2020 | | Contributor(s):: Therese Shelton
In this modeling activity, students examine the spring-mass-dashpot 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....
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.
14 Jul 2020 | | Contributor(s):: Therese Shelton, Brian Winkel
We examine the spring-mass-dashpot 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.
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.
2020-Winkel, Brian - 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 spring-mass using...
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...
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 first-order ordinary differential equations (which...
2020-Winkel, Brian - 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...
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.
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...
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...
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...
24 Apr 2018 | | Contributor(s):: Michael Karls
The goal of this project is to set up and numerically solve a first-order 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...
2018-Karls, Michael - Presentation - 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, Two-Year College, Four-Year Institution at Joint Mathematics Meetings, San Diego CA, 9-13...
2012-Kerckhove, Michael - From Population Dynamics to Partial Differential Equations.
10 Sep 2017 | | Contributor(s):: Brian Winkel
Kerckhove, Michael. 2012. From Population Dynamics to Partial Differential Equations. The Mathematica Journal. 14: 1-18.See https://content.wolfram.com/uploads/sites/19/2012/12/Kerckhove.pdf. Abstract: Differential equation models for population dynamics are now standard...
2002-Fay, T. - The Pendulum Equation.
08 Sep 2017 | | Contributor(s):: Brian Winkel
Fay, T. 2001.The Pendulum Equation. Int. J. Math. Educ. Sci. Technology. 33(4): 505-519.See https://www.tandfonline.com/doi/abs/10.1080/00207390210130868. Abstract:We investigate the pendulum equation q’’(t) + l2 sin(q) = 0 and two approximations for...
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.