21 Aug 2019 | | Contributor(s):: Kurt Bryan
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...
05 Mar 2019 | | Contributor(s):: Kurt Bryan
This material introduces the topic of ``stiffness'' for a system of ordinary differential equations (ODE's), through a series of examples.Stiffness is a property that a system of ODE's may possess that make it difficult to solve numerically with standard methods, and it is a...
10 Jan 2019 | | Contributor(s):: Brian Winkel
We ask students to develop two numerical methods for solving first order differential equations geometrically and to compute numeric solutions and compare them to the analytic solutions for a number of different step sizes.
18 Sep 2018 | | Contributor(s):: Eric Stachura, Robert Krueger
In this scenario, students will begin by carefully reading through the problem statement and uncovering which information is useful. Students will derive a system of differential equations which describe the flight path of a drone delivering a package. Techniques used to derive the analytical...
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...
18 Aug 2018 | | Contributor(s):: Suruchi Singh
The heat equation is an important partial differential equation (PDE) which describes the distribution of heat in a given region over time. Here we learn to solve a heat equation numerically. It is difficult to study the behavior of temperature in problems with interfaces analytically so...
The Logistic Differential Equation
03 Mar 2018 |
The Logistic Differential Equation. Notes. 7 pp.Goals from the notes:• MATH: To analyze the behavior of solutions of an ordinary differential equation geometrically .• MATH: To analyze stability behavior of equilibria of an ordinary differential equation geometricallyand...
03 Mar 2018 | | Contributor(s):: Nicola Bellomo
Bellomo, Nicola , Elena De Angelis, and Marcello Delitala. 2007. Lecture Notes on Mathematical Modelling in Applied Sciences, Lecture Notes. 168 pp.From the Opening of the Notes:The Lecture Notes collected in this book refer to a university course delivered at the Politecnico of Torino to...
28 Nov 2017 | | Contributor(s):: Brian Winkel
Dios, Araceli Queiruga. Ascensión Hernández Encinas, Jesús Martín Vaquero, Ángel Martín del Rey, Juan José Bullón Pérez, and Gerardo Rodríguez Sánchez. 2015. How Engineers deal with Mathematics solving...
2009-Wilson-Differential Equation Models for Forecasting Highway Traffic Flow
23 Sep 2017 | | Contributor(s):: Brian Winkel
Wilson, R. Eddie. 2009. Differential Equation Models for Forecasting Highway Traffic FlowPresentation at Conference on Traffic Modelling. The Open University, Milton Keynes, UK. 31 March. 32 slides. This talk builds the mathematical model for traffic flow and addresses the issues of...
2017Krueger-Parameter Estimation Methods in Microbioloogy
21 Sep 2017 | | Contributor(s):: Brian Winkel
Krueger, Justin M. 2017. Parameter Estimation Methods for Ordinary Differential Equation Models with Applications to Microbiology. PhD Thesis. 109 pp.Abstract: The compositions of in-host microbial communities (microbiota) play a significant role in host health, and a better understanding of the...
2005-Howard-Modeling with Differential Equations
10 Sep 2017 | | Contributor(s):: Brian Winkel
Howard P. 2005. Modeling with ODE. Notes. 48 pp.Great exposition and lots of Modeling Scenarios almost laid out completely as exercises.From the textOverviewA wide variety of natural phenomena such as projectile motion, the flow of electric current, and the progression of chemical reactions are...
2005-Lie-Intro to Math Modelling ODEs and Heat Equation
10 Sep 2017 | | Contributor(s):: Brian Winkel
2005 Lie, Knut–Andreas. Introduction to Mathematical Modelling: Ordinary Differential Equations and Heat Equations SINTEF ICT, Dept. Applied Mathematics PowerPoint slide. 45 slides. www.uio.no/studier/emner/matnat/ifi/INF2340/v05/foiler/sim02.pdf . Accessed 9...
09 Sep 2017 | | Contributor(s):: Brian Winkel
Gonze, Didier. 2013. Numerical methods for Ordinary Differential Equations. Notes. 15 pp.http://homepages.ulb.ac.be/~dgonze/TEACHING/numerics.pdf. Accessed 8 September 2017.The paper begins,“Differential equations can describe nearly all systems undergoing change. They are widespread...
2008-LipsmanEtAl-SCHOL Project Using Sofware Teach ODE
08 Sep 2017 | | Contributor(s):: Brian Winkel
Lipsman, R. L., J. E. Osborn, and J. M. Rosenberg. 2008. The SCHOL Project at the University of Maryland: Using Mathematical Software in the Teaching of Sophomore Differential Equations. Journal of Numerical Analysis, Industrial and Applied Mathematics. 3(1-2): 81-103.This is a publication of...
2009-EricksonEtAl-Computational Differential Equations Text
07 Sep 2017 | | Contributor(s):: Brian Winkel
Eriksson, K., D. Estep, P. Hansho, C. Johnson. 2009. Computational Differential Equations. 521 pp. http://www.thebookishblog.com/computational-differential-equations.pdf . Accessed 7 September 2017.From the Preface, “This book, together with the companion volumes Introduction to...
19 Sep 2016 | | Contributor(s):: Brian Winkel
Blomhøj, M, T.H. Kjeldsen, and J. Ottesen. 2014. Compartment Models.From the Introduction of this 47 page chapter the authors say,"Background: It is important to master the ability to develop models. Modeling of dynamical systems plays a very important role in applied science, and...
Presently. serving as an Assistant Professor of Mathematics in Department of Basic Sciences and Related Studies at Mehran University of Engineering and Technology, Jamshoro, Pakistan.Completed...