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    Modeling Scenario
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    1-070-FisheryHarvest-ModelingScenario
    Students model with logistic growth, harvesting, and diffusion in analyzing ocean fisheries of the Atlantic cod. We help students build models, ever more complex, to capture physical realities. At each stage we ask students to reflect on the model.
    logistic Diffusion management harvest fishery
    Modeling Scenario
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    1-008-HangTime-ModelingScenario
    We present a modeling opportunity for students in which they model the vertical position of a basketball player taking a jump shot. The goal of the scenario is to get students to consider the meaning of the notion ``hang-tune.''
    gravity hang tim Newton's Second Law of Motion jump shot
    General Resource
    63

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    14

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    Instructor Solutions for SIMIODE Textbook
    This is a complete set of solutions for all projects, exercises, and reading exercises and is restricted to those registered as Instructors
    Modeling Scenario
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    6-001-Epidemic-ModelingScenario
    This paper presents real-world data, a problem statement, and discussion of a common approach to modeling that data, including student responses. In particular, we provide time-series data on the number of boys bedridden due to an outbreak of...
    data difference equations parameter estimation continuous epidemic discrete boarding school
    Modeling Scenario
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    28

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    3-065-UpDown-ModelingScenario
    We model the height of a launched object which is subject to resistance proportional to velocity during its flight. We ask questions about the motion as well, e.g., highest point or apex and terminal velocity.
    terminal velocity Newton's Second Law of Motion velocity motion apex
    Modeling Scenario
    36

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    37

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    1-145-FastPitch-ModelingScenario
    We consider the problem of comparing pitch velocities using measurement methods in different eras of baseball.
    Measurement resistance air resistance baseball pitcher fast
    Modeling Scenario
    31

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    76

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    1-076-ClimateBifurcation-ModelingScenario
    We cover simple zero and one dimensional models for the mean temperature of the Earth. These models can exhibit bifurcations.
    energy balance climate energy albedo Hysteresis bifurcation ice-age greenhouse balance Stefan Boltzmann Law
    Modeling Scenario
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    16

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    1

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    3-104-BungeeJumping-ModelingScenario
    In this project, students design a bungee jumping cord (cross-sectional area and length) that will keep jumpers safe. Students communicate their recommendations as a letter to a client interested in starting a bungee jumping business.
    design falling mass spring\ bungee elesticity recommendation consult
    Technique Narrative
    33

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    9

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    1-015-DimensionlessVariables-TechniqueNarrative
    This material introduces the idea of ``rescaling'' for ordinary differential equations (ODE's) by the use of dimensionless variables. In practice this is an extremely common and useful prelude to the analysis and solution of ODE's.
    linearization dimensional analysis time scale scaling dimensionless variables spatial scale
    Technique Narrative
    37

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    14

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    9-001-SkinBurnModelNumericalMethods-TechniqueNarrative
    The heat equation is an important partial differential equation (PDE) which describes the distribution of heat in a given region over time. Numerical methods play an important role in solving these.
    Maternal-Fetal interface heat equation Conservation of Energyt heat flux Euler's forward method central difference skin burn hyperthermia thermal conductivity layers
    Modeling Scenario
    37

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    13

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    7-011-CoupledSystemLaplace-ModelingScenario
    Differential equations and Laplace transforms are an integral part of control problems in engineering systems. We consider a baby warming device.
    transfer function polycarbonate baby heater coupled system heating
    Technique Narrative
    34

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    14

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    7-006-LaplaceTransformBirth-TechniqueNarrative
    We present a way of introducing the Laplace Transform as the continuous analogue of a power series expression of a function.
    Transformations power series
    Technique Narrative
    56

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    15

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    5-030-LinNonHomoSystemSol-TechniqueNarrative
    We offer strategies for solving linear systems of nonhomogeneous differential equations using a conjectured solution strategy for a system of constant coefficient, linear, n
    strategies discovery learning eigenvectors eigenvalue
    Technique Narrative
    36

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    12

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    5-012-LinearSystemConjecture-TechniqueNarrative
    Students go from the solution for y'(t) = k*y(t) to a natural extension to the solution conjecture of a system of two constant coefficient, homogeneous, linear differential equations introducing eigenvalues and eigenvectors through student...
    discovery learning conjecture solution substitution
    Technique Narrative
    31

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    8

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    7-005-OverViewLaplaceTransforms-TechniqueNarrative
    This is a specialized overview of Laplace Transform application to solving differential equations in Mathematica.
    integration Laplace transform Inverse Laplace transofrm integration by parts