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    Potential Scenario
    221

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    51

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    2020-Cline_Fasteen_Francis_Sullivan_Wendt-Vision_for_Projects_Across_Mathematics_Curriculum
    We consider the use of projects in math courses as a mechanism for promoting coding, communication, and interdisciplinary application of math skills. Final projects play an important role, but we also discuss several alternate types of projects.
    modelinginterdisciplinarywritingcodingprojecttechnical writing
    Modeling Scenario
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    256

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    3-092-WirelessPower-ModelingScenario
    We present an engineering application (wireless power transmission) modelled by a coupled system of two linear second-order differential equations with constant coefficients. One equation is homogeneous while the other one is non-homogeneous.
    DESMOSwireless power transmissionelectric circuitsKirchhoff's Voltage Law
    Potential Scenario
    211

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    83

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    2014-XM-Huang-Ordinary Differential Equation Model and its Application in the Prediction Control of Population
    In this paper, we study two kinds of ordinary differential equation models, i.e., Malthus model and Logistic model, and discuss their applications in the prediction control of population.
    population dynamicsLogistic modelMalthus ModelPopulation Prediction Control
    Article or Presentation
    177

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    79

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    SIMIODE Spring 2024 Webinars - WikiModel
    WikiModel is cloud-based application and requires no installation and is run via a web-browser to facilitate rapid implementation. Equations are typed in as they appear in a textbook. ODEs are automatically integrated via Runge-Kutta methods.
    modelingSoftwaretoolapplicationWikiModelmodeling cycle
    Potential Scenario
    208

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    82

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    2018-W_Hohenauer-Physical modelling based on first order ODEs
    An introduction in techniques to solve first order ODE´s is given. Barometric formula, charging and discharging of a capacitor including its application for AMV, magnetic induction and growth effects are discussed.
    dischargecapacitormagnetic fieldinductionmagnetic induction
    Potential Scenario
    197

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    102

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    2018-LA_Peletier-Ordinary Differential Equations in Pharmacodynamics
    Good mix of theory, application, solution technique in a number of areas of applications of differential equations. Develops qualitative behavior issues. Exercises, but not about models, more about the mathematics only.
    compartment modelpharmacokineticspharmacodynamicsorbitsturnover
    Potential Scenario
    145

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    74

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    2004-Ledzewicz-Schattler-Application of Control Theory in Modelling Cancer Chemotherapy
    In this paper we discuss how to incorporate more realistic medical aspects of chemotherapy which hitherto have been neglected in the models.
    optimal controldrug resistancepharmacokineticspharmacodynamicschemotherapy
    Potential Scenario
    137

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    49

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    2004-Charalampos_Toumasis-A mathematical diet model
    This article describes an application of simple differential equations in the field of dietetics as it may be presented to a calculus class or a high school mathematics club.
    dietdietetics
    Potential Scenario
    204

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    26

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    2014-John_Cain-Chemical Reaction Kinetics Mathematical Underpinnings
    The usual way of deriving kinetic equations involves application of the principle of conservation of mass in conjunction with the law of mass action. Here, examples of kinetic models for several basic processes are discussed.
    kineticsbiochemical reactionreactantsproducts
    Article or Presentation
    154

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    29

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    2013-Brian_Winkel-An_Optimal_Control_Model_in_Insect_Colonies
    we find and develop background material on an application of optimal control theory to model the evolutionary strategy of an insect colony to produce the maximum number of queen or reproducer insects in the colony at the end of a season.
    insect colonyoptimal controlparameter
    Modeling Scenario
    398

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    273

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    1-138-InnerEarDrugDelivery-ModelingScenario
    Students examine local drug delivery to the cochlea. The delivery system is modeled as a liquid mixing problem. Students formulate the differential equation, and solve the equation using separation of variables or integrating factor.
    concentrationdrug deliveryinner earcochleahearing loss
    Potential Scenario
    117

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    50

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    2007-Bellomo-De_Angelis-Delitala-Lecture Notes on Mathematical Modelling in Applied Sciences
    The Lectures Notes correspond to the first part of the course devoted to modelling issues to show how the application of models to describe real world phenomena generates mathematical problems to be solved by appropriate mathematical methods.
    spring massLegendre polynomialsintegro-differential equationskinetic theory
    Potential Scenario
    130

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    61

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    2017-Adolfo_Rumbos-Differential Equations and modeling
    The study of any phenomenon in the physical or biological sciences, in which continuity and differentiability assumptions about the quantities in question can be made, invariably leads to a differential equation, or a system of differential...
    pendulumLotka Volterra equationsexistenceuniqueness
    Technique Narrative
    468

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    109

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    7-005-OverViewLaplaceTransforms-TechniqueNarrative
    This is a specialized overview of Laplace Transform application to solving differential equations in Mathematica.
    integrationLaplace transformInverse Laplace transofrmintegration by parts
    Modeling Scenario
    350

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    613

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    1-155-CruiseControl-ModelingScenario
    In this project we illustrate the design of a proportional-integral-derivative (PID) cruise control algorithm for an automobile. PID control is one of the most common techniques in control engineering.
    PID controllerfeedback controlControl theorycruise controlautomobileclosed-loop controlinput-ouputblock diagram
    Potential Scenario
    254

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    85

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    2023-Roberto_Camassaa-Richard_McLaughlina-Tauberian identities and the connection to Wile E Coyote physics
    The application of the motion of a vertically suspended mass-spring system released under tension is studied focusing upon the delay timescale for the bottom mass as a function of the spring constants and masses.
    HangtimeTauberian IdentitiesRoad RunnerWile E. Coyote
    Potential Scenario
    160

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    80

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    2016-Helena_Sofia_Rodrigues-Application of SIR epidemiological model new trends
    In this paper, the basic transmission model is analyzed, as well as simple tools that allows us to extract a great deal of information about possible solutions. A set of applications - traditional and new - is described to show importance of this...
    epidemiologybasic reproduction numberSIR
    Potential Scenario
    163

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    69

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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.
    least-squares approximationSpline modelingMonte Carlo simulationsvariable selectionadaptive LASSO
    Free Online Textbook
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    2014-Andre_De Ross-Modeling Population Dynamics
    This course is intended as an introduction to the formulation, analysis and application of mathematical models that describe the dynamics of biological populations.
    predator-preycompetitionpopulationgrowthbifrucationtext
    Modeling Scenario
    357

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    265

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    1-142-WaterBottles-ModelingScenario
    This project involves the application of Newton's law of cooling to the study of insulated water bottles. Students have the option to conduct experiments with their own bottles outside of class or use data included in the student version.
    data collectionexperimenthalf-lifeNewton's Law of Coolingwater bottle