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    2012-Michael_Kerckhove-From Population Dynamics to Partial Differential Equations
    This article illustrates PDE models for location-dependent carrying capacities, migrations, and the dispersion of a population.

    Keywords: population dynamicslogistic equationlocation-dependent carrying capacities

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    2011-Yuan-EtAl-Real life applications of ODEs for Undergraduates
    This study introduces real-life mathematical theories and models of international relationships suitable for undergraduate ordinary differential equations, by investigating contradicts between...

    Keywords: arms raceRichardson modelBattle of Curupaytíinternational relationships

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    2008-Padir-EtAl-Teaching Differential Equations in a Diverse Classroom
    The interesting portion of this paper are the descriptions of student projects offered: Vibrations of a 3-Story Building in an Earthquake, Triple Pendulum, Nonlinear Circuit. Phase portraits were...

    Keywords: circuitearthquakevibrationpendulumbuikldingtriple pendumlumnonlinear circuit

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    2001-Knisley-Kerley-Using data to motivate the models used in introductory differential equations
    In this paper, the data itself is used to motivate mathematical models in introductory mathematics courses. In doing so, various regression and optimization techniques are illustrated.

    Keywords: regressionlogisticTorricelli's Lawgrowthperiodic process

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    1999-McCartney-Carey-Modelling Traffic Flow Solving and Interpreting Differential Equations 
    A simple mathematical model for how traffic flows along a road is introduced.

    Keywords: traffictraffic flow

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    1999-Lomen-Lovelock-Data Sets from text Differential Equations Graphics-Models-Data
    Data selected by field is presented, e.g., chemistry, electricity, growth, motion, population, miscellaneous.

    Keywords: dataEstimate

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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...

    Keywords: kineticsbiochemical reactionreactantsproducts

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    1997-Jeff_Graham-Julia_Barnes-A Laboratory Experience for Students of Differential Equations Using RLC Circuits
    Acknowleging that applied mathematics courses rarely offer any hand-on experiences the authors constructed an RLC circuit from which they collected data and validated the differential equation of...

    Keywords: datacollectionslaboratorycircuitRLC

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    2011-Brian_Winkel-Cross_coursing_in_mathematics-physical_modeling_in_differential_equations_crossing_to_discrete_dynamical_systems
    We give an example of cross coursing in which a subject or approach in one course in undergraduate mathematics is used in a completely different course.

    Keywords: differential equationsmathematical modeldifference equationcross courseconvert

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    2012-R_B_Ogunrinde-J_Sunday-On_some_models_based_on_second_order_differential_equations
    This paper presents some models based on second order differential equations. This is a very straightforward article with good explanations of modeling assumptions.

    Keywords: combatcombat modelspecies interaction

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    2016-Simon_Malham-Differential_Equations_and_Linear_Algebra
    This is a nice set of notes on which a course can be based. There is ample material on first and second order, linear systems, and Laplace Transform methods for setting up and solving differential...

    Keywords: textbooklinear algebraLaplace transform

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    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...

    Keywords: Integrating Factor

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    1-054-GrowthInFarmland-ModelingScenario
    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,...

    Keywords: fittingfarmfarmland

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    6-006-ZombieGameHvZ-ModelingScenario
    Invented in 2005, Humans vs. Zombies, or HvZ, is a game of tag, predominantly played at US college campuses. In this activity, students use systems of non-linear differential equations to model...

    Keywords: zombiesSIR modelsGame

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    6-016-PandemicModeling-ModelingScenario
    The recent coronavirus outbreak has infected millions of people worldwide and spread to over 200 countries. How can we use differential equations to study the spread of coronavirus?

    Keywords: population dynamicsinfectious diseasediseaseEbolaeSIR modelsCOVID19pandemicepidemicreproduction number

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    2015-Khan-EtAl-How differential equations influence the tumor growth via mathematical models
    This work demonstrates the importance of differential equations to develop mathematical model of tumor growth.

    Keywords: tumorcancdercancerous cellsimmunotherapymalignant

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    2017-Craig_Tracy-Lectures on Differential Equations
    These notes are for a one-quarter course in differential equations. The approach is to tie the study of differential equations to specific applications in physics with an emphasis on oscillatory...

    Keywords: physicsoscillation

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    1981-Geoffrey_Berresford-Differential Equations and Root Cellars
    This is a classic module from UMAP in which the heat equation in one dimension is fully developed by using the standard technique of measuring the heat flow in and out of a small element of mass...

    Keywords: temperaturethermal conductivityheat flowthermal diffusivityroot cellar

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    2007-Joseph_Myers-Brian_Winkel-Modeling_a_Mystery_Circuit_in_Mathematics_Class_Using_Differential_Equations_Laplace_Transforms_and_Transfer_Functions
    We discuss the introduction, student discovery, and teaching of a system of differential equations which model a circuit.

    Keywords: circuitLaplace transformtransfer functionmystery circuitvoltage frequencytwo loop circuit

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    2011-Richard_Fitzpatrick-Newtonian_Dynamics
    This 300 page text is packed with motivational physics. Indeed, Professor Fitzpatrick brings us to the origins of why differential equations are the dominant tools of mathematics in the study of...

    Keywords: modelingtextbookphysicsbifurcation

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