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    Free Online Textbook
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    2012-Brian_Ingalls-Mathematical Modelling in Systems Biology An Introduction
    This is a comprehensive text with much biology background to motivate the mathematical modeling, exercises and answers, and many rich examples.
    spatialsensitivity analysisgene regulatory networksstochasticbifurcationmetabolic networkselectrophysiologytransductionrate lawsbiochemical reactions
    Modeling Scenario
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    5-076-LanchesterLaws-ModelingScenario
    Lanchester's laws are used to calculate the relative strengths of military forces. The Lanchester equations are differential equations describing the time dependence of two armies' strengths A and B as a function of time,
    Lanchester's lawssensitivity analysisanalysis
    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
    Potential Scenario
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    2017-D_Goulet-Modeling, Simulating, and Parameter Fitting of Biochemical Kinetic Experiments
    In many chemical and biological applications, systems of differential equations containing unknown parameters are used to explain empirical observations and experimental data. The differential equations are typically nonlinear.
    optimizationBiochemistrysensitivity analysischromatographymass actioncluster analysisconservation lawsdimerizationestrogen receptor protein
    Potential Scenario
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    2010-Singh-Mishra-athematical modeling approach to study growth rate of grassroots technological innovations
    In this paper we have proposed a simple mathematical model by using ordinary differential equation to know the spread rate of technological innovations in rural India.
    logisticexponentialsigmoidtechnological innovationsasymptoticspread of innovation
    Potential Scenario
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    60

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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
    Modeling Scenario
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    707

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    1-124-WorldPopulation-ModelingScenario
    We build models of world population using data to estimate growth rate.
    population dynamicshumangrowth ratevarying growth rate
    Potential Scenario
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    2012-Shargel-Yu-AccessPharmacy-Applied Biopharmaceutics and Pharmacokinetics
    Step by step formation of drug absorption models is shown with many good graphics of system and plots. Solutions are offered but no solution methods are shown.
    Michaelis-MentenEnzymesubstratecompartmentpharmacokineticsrate constanturinary dataabsorption rate
    Potential Scenario
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    2009-Das-EtAl-Bioeconomic harvesting of a pre-predator fishery
    This paper deals with the problem of non-selective harvesting of a prey–predator system by using a reasonable catch-rate function instead of usual catch-per-unit-effort hypothesis.
    predator-preyharvestingPontryagin’s maximum principlebioeconomicbionomic equilibriumbiotechnical productivitycatch-rate functionoptimal equilibrium
    Potential Scenario
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    2005-DieboldEtAl-Modeling Bond Yields In Finance And Macroeconomics
    From a macroeconomic perspective, the short-term interest rate is a policy instrument under the direct control of the central bank. From a finance perspective, long rates are risk-adjusted averages of expected future short rates.
    financeinterest ratebond yieldmacroeconomics
    Modeling Scenario
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    7-040-TankInterruptMixing-ModelingScenario
    We present a first order differential equation model for the interrupted mixing of a tank with salt water. We offer two solution strategies (1) two step approach and (2) Laplace Transforms.
    Laplace transforminverse Laplace Transformsalttankmixinginterrupt
    Modeling Scenario
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    1-085-DrugBolus-ModelingScenario
    Given data on the concentration of a drug in the plasma of a human in mg/L at certain time intervals in hours can we determine the rate at which the drug leaves the plasma as well as the initial amount administered in a intravenous bolus of the drug?
    concentrationsum of square errorsbolusdrugrate constantadminister
    Modeling Scenario
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    504

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    3-076-CircuitBuilding-ModelingScenario
    In this project students will establish a mathematical model for an electric circuit as a second-order ordinary differential equation with constant coefficients.
    simulationexperimentMultisimcircuitinductancecapacitorKirchhoff's Voltage Lawresistor
    Modeling Scenario
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    1-036-NeutralBuoyancy-ModelingScenario
    An object may hang suspended at, say, ten foot depth in a column of water if at ten feet underwater the density of the object equals the density of water. We study this phenomenon
    DensitybuoyancyArchimedes’ Principlefloatneutral buoyance
    Potential Scenario
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    85

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    2018-Franklin_Chen-Teaching Kinetics through Differential Equations Constructed with a Berkeley MadonnaTM Flow Chart Model
    This kinetics manual has been successfully implemented in Physical Chemistry at UW-Green Bay in the fall semester of 2017, with the students’ success rate greater than 80%.
    kineticsPhysical ChemistryLotka Volterra equationsBerkeley Madonna platform
    Potential Scenario
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    70

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    2010-Del-Ciello-EtAl-Modeling Disease
    We model the transmission of a disease through a population. Such modeling is very important to the study of epidemiology and the practice of medicine.
    diseasespreadcarriessymptomaticasymptomatic
    Potential Scenario
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    2004-Hill-Lozowski-Sampson-Experiments on ice spikes and a simple growth model
    We observed ice-spike growth using time-lapse digital photography, using two water types in two different containers.
    iceice spikebulk heat transfermass conservation
    Modeling Scenario
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    1-170-CensusModeling-ModelingScenario
    Students who have studied models for population are likely to be familiar with the exponential and the logistic population models. The goal here is to explore the role of modeling assumptions in choosing which model to use.
    logistic growthexponentialpopulationU.S. Census DataassumptionGoogle SheetsUnites StatesGuatemala
    Potential Scenario
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    2012-Augustus-Wali-Mathematical Modeling of Uganda Population Growth
    The purpose of this paper focuses on the application of logistic equation to model the population growth of Uganda using data from 1980 to 2010 (inclusive).
    population growthlogistic growthDrug and Alcohol detoxificationcarrying capacityvital coefficients
    Potential Scenario
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    1972-Suresh_Sethi-Optimal Control of the Vidale-Wolfe Advertising Model
    This paper considers an optimal-control problem for the dynamics of the Vidale-Wolfe advertising model, the optimal control being the rate of advertising expenditure to achieve a terminal market share within specified limits.
    Optimal Control Theoryadvertisingsales