
2019Zhu, Linhe, Hongyong Zhao, and Haiyan Wang  Partial differential equation modeling of rumor propagation in complex networks with higher order of organization.
04 Apr 2020  Contributor(s):: Brian Winkel
Zhu, Linhe, Hongyong Zhao, and Haiyan Wang. 2019. Partial differential equation modeling of rumor propagation in complex networks with higher order of organization. Chaos: An Interdisciplinary Journal of Nonlinear Science....

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...

2009Wilson, R. Eddie  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 Flow. Presentation 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...

2001Noymer, Andrew  The transmission and Persistence of "Urban Legends": Sociological Application of AgeStructures 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. See https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2846379/ . Accessed 10 September...

2017Roux, Jean Mathematical Models in Air Quality Problems  Notes
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,...

2013Rumbos, Adolfo  Mathematicd Modeling
11 Sep 2017   Contributor(s):: Brian Winkel
Rumbos, Adolfo. 2013. Mathematics 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...

2017Emerson, Bruce  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...

2007Steffensen, Mogen  Differential Equations 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...

2012Kerckhove, Michael  From Population Dynamics to Partial Differential Equations.
10 Sep 2017   Contributor(s):: Brian Winkel
Kerckhove, Michael. 2012. From Population Dynamics to Partial Differential Equations. The Mathematica Journal. 14: 118.See https://content.wolfram.com/uploads/sites/19/2012/12/Kerckhove.pdf. Abstract: Differential equation models for population dynamics are now standard...

2013Doboszczak, Stefan and Virginia Forstall  Mathematical modeling by differential equations Case study: 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. See www.norbertwiener.umd.edu/Education/m3cdocs/Presentation2.pdf . Accessed 8 September...

2014Enderling, Heiko and Mark Chaplain  Mathematical Modeling of 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.See https://pubmed.ncbi.nlm.nih.gov/24283955/. Abstract: Using mathematical models to simulate dynamic biological processes has a long...

2017Trinka, Jordan  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://www.simiode.org/blog/2016/10/athreefoldapproachtotheheatequationdatamodelingnumerics

1981Berresford, Geoffrey C.  Differential Equations and Root Cellars
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...

9012SPDEGuitarTuning
04 Jun 2015   Contributor(s):: Brian Winkel
We present a derivation of a partial differential equation which models the motion of a string held at both ends, a case of the onedimensional wave equation. We immediately offer numerical solutions in a computer algebra system (we use Mathematica, but any...