
5010SMatrixExponential
12 Sep 2019  Technique Narratives
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...

5010TMatrixExponential
12 Sep 2019  Technique Narratives
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...

1082TMirrorMirror
21 Aug 2019  Modeling Scenarios
This project models the ``Foucault Knife Edge Test,'' an optical test commonly used by amateur astronomers who make their own mirrors for reflecting telescopes. The goal of the test is to estimate the shape of the surface of a mirror from optical reflection data. The model results in a...

1109TEmployeeAttrition
25 Mar 2019  Modeling Scenarios
This scenario models the loss of employees and the employer's attempt to retain them through stock options. It most naturally is solved with a firstorder linear decay model with two populations. This is intended for introductory students and is paired well with exponential growth/decay...

2017Bonin EtAl  Math Modeling Based on ODE for Vaccinology
09 Dec 2018  Potential Scenario Ideas
Bonin, C.R.B. Et al. 2017. Mathematical modeling based on ordinary differential equations: A promising approach to vaccinology. Human Vaccines and Immunotherapy. 13(2): 484–489.Abtract: New contributions that aim to accelerate the development or to improve the efficacy and safety of...

2001TextSNumericalMethodsComparisons
18 Aug 2018  Technique Narratives
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...

2001TextTNumericalMethodsComparisons
18 Aug 2018  Technique Narratives
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...

6018SExploringSIRModel
30 May 2018  Modeling Scenarios
Students will transform, solve, and interpret Susceptible Infected Recovered (SIR) models using systems of differential equation models. The project is progressively divided into three parts to understand, to apply, and to develop SIR models. Part one focuses on understanding and interpreting...

6018TExploringSIRModel
30 May 2018  Modeling Scenarios
Students will transform, solve, and interpret Susceptible Infected Recovered (SIR) models using systems of differential equation models. The project is progressively divided into three parts to understand, to apply, and to develop SIR models. Part one focuses on understanding and interpreting...

6070TBeerBubbles
24 Apr 2018  Modeling Scenarios
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...

2016CamporesiImpulsive response method using factorization.
03 Mar 2018  Potential Scenario Ideas
Camporesi, Roberto. 2016. A fresh look at linear ordinary differential equations with constant coefficients. Revisiting theimpulsive response method using factorization. Int. J. Math. Educ. Sci. Technol. 47(1): 8299Summary: We present an approach to the impulsive response method for solving...

2003RasmussenKeynesLinesOfEigenVectorsSolutionsToSytemsOfLinearDifferentialEquations
03 Mar 2018  Potential Scenario Ideas
Rasmussen, Chris and Michael Keynes. 2003. Lines of Eigenvectors and Solutions to Systems of Linear Differential Equations. PRIMUS. 13(4): 308320.Abstract: The purpose of this paper is to describe an instructional sequence where students invent a method for locating lines of...

Mike Karls  Incorporating a Modeling First Approach into a Traditional ODE Course
18 Jan 2018  Presentations
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...

2012KerckhoveMathematica Pop Dynamics Tutorial PDE
10 Sep 2017  Potential Scenario Ideas
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)...

2012NokkaewEtAlEstimation Of Algae Growth Mode lParameters Using Genetic Algorithm
08 Sep 2017  Potential Scenario Ideas
Nokkaew, A. Et Al. Estimation of Algae Growth Model Parameters by a Double Layer Genetic Algorithm. WSEAS TRANSACTIONS on COMPUTERS. 11(11): 377386. http://www.wseas.org/multimedia/journals/computers/2012/56122.pdf . Accessed 7 September 2017.ABSTRACT: This paper presents a double layer...

2002FayThePendulumEquation
08 Sep 2017  Potential Scenario Ideas
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...

A Particular Solutions Formula For Inhomogeneous Arbitrary Order Linear Ordinary Differential Equations
24 May 2017  Articles and Publications
A particular solution for any nonhomogeneous linear second, third, and fourth order ordinary differential equation is generally determined. Applying what was determined thus; and following by example a particular solution formula for arbitrary order is obtained. Finding a particular solutions to...

On the General Solution of Initial Value Problems of Ordinary Differential Equations Using the Method of Iterated Integrals
10 Jan 2017  Articles and Publications
Our goal is to give a very simple, effective and intuitive algorithm for the solution of initial value problem of ordinary differential equations of first order and higher order with constant, variable or nonlinear coefficients and systems of these ordinary differential equations. We find...

1033TSouthernBarbeque
22 Jun 2016  Modeling Scenarios
We offer raw data collected from two thermometers used in the smoking process of Southern barbecue. One thermometer measures the temperature inside of the smoke chamber and the other measures the internal temperature of the meat. This data can be used to model and predict the amount...

Different Technologies in Use
22 Feb 2016  Articles and Publications
We offer a student posting at the Differential Equations and Fourier Series group found on FaceBook to illustrate the different technologies in use. We believe what follows illustrates the different technologies faculty and students can use and their preferences for many different reasons....