Tags: partial differential equation

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  1. 9-020-S-HeatDiffusion

    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...

  2. 9-005-S-InvasiveSpeciesModel

    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...

  3. 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...

  4. 2001-Noymer-Urban 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 Age-Structures 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:...

  5. Roux-Mathematical 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...

  6. 2013-DoboszczakForstall-Modeling 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...

  7. 2013-Rumbos-Mathematics 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...

  8. 2011-Rodriguez-PDE 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...

  9. 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...

  10. 2007-Steffensen-DEs 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...

  11. 2012-Kerckhove-Mathematica 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: 1-18.Abstract: Differential equation models for population dynamics are now standard fare in single-variable calculus. Building on these ordinary differential equation (ODE)...

  12. 2013-DoboszczakForstall-Modeling 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...

  13. 2014-EnderlingChaplain-Modeling 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): 1-7.Abstract: Using mathematical models to simulate dynamic biological processes has a long history. Over the past couple of decades or so, quantitative...

  14. 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 two-dimensional domain of the Puget Sound using a finite element numerical solution to the advection-diffusion equation coupled with a finite difference numerical solution to the Navier-Stokes equations. We offer two models of...

  15. Shawn Ryan

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  16. A Three-Fold 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 Three-Fold Approach to the Heat Equation:...

    https://simiode.org/blog/2016/10/a-three-fold-approach-to-the-heat-equation-data-modeling-numerics

  17. 1981-Berresford-Root 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...