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  1. 2008-YangEtAl-A Differential Equation Model of HIV Infection of CD T-Cells with Delay

    02 Sep 2018 | Contributor(s):: Brian Winkel

    Yang, Junyuan , Xiaoyan Wang, and Fengqin Zhang. 2008. A Differential Equation Model of HIV Infection of CD T-Cells with DelayAbstract: An epidemic model of HIV infection of CD4+ T-cells with cure rate and delay is studied. We include a baseline ODE version of the model, and a...

  2. 1-053-S-SlimeSpread

    30 Aug 2018 | Modeling Scenarios | Contributor(s):: Brian Winkel

    We offer a video showing real time spread of a cylinder of slime and challenge students to build a mathematical model for this phenomenon.

  3. 6-003-S-SchoolFluEpidemic

    28 Aug 2018 | Modeling Scenarios | Contributor(s):: Darrell Weldon Pepper

    We offer a model of the spread of flu in a school dormitory and are asked to find when the flu levels reach their peak and explain long term behavior of the spread of the flu.

  4. 1-141-S-M&MGameRevisited

    27 Aug 2018 | Modeling Scenarios | Contributor(s):: Mehdi Hakim-Hashemi

    In this project students will learn to find a probability distribution using the classical M&M game in SIMIODE.

  5. 1-108-S-PoissonProcess

    27 Aug 2018 | Modeling Scenarios | Contributor(s):: Mehdi Hakim-Hashemi

    In this project students learn to derive the probability density function (pdf) of the Poisson distribution and the cumulative distribution (cdf) of the waiting time. They will use them to solve problems in stochastic processes.

  6. 1-015-Text-S-DimensionlessVariables

    25 Aug 2018 | Technique Narratives | Contributor(s):: Kurt Bryan

    This material introduces the idea of ``rescaling'' for ordinary differential equations (ODE's) by the introduction of dimensionless variables. In practice this is an extremely common and useful prelude to the analysis and solution of ODE's, and yet is not often taught in an...

  7. 1-118-S-SolowEconomicGrowth

    22 Aug 2018 | Modeling Scenarios | Contributor(s):: Yuri Yatsenko

  8. 7-040-S-TankInterruptMixing

    22 Aug 2018 | Modeling Scenarios | Contributor(s):: Norman Loney

    We present a differential equation model for the interrupted mixing of a tank with salt water. We offer two solution strategies (1) two step approach and (2) Laplace Transforms.

  9. 7-020-S-ThermometerInVaryingTempStream

    22 Aug 2018 | Modeling Scenarios | Contributor(s):: Norman Loney

    We present a differential equation model for the temperature of a mercury thermometer which is sitting in a stream of water whose temperature oscillates. We suggest a solving strategy which uses Laplace Transforms.

  10. 1-138-S-InnerEarDrugDelivery

    20 Aug 2018 | Modeling Scenarios | Contributor(s):: Jue Wang

    Hearing loss is difficult to treat due to the inner ear location and structure. Drawing from this challenging case, this scenario guides students to transform a treatment protocol into a mathematical model. Students engage in pre-clinical studies to examine local drug delivery to the cochlea....

  11. 4-055-S-ShatterWineGlass

    20 Aug 2018 | Modeling Scenarios | Contributor(s):: Jue Wang

    This module takes students through real life scenarios to examine resonance and its destructive power using differential equation models. What is resonance? How does it happen? Why is it important? Three cases are presented: shattering a wine glass, collapse of a suspension bridge, and crash of...

  12. 2-001-Text-S-NumericalMethodsComparisons

    18 Aug 2018 | Technique Narratives | 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...

  13. 9-001-Text-S-SkinBurnModelNumericalMethods

    18 Aug 2018 | Technique Narratives | 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...

  14. 1-067-S-ModelingWithSigmoidCurves

    18 Aug 2018 | Modeling Scenarios | Contributor(s):: Natali Hritonenko

    The assignment considers two well-known models of population growth, Verhulst-Pearl and Gompertz models, for which qualitative and quantitative analyses are provided. The graphs of the corresponding functions have a sigmoidal or S-shape. The assignment contains two opposite, but related tasks:...

  15. 1-032-S-DigoxinElimination

    17 Aug 2018 | Modeling Scenarios | Contributor(s):: Therese Shelton

    We model the concentration of digoxin eliminated from the human body at a rate proportional to the concentration. This is a ``first-order reaction'' in the language of pharmacokinetics -- the study of how drugs move in the body. This activity can be used to introduce compartmentalized...

  16. 1-131-S-CaffeineElimination

    15 Aug 2018 | Modeling Scenarios | Contributor(s):: Therese Shelton

    We model the concentration of caffeine eliminated from the human body at a rate proportional to the concentration. This is a reaction in the language of pharmacokinetics -- the study of how drugs move in the body. This simple activity can be used to introduce differential equations, and it can...

  17. 1-130-S-AspirinAbsorption

    15 Aug 2018 | Modeling Scenarios | Contributor(s):: Therese Shelton

    We model the amount of aspirin absorbed by the human body at a constant rate. This is a ``zero-order reaction'' in the language of pharmacokinetics -- the study of how drugs move in the body. This simple activity can be used to introduce differential equations and it can be used to...

  18. 1-089-S-SpreadOfDisease

    15 Aug 2018 | Modeling Scenarios | Contributor(s):: Shinemin Lin

    In this project we use the algebra based concept “difference quotient” to solve differential equations models with the help of Excel.

  19. 1-054-S-GrowthInFarmland

    14 Aug 2018 | Modeling Scenarios | Contributor(s):: Richard Spindler

    An enriching project developing a model from data with missing temporal information is described. Students fit functions to the data that leads to the creation of a differential equations model, which they then are required to analyze in multiple ways. Different fits, modeling approaches, and...

  20. 6-007-S-FunctionsAndDerivativesInSIRModels

    12 Aug 2018 | Modeling Scenarios | Contributor(s):: Meredith Greer