We are migrating our materials to QUBES. Please pardon the construction. Close

Resources

Applied Filters
    Text Search:
    Keywords:
    Resource Type
    Differential Equation Type
    Technique
    Qualitative Analysis
    Application Area
    Course
    Course Level
    Lesson Length
    Technology
    Approach
    Skills
    Key Scientific Process Skills
    Assessment Type
    Pedagogical Approaches
    Vision and Change Core Competencies - Ability
    Principles of How People Learn
    Bloom's Cognitive Level
    Includes clear efforts on Issues
    Technique Narrative
    68

    views

    105

    downloads

    0

    comments

    5-005-StiffDifferentialEquations-TechniqueNarrative
    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 posses that make it difficult to solve numerically.
    Euler's method explicit methods implicit methods stiff sitffness stiff differential equation instability
    Technique Narrative
    405

    views

    13

    downloads

    0

    comments

    3-090-ChebyshevPolynomialSolution-TechniqueNarrative
    The Chebyshev equation is presented as a vehicle to view series solutions techniques for linear, second order homogeneous differential equations with non-constant coefficients.
    series soluotion polynomial solutions Chebyshev polynomials Chebyshev differential equations
    Technique Narrative
    67

    views

    18

    downloads

    0

    comments

    2-005-LinearizeItAll-TechniqueNarrative
    Linear approximations are often used to simplify nonlinear ordinary differential equations (ODEs) for ease in analysis. The resulting linear approximation produces an ODE where closed form solutions may be obtained.
    computation error Torricelli's Law data fitting linear approximation
    Technique Narrative
    51

    views

    21

    downloads

    0

    comments

    1-030-RandomPerturbation-TechniqueNarrative
    After a brief historical view of this problem, we will demonstrate the derivation of first order linear differential equations with random perturbations.
    random perturbation Brownian motion Langevin equation Riemann-Steiltjes integral Wiener process Ito's calculus
    Technique Narrative
    46

    views

    50

    downloads

    0

    comments

    1-010-AtmosphericCO2Bifurcation-TechniqueNarrative
    Students are introduced to the concept of a bifurcation in a first-order ordinary differential equation (ODE) through a modeling scenario involving atmospheric carbon dioxide whish is taken as a parameter and temperature is a function of time.
    carbon dioxide Surface Atmosphere Exchange bifurcation fold bifurcation saddle node
    Technique Narrative
    60

    views

    21

    downloads

    0

    comments

    1-009-Bifurcation-TechniqueNarrative
    We lead students to investigate first-order differential equations that contain unknown parameters. Students discover what happens to the qualitative behavior of solutions to these equations as these parameters vary.
    bifurcation qualitative behavior bifurcation diagram
    Technique Narrative
    48

    views

    30

    downloads

    0

    comments

    1-002-IntegratingFactor-TechniqueNarrative
    We develop a strategy to solve first order differential equations by transforming one side of the equation to the derivative of a product of two functions, thereby making it easy to antidifferentiate that side.
    Integrating Factor
    Technique Narrative
    63

    views

    22

    downloads

    0

    comments

    1-001-SepartionOfVariables-TechniqueNarrative
    We discuss strategies to solve first order, ordinary differential equations with mathematical models when the variables may be separated.
    solutions strategy method applications
    Modeling Scenario
    49

    views

    36

    downloads

    0

    comments

    1-033-SouthernBarbeque-ModelingScenario
    We offer raw data collected from two thermometers used in the smoking process of Southern barbecue. One thermometer measures the temperature inside of the smoke chamber and the other measures the internal temperature of the meat.
    nonlinear regression logistic Newton's Law of Cooling-Warming barbecue
    Modeling Scenario
    57

    views

    21

    downloads

    0

    comments

    1-029-ConeToCubeFlow-ModelingScenario
    An inverted right circular cone with a hole at the bottom is suspended above an open-topped cube which also has a hole in the center of the bottom. The cone is filled with water and we model water flow from cone to cube and out the bottom of the...
    water flow Torricelli's Law cone cube
    Modeling Scenario
    48

    views

    24

    downloads

    0

    comments

    1-025-MixingItUp-ModelingScenario
    Students build three different models for levels of salt in a tank of water and at each stage the level of complexity increases with attention to nuances necessary for success.
    compartment salt tank mixing
    Modeling Scenario
    69

    views

    23

    downloads

    0

    comments

    1-024-MalariaControl-ModelingScenario
    This project offers students a chance to make policy recommendations based on the analysis of models using both linear (exponential decay) and non-linear (logistic growth) differential equations.
    population dynamics malaria Policy Decision-making Euler's method pharmacokinetics mosquito improved Euler's method Huen's method US Army
    Modeling Scenario
    49

    views

    19

    downloads

    0

    comments

    1-021-FeralCatControl-ModelingScenario
    Students act as professional mathematical consultants and write a report analyzing the client's problem. The client company is a fictional organization which advocates for the use of trap-neuter-return (TNR) as a control method for feral cat...
    population growth control feral cats population control neuter trap-kill trap-neuter-return
    Modeling Scenario
    41

    views

    16

    downloads

    0

    comments

    1-020-IceMelt-ModelingScenario
    We offer up the claim of a store catalog that its ice ball mold allows users to ``. . . make ice balls that outlast cubes and won't water drinks down.'' We ask students to build a mathematical model to defend or contradict this claim.
    sphere ice melt cube
    Modeling Scenario
    37

    views

    12

    downloads

    0

    comments

    1-014-DrainingContainers
    Given two rectangular circular cylinders of water with the same volume, but different radii, with a small bore hole of same radius on the center of the bottom through which water exits the cylinder, which empties faster?
    containers tank flow Torricelli's Law draining fixed volume