
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...

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...

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...

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...

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...

2011Zhao Systems Biology  Differential Equations  Survey
24 Jun 2015  Potential Scenario Ideas
Zhao, D. I. 2011. Differential Equation Models for Systems Biology: A Survey. Computational Analysis and Modeling, Lousiana Tech University, Ruston LA USA. 30 pp. http://www.advancedcomputing.cn/sys_bio_review.pdf . Accessed 22 June 2015.Abstract: In this paper, we will...

TextOrdinary Differential Equations
23 Jun 2015  Articles and Publications
Nagy, Gabriel. 2015. Ordinary Differential Equations. Mathematics Department, Michigan State University, East Lansing MI USA. 333 pp. http://users.math.msu.edu/users/gnagy/teaching/ode.pdf . Accessed 22 June 2015.This text is free and downloadable. The coverage is formal with proofs of...

7005TTextLaplaceTransformOverView
06 Jun 2015  Technique Narratives
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.

3001TSpringMassDataAnalysis
05 Jun 2015  Modeling Scenarios
We offer data on the position of a mass at the end of a spring over time where the spring mass configuration has additional damping due to taped flat index cards at the bottom of the mass. The general modeling of a spring mass configuration and the estimation of parameters form the core of this...

6030TSaltTorricelli
04 Jun 2015  Modeling Scenarios
We build on a model (Torricelli's Law ) for the height of a falling column of water with a small hole in the container at the bottom of the column of water. We use data from one video of a falling column of water and the resulting Torricelli's Law model to estimate a parameter in...

1027TStochasticProcesses
04 Jun 2015  Modeling Scenarios
We build the infinite set of first order differential equations for modeling a stochastic process, the socalled birth and death equations. We will only need to use integrating factor solution strategy or DSolve in Mathematica for success. We work to build our model of random events which...