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    Technique Narrative
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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 interfaceheat equationConservation of Energytheat fluxEuler's forward methodcentral differenceskin burnhyperthermiathermal conductivitylayers
    Potential Scenario
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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
    Potential Scenario
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    2014-Chivers-EtAl-Predator-prey systems depend on a prey refuge
    We present an agent-based model which does not require the factors or constraints of previous models to reproduce all six patterns in persistent populations.
    Individual & Agent Based Modelingpredator-preythink-pair-shareslynxrefugeprey switchingMustela-Clethrionomys systempatter oriented
    Potential Scenario
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    2001-Cheng-Teaching mathematical modelling in Singapore schools
    The purpose of this paper is to examine the possibility of introducing the teaching of mathematical modelling to the secondary school curriculum in Singapore.
    teachinglogisticsecondary school mathematicsBarnacle GeeseSingapore
    Article or Presentation
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    47

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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.
    circuitLaplace transformtransfer functionmystery circuitvoltage frequencytwo loop circuit
    Potential Scenario
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    2007-I-Liang_Chern-Mathematical Modeling and Differential Equations
    In this course, I will mainly focus on, but not limited to, two important classes of mathematical models by ordinary differential equations: • population dynamics in biology • dynamics in classical mechanics.
    population dynamicsecologydynamicsclassical mechanicschemical reaction
    Free Online Textbook
    216

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    55

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    2016-I-Liang_Chern-Mathematical Modeling_and_Ordinary_Differential_Equations
    We let the author's Table of Contents speak for itself.
    differential equationsmodelingtextbook
    General Resource
    200

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    46

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    2003-Knorrenschild-Gross-Text Books on Mathematical Modeling in Biology
    Text Books on Mathematical Modeling in Biology Compiled from the Internet by Michael Knorrenschild,
    biologyMathematical Biologytextbooktext
    Potential Scenario
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    1989-EY_Rodin-K_Egan-Mathematics modelling of the rate of chemical reactions
    The development of improved designs for chemical reactors as well as the prediction of optimal operating conditions in chemical production are based on an understanding of the rates at which chemical processes occur.
    kineticsfirst orderreactionsecond orderzeroth order
    Article or Presentation
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    53

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    2008-Brian_Winkel-Fourier_Series-Optimization_Opportunity
    We discuss the introduction of Fourier series as an immediate application of optimization of a function of more than one variable.
    optimizationdiscoveryFourierFourier seris
    Modeling Scenario
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    1-064-TorricelliBox-ModelingScenario
    The time it takes a column of water to empty and the time it takes the same volume of column of water with a box (various sizes) submerged in the column of water are compared through modeling with Torricelli's Law.
    groundwater flowcolumn of waterTorricelli's Lawwater displacementsubmerged box
    Article or Presentation
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    50

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    2014-C_W_Groetsch-S_A_ Yost-Vertical Projection_in_a_Resisting_Medium_Revelations_on_Observations_of_Mersenne
    This article, inspired by a 17th-century woodcut, validates empirical observations of Marin Mersenne (1588–1648) on timing of vertically-launched projectiles for a general mathematical model of resistance.
    resistanceprojectile motionprojectilefluidMersenne
    Potential Scenario
    156

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    1989-R_Blickhan-Spring Mass Model For Running-Hopping
    A simple spring—mass model consisting of a massless spring attached to a point mass describes the interdependency of mechanical parameters characterizing running and hopping of humans as a function of speed.
    spring massjumpjumping
    Modeling Scenario
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    138

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    6-030-SaltAndTorricelli-ModelingScenario
    We build on a model for the height of a falling column of water with a small hole in the container at the bottom of the column of water. We use data from one video of a falling column of water.
    whole picturetankmixingflowcolumn of watersalt mixinggraduated cylinderapertureTorricelli's Law
    Potential Scenario
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    2003-Richard-Carson-Tracer kinetic modeling in PET
    The use of radiopharmaceuticals and the imaging of their biodistribution and kinetics with modern instrumentation are key components to successful developments in PET.
    Metabolismtomographyradiopharmaceuticalspositron emission
    Potential Scenario
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    2013-Michael-Evans-Growth and Decay
    Sometimes, we can describe processes of growth and decay—whether physical, chemical, biological or sociological—by mathematical models.
    exponential growthexponential decayisotopespopulationsresource depletion
    Potential Scenario
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    46

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    2008-Abramson-Mathematical modeling of the spread of infectious diseases
    These are informal notes, mostly based on the bibliography listed at the end and on recent papers in the field. The practical use of these models is based on the fact that they can be kept realistic enough.
    infectious diseaseepidemiccowpoxsmallpoxcomplex networks
    Technique Narrative
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    232

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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 antidifferentiate that side.
    Integrating Factor
    Potential Scenario
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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
    Potential Scenario
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    2018-Banerjee-EtAl-Prey-Predator Model with a Nonlocal Bistable Dynamics of Prey
    The primary goal of our present work is to consider nonlocal consumption of resources in a spatiotemporal prey-predator model with bistable reaction kinetics for prey growth in the absence of predators.
    predator-preynonlocal consumptionTuring bifurcationspatial Hopf bifurcationspatio-temporal patternprey growth