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  1. 9-001-Text-T-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...

  2. 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...

  3. 1-067-T-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:...

  4. 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:...

  5. 1-032-T-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...

  6. 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...

  7. 1-131-T-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 ``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...

  8. 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...

  9. 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...

  10. 1-130-T-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...

  11. 1-089-T-SpreadOfDisease

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

    Many students fear the term “Differential Equations.”  They think it is scary mathematics.  In this project I want to use the algebra based concept “difference quotient” to solve differential equations models with the help of Excel. That means even students with...

  12. 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.

  13. 1-054-T-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...

  14. 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...

  15. 6-007-S-FunctionsAndDerivativesInSIRModels

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

  16. 6-007-T-FunctionsAndDerivativesInSIRModels

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

    Given a system of differential equations, how do the solution graphs compare with the graphs of the differential equations? Students tackle this question using SIR models for well-known infectious diseases. The students view graphs both of solution curves and of the differential equations in the...

  17. 5-026-S-Evictions

    12 Aug 2018 | Modeling Scenarios | Contributor(s): Mary Vanderschoot

  18. 5-026-T-Evictions

    12 Aug 2018 | Modeling Scenarios | Contributor(s): Mary Vanderschoot

    In this project, students develop two SIS models to study eviction trends in a population of non-homeowner households using an actual eviction rate. (The Eviction Lab at Princeton University has developed a nationwide database of evictions based on 83 million eviction records.) As the first...

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

    29 Jul 2018 | Free Online Texts | Contributor(s): Mohammed K A Kaabar

    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...

  20. Kaabar, Mohammed-2018-A First Course in Linear Algebra: Study Guide for the Undergraduate Linear Algebra Course

    29 Jul 2018 | Free Online Texts | Contributor(s): Mohammed K A Kaabar

    There are five chapters: Systems of Linear Equations, Vector Spaces, Homogeneous Systems, Characteristic Equation of Matrix, and Matrix Dot Product. It has also exercises at the end of each chapter above to let students practice additional sets of problems other than examples, and they can also...