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  1. 7-040-S-TankInterruptMixing

    22 Aug 2018 | Modeling Scenarios

    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.

  2. 2-001-Text-S-NumericalMethodsComparisons

    18 Aug 2018 | Technique Narratives

    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...

  3. 2-001-Text-T-NumericalMethodsComparisons

    18 Aug 2018 | Technique Narratives

    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...

  4. 1-067-T-ModelingWithSigmoidCurves

    18 Aug 2018 | Modeling Scenarios

    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:...

  5. 1-067-S-ModelingWithSigmoidCurves

    18 Aug 2018 | Modeling Scenarios

    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:...

  6. 1-032-T-DigoxinElimination

    17 Aug 2018 | Modeling Scenarios

    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...

  7. 1-032-S-DigoxinElimination

    17 Aug 2018 | Modeling Scenarios

    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...

  8. 1-131-T-CaffeineElimination

    15 Aug 2018 | Modeling Scenarios

    We model the concentration of caffeine 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 simple activity can be used to introduce differential...

  9. 1-130-S-AspirinAbsorption

    15 Aug 2018 | Modeling Scenarios

    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...

  10. 1-130-T-AspirinAbsorption

    15 Aug 2018 | Modeling Scenarios

    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...

  11. Kaabar, Mohammed-2018-A Friendly Introduction to Differential Equations

    29 Jul 2018 | Free Online Texts

    In this book, there are five chapters: The Laplace Transform, Systems of Homogeneous Linear Differential Equations (HLDE), Methods of First and Higher Orders Differential Equations, Extended Methods of First and Higher Orders Differential Equations, and Applications of Differential Equations. In...

  12. 1-081-S-TumorGrowth

    09 Jun 2018 | Modeling Scenarios

    Students will transform, solve, and interpret a tumor growth scenario using non-linear differential equation models. Two population growth models (Gompertz and logistic) are applied to model tumor growth. Students use technology to solve the Gompertz model and answer a series of questions...

  13. 1-081-T-TumorGrowth

    09 Jun 2018 | Modeling Scenarios

    Students will transform, solve, and interpret a tumor growth scenario using non-linear differential equation models. Two population growth models (Gompertz and logistic) are applied to model tumor growth. Students use technology to solve the Gompertz model and answer a series of questions...

  14. 6-018-S-ExploringSIRModel

    30 May 2018 | Modeling Scenarios

    Students will transform, solve, and interpret Susceptible Infected Recovered (SIR) models using systems of differential equation models. The project is progressively divided into three parts to understand, to apply, and to develop SIR models. Part one focuses on understanding and interpreting...

  15. 6-018-S-ExploringSIRModel

    30 May 2018 | Modeling Scenarios

    Students will transform, solve, and interpret Susceptible Infected Recovered (SIR) models using systems of differential equation models. The project is progressively divided into three parts to understand, to apply, and to develop SIR models. Part one focuses on understanding and interpreting...

  16. 6-018-T-ExploringSIRModel

    30 May 2018 | Modeling Scenarios

    Students will transform, solve, and interpret Susceptible Infected Recovered (SIR) models using systems of differential equation models. The project is progressively divided into three parts to understand, to apply, and to develop SIR models. Part one focuses on understanding and interpreting...

  17. 6-018-T-ExploringSIRModel

    30 May 2018 | Modeling Scenarios

    Students will transform, solve, and interpret Susceptible Infected Recovered (SIR) models using systems of differential equation models. The project is progressively divided into three parts to understand, to apply, and to develop SIR models. Part one focuses on understanding and interpreting...

  18. 6-026-T-IsleRoyaleModeling

    20 May 2018 | Modeling Scenarios

    The primary aim of this project is to draw a connection between differential equations and vector calculus, using population ecology modeling as a vehicle. This setting allows us to also employ multivariable optimization as a means of model fitting and multivariable integration in the context of...

  19. 1-105-T-AnimalFall

    15 Apr 2018 | Modeling Scenarios

    This project uses Newton's Second Law of Motion to model a falling animal with a resistance term proportional to cross sectional area of the animal, presumed to be spherical in shape.

  20. 3-095-T-ShotInWater

    05 Apr 2018 | Modeling Scenarios

    This project uses Newton's Second Law of Motion in conjunction with a quadratic model for the resistance experienced by a bullet moving through water to analyze a classic action movie scene: Do bullets moving through water slow as dramatically as depicted in the movies, so that someone a few...