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...
04 Apr 2020 | | Contributor(s):: Brian Winkel
2016-BoninEtAl-MathModelsApproachInVaccinologyBonin, Carla Rezende Barbosa, Guilherme Cortes Fernandes, Rodrigo Weber dos Santos, and Marcelo Loboscoa. 2016. Mathematical modeling based on ordinary differential equations: A promising approach to vaccinology. Hum...
12 Sep 2019 | | Contributor(s):: Kurt Bryan
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...
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...
2017-Bonin EtAl - Math Modeling Based on ODE for Vaccinology
09 Dec 2018 | | Contributor(s):: Brian Winkel
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...
18 Aug 2018 | | Contributor(s):: Swarn Singh
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...
30 May 2018 | | Contributor(s):: Stanley Florkowski, Ryan Miller
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 SIR...
2016-Camporesi-Impulsive response method using factorization.
03 Mar 2018 | | Contributor(s):: Roberto Camporesi
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): 82-99Summary: We present an approach to the impulsive response method for solving...
03 Mar 2018 | | Contributor(s):: Chris Rasmussen, Michael Keynes
Rasmussen, Chris and Michael Keynes. 2003. Lines of Eigenvectors and Solutions to Systems of Linear Differential Equations. PRIMUS. 13(4): 308-320.Abstract: The purpose of this paper is to describe an instructional sequence where students invent a method for locating lines of...
2012-NokkaewEtAl-Estimation Of Algae Growth Mode lParameters Using Genetic Algorithm
08 Sep 2017 | | Contributor(s):: Brian Winkel
Nokkaew, A. Et Al. Estimation of Algae Growth Model Parameters by a Double Layer Genetic Algorithm. WSEAS TRANSACTIONS on COMPUTERS. 11(11): 377-386. http://www.wseas.org/multimedia/journals/computers/2012/56-122.pdf . Accessed 7 September 2017.ABSTRACT: This paper presents a double layer genetic...
A Particular Solutions Formula For Inhomogeneous Arbitrary Order Linear Ordinary Differential Equations
24 May 2017 | | Contributor(s):: CLAUDE MICHAEL CASSANO
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 | | Contributor(s):: Ahsan Amin
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...
22 Jun 2016 | | Contributor(s):: Troy Henderson
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...
2011-Zhao-Systems Biology - Differential Equations - Survey
24 Jun 2015 | | Contributor(s):: D. I. Zhao
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...
06 Jun 2015 | | Contributor(s):: Brian Winkel
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. This is done in a Mathematica notebook with pdf provided.
06 Jun 2015 | | Contributor(s):: Karen Bliss
Adapted from 1-11-Kinetics, SIMIODE modeling scenario. We help students see the connection between college level chemistry course work and their differential equations coursework. We do this through modeling kinetics, or rates of chemical reaction. We study zeroth, first, and...
04 Jun 2015 | | Contributor(s):: Brian Winkel
We build the infinite set of first order differential equations for modeling a stochastic process, the so-called 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...
04 Jun 2015 | | Contributor(s):: Brian Winkel
We provide data (in EXCEL and Mathematica files) on evaporation of 91% isopropyl alcohol in six different Petri dishes and one conical funnel and on evaporation of water in one Petri dish. We ask students to develop a mathematical model for the rate of evaporation for the alcohol mixture...