
9020SHeatDiffusion
14 Oct 2019   Contributor(s):: Kimberly Spayd, James Puckett
This project guides students through experimental, analytical, and numerical techniques for understanding the heat (diffusion) equation with nonhomogeneous boundary conditions. In particular, students collect data and model a physical scenario in which heat energy diffuses through a long, thin...

9005SInvasiveSpeciesModel
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...

2009WilsonDifferential 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...

2001NoymerUrban Legend Sociological Application Epidemic Models
12 Sep 2017   Contributor(s):: Brian Winkel
Noymer, Andrew. 2001. The transmission and Persistence of “Urban Legends”: Sociological Application of AgeStructures Epidemic Models. J Math Sociol. Jan 1; 25(3): 1–98. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2846379/ . Accessed 10 September 2017.Abstract:...

RouxMathematical Models in Air Quality Problems
11 Sep 2017   Contributor(s):: Brian Winkel
Roux, Jean. Mathematical Models in Air Quality Problems. Notes. 26 pages.Presents many models with analysis in air quality control. Starts with chemical kinetics models and builds complexity to PDE models.Keywords: differential equation, model, finite difference, chemical kinetics, finite...

2013DoboszczakForstallModeling Traffic Flow
11 Sep 2017   Contributor(s):: Brian Winkel
Doboszczak, Stefan and Virginia Forstall. 2013. Mathematical modeling by differential equations Case study: Traffic flow. PowerPoint. 52 slides.This presentation addresses modeling traffic flow models and does a terrific job in explaining the model building of the partial differential...

2013RumbosMathematics Modeling
11 Sep 2017   Contributor(s):: Brian Winkel
Rumbos, Adolfo. 2013. Mathematica Modeling. Draft Text. 95 pp.Chapter 3 deals with traffic flow models and does a terrific job in explaining the model building of the partial differential equation for traffic density at position x and time t. It then goes on to solve and interpret the...

2011RodriguezPDE Models in Crime Modeling
11 Sep 2017   Contributor(s):: Brian Winkel
Rodriguez, Nancy. 2011. Applied PDEs in Crime Modeling and Biological Agregstion. PhD Thesis. 137 pp.Builds a model of burglaries in California city and uses tha model to reflect law enforcement efforts. Uses stability analysis. While highly theoretical the model is interesting and could...

Wonderful World of Differential Equations
11 Sep 2017   Contributor(s):: Brian Winkel
Wonderful World of Differential Equations. Notes. 52 pp. http://coccweb.cocc.edu/bemerson/PhysicsGlobal/Courses/PH213/PH213Learning/PH213WebR/documents/DiffEqIntro.pdf . Accessed 11 September 2017.This is a terrific set of noted with models and applications woven into the material at every...

2007SteffensenDEs in Finance and Life Insurance
10 Sep 2017   Contributor(s):: Brian Winkel
Steffensen, Mogen. 2007. Differential Equations in Finance and Life Insurance. In: Jensen, B.S. and Palokangas, T. (2007) Stochastic Economic Dynamics. CBS press.From the opening of the paper,“The mathematics of finance and the mathematics of life insurance were always...

2012KerckhoveMathematica Pop Dynamics Tutorial PDE
10 Sep 2017   Contributor(s):: Brian Winkel
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)...

2013DoboszczakForstallModeling Traffic Flow
09 Sep 2017   Contributor(s):: Brian Winkel
Doboszczak, Stefan and Virginia Forstall. 2013. Mathematical modeling by differential equations Case study: Traffic flow. PowerPoint Slides. 52 slides. University of Maryland. www.norbertwiener.umd.edu/Education/m3cdocs/Presentation2.pdf . Accessed 8 September 2017.Partial...

2014EnderlingChaplainModeling Tumor Growth And Treatment
05 Sep 2017   Contributor(s):: Brian Winkel
Enderling, Heiko and Mark Chaplain. 2014. Mathematical Modeling of Tumor Growth and Treatment. Current Pharmacological Design. 20(00): 17.Abstract: Using mathematical models to simulate dynamic biological processes has a long history. Over the past couple of decades or so, quantitative...

Modeling Contaminant Flow in the Puget Sound  Senior Thesis
01 Jun 2017   Contributor(s):: Jordan Christopher Trinka
In this paper, we mathematically model contaminant flow in a twodimensional domain of the Puget Sound using a finite element numerical solution to the advectiondiffusion equation coupled with a finite difference numerical solution to the NavierStokes equations. We offer two models of...

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A ThreeFold Approach to the Heat Equation: Data, Modeling, Numerics
13 Oct 2016 
Posted by Brian Winkel
James Puckett and Kimberly Spayd have authored a wonderful article in the current issue of PRIMUS with full citation:
Spayd, K. and J. Puckett. 2016. A ThreeFold Approach to the Heat Equation:...
https://simiode.org/blog/2016/10/athreefoldapproachtotheheatequationdatamodelingnumerics

1981BerresfordRoot Cellars and Differential Equations
25 Jun 2015   Contributor(s):: Geoffrey C. Berresford
Berresford, Geoffrey C. 1981. Differential Equations and Root Cellars. UMAP Unit 554. 23 pp. 23 pp. Available from http://www.comap.com. This is a classic module from UMAP in which the heat equation in one dimension is fully developed by using the standard technique of measuring the heat...