Tags: Numerical Methods

All Categories (1-20 of 28)

  1. 1-124-S-WorldPopulation

    30 May 2020 | | Contributor(s):: Lenka Pribylova, Jan Sevcik, Pavel Morcinek, Brian Winkel

    We build models of world population using data to estimate growth rate.CZECH LANGUAGE VERSION  We have placed in Supporting Docs a Czech version of this Student Modeling Scenario. Name will be x-y-S-Title-StudentVersion-Czech.

  2. 2018-BlomhojEtAl-CompartmentModels

    01 Apr 2020 | | Contributor(s):: Brian Winkel

    2018-BlomhojEtAl-CompartmentModelsM. Blomhøj, T.H. Kjeldsen, and J. Ottesen. 2018. Compartment models. Lecture Notes 47 pp.    Chapter 1 - Compartment ModelsBackground: It is important to master the ability to develop models. Modeling of dynamical...

  3. 2010-Chicone-MathModelingANDChemicalKinetics

    26 Mar 2020 | | Contributor(s):: Brian Winkel

    2010-Chicone-MathModelingANDChemicalKineticsChicone, C.  2010. Mathematical Modeling and Chemical Kinetics. Notes. 14 pp.Motivated by physical science motion laws the author moves into kinetics and life science applications of differential equations.From early section...

  4. Adebesin Sodiq Ayobami


  5. 1-082-S-MirrorMirror

    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...

  6. 5-005-Text-S-StiffDifferentialEquations

    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...

  7. 1-003-S-Text-IntroNumericalMethods

    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. 

  8. 6-024-S-DronePackageDelivery

    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...

  9. 2-001-Text-S-NumericalMethodsComparisons

    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...

  10. 9-001-Text-S-SkinBurnModelNumericalMethods

    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...

  11. 6-070-S-BeerBubbles

    24 Apr 2018 | | Contributor(s):: Michael Karls

    The goal of this project is to set up and numerically solve a first-order nonlinear ordinary differential equation (ODE) system of three equations in three unknowns that models beer bubbles that form at the bottom of a glass and rise to the top.  The system solution is then used to verify...

  12. 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...

  13. 2007-Bellomo EtAl-LectureNotes-MathModelingInAppliedScience

    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...

  14. 2015-DiosEtAl-HowEngineersDealWithMathematicsSolvingDifferentialEquations

    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 Differential...

  15. 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...

  16. 2017-Krueger-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...

  17. 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...

  18. 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...

  19. 2013-Gonze-Numerical MethodsforODE

    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...

  20. 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 the...

Footer - a work in progress.