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    2017-Jean-Roux-Mathematical Models in Air Quality Problems
    Presents many models with analysis in air quality control. Starts with chemical kinetics models and builds complexity to PDE models.

    Keywords: air pollution effects on forest ecosystemsfinite volume methodboundary layerchemical kineticsfinite differenceemissionsdepositionsadvection

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    1994-M_Yamaguti-Discrete Models in Social Sciences
    Also, a finite difference model in sociology is given as a chaotic phenomenon.

    Keywords: economicschaossociologydiscretediscretization

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    2018-Adeniji-EtAl-InverseProblemHolling-TannerModel
    We consider the inverse problem of parameter identification of nonlinear system of ODEs for a specific case of complete information about solution of the Holling-Tanner model for finite number of...

    Keywords: goal functionabsolute error curvesinvers methodholling-Tanner model

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    Leslie/Lefkovitch Matrix Models for Age or Stage-structured Populations
    This Excel workbook uses the Leslie matrix model for population projection of age-class structured populations, and also allows Lefkovitch matrix models for stage-class structured populations.

    Keywords: survivalpopulation ecologyfecundityLeslie matrixeigenvalueseigenvectorsLefkovitch matrixage-class structured populationsstage-class structured populationsreproductive value

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    5-036-HalfCarVibration-ModelingScenario
    Vibration vehicle models provide an opportunity to integrate vehicle-based vibrations into a mechanical engineering vibrations course. The project is on a multiple-degree-of-freedom (MDOF)...

    Keywords: vibrationvehiclehalf-car modelfinite element analysisshock absorberssuspension

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    1-089-SpreadOfDisease-ModelingScenario
    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 only a College Algebra...

    Keywords: SIR modelProportionderivativedifference quotientSleeping Beautycontagious disease

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    2014-Bozkurt-Peker-Mathematical modelling of HIV epidemic and stability analysis
    A nonlinear mathematical model of differential equations with piecewise constant arguments is proposed. This model is analyzed by using the theory of both differential and difference equations to...

    Keywords: diseaselogisticHIVpiecewise constantIndia

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    2017-Justin_Krueger-Parameter Estimation Methods for Ordinary Differential Equation Models with Applications to Microbiology
    We demonstrate the feasibility of principal differential analysis using simulation studies and then apply the method to intestinal and vaginal microbiota data.

    Keywords: microbiologyLotka Volterrramicrobiota

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    3-069-HeatInBar-ModelingScenario
    The temperature distribution along a uniform slender bar due to conduction and convection is investigated through experimental, analytical, and numerical approaches.

    Keywords: heat transferexperimentconductionconvectionboundary conditionsfinite volume method

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    Trout modeling example
    This is an open-ended modeling example using difference equations and Algebra II skills.

    Keywords: population biology

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    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.

    Keywords: series soluotionpolynomial solutionsChebyshev polynomialsChebyshev differential equations

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    2-001-NumericalMethodsComparisons-TechniqueNarrative
    This material teaches the basics of numerical methods for first order differential equations by following graphical and numerical approaches. We discuss the order of accuracy of the methods and...

    Keywords: Euler's methodimproved Euler's methodRK3 methodsRK4 methodsorder of accuracyabsolute errorCPU time

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    1994-S_S_Everingham-C_Peter_Rydell-Modeling the Demand for Cocaine
    This is a report prepared for the Office of National Drug Control Policy of the United States Army by the Rand Corporation. The report contains lots of data and builds a two compartment difference...

    Keywords: drugstwo compartmentcocainedemand

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    2009-Brian_Winkel-Population_modelling_with_MandMs
    Several activities in which population dynamics can be modeled by tossing M&M’s® candy are presented.

    Keywords: simulationparameter estimationimmigrationdeathdifference equation

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    1999-Richard_Single-Different quotients-derivatives-and data through modeling with slime
    In this article, I present an experiment that can be conducted in a calculus class to investigate the difference quotient and the derivative, using mathematical modeling with student-collected data.

    Keywords: data analysisslimedifference quotientspread of slime

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    1991-Thoddi_Kotiah-Difference and differential equations in the mathematics of finance
    Many problems arising in the mathematics of finance involve identical money flows at regular time intervals and are typically solved by appropriate valuation at a focal date or by setting up an...

    Keywords: financesavingsgrowth fundinterestmortgageannuitydepreciation

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    1-095-RatingChessPlayers-ModelingScenarios
    The goal of this activity is to have students build a mathematical model involving a system of first order difference equations from a verbal description of a scenario.

    Keywords: simulationchessElo's methodchess rating

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    10-001-TilingHallway-ModelingScenario
    Students investigate difference equations through tiling hallways. They observe patterns in the tiling which lead to a difference equation. Solutions will be calculated by iteration. and the shift...

    Keywords: Geometryiterationtilingrecurrenceshift operatorpatternsclosed formanalytic solution

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    2015-Zhang-EtAl-On the Selection of ODE Models with Application to Predator-Prey Dynamical Models
    We propose a computationally inexpensive approach that employs statistical estimation of the full model, followed by a combination of a least squares approximation (LSA) and the adaptive Lasso.

    Keywords: least-squares approximationSpline modelingMonte Carlo simulationsvariable selectionadaptive LASSO

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    8-002-TrigSumRepresentation-TechniqueNarrative
    Students discover how to represent functions as sums of trigonometric functions and the value of such representations in many fields. This is an introduction to the study of Fourier Series.

    Keywords: estimationTrigonometryTrigonometric Functionssum of square errorsfinite sumFourier seriesFouriere sumspectrumapproximatiopn

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