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    1-051-OneTankSaltModel-ModelingScenario
    A large tank initially contains 60 pounds of salt dissolved into 90 gallons of water. Salt water flows in at a rate of 4 gallons per minute, with a salt density of 2 pounds per gallon....

    Keywords: compartmentsalttankmixingflow

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    1-062-BacteriaGrowth-ModelingScenario
    We offer students a simulation experience or data from a simulation and ask them to model the simulation using several approaches: exponential growth fit, difference equation, differential...

    Keywords: bacteriaexponentialgrowth

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    1-065-AlgalBlooms-ModelingScenario
    This modeling scenario investigates the massive algal blooms that struck Lake Chapala, Mexico, starting in 1994.

    Keywords: direction fieldstool:dfieldalgaeharmful algae bloomspopulationcompartmentLake Chapala

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    1-068-WaterBottleCooling-ModelingScenario
    Students create of a differential equation describing how fluid in a water bottle will change its temperature to approach the ambient temperature in a room.

    Keywords: bNewton's Law of Coolingwater bottleautonomousbottle

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    Water Movement through a Membrane: The Van't Hoff Equation
    This module introduces the van't Hoff equation in the context of understanding the metabolic activity of the epithelial cells lining the stomach. It is intended for an introductory biology audience.

    Keywords: AlgebraInequalitiesCellular Processes

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    2008-Chernyshov-EtAl-The Problem of Modelling of Economic Dynamics in Differential Form
    The authors have tried to analyze procedures of the construction of differential equations that are employed for modeling of macroeconomic processes. The results prove to be rather unexpected.

    Keywords: Fredholm integral equation ofLeontief’s modelmacroeconomic processes

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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.

    Keywords: predator-preyharvestingPontryagin’s maximum principlebioeconomicbionomic equilibriumbiotechnical productivitycatch-rate functionoptimal equilibrium

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    1-001s-StochasticMDeathImmigration-ModelingScenario
    We develop a mathematical model of a death and immigration process using m&ms as a stochastic process with the help of probability generating functions (pgf). We start with 50 m&ms in a bag.

    Keywords: simulationdatalogisticimmigrationstochasticdeathfitting

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    1-001d-HotelPopulationDecay-ModelingScenario
    You will be modeling the following situation: 100 people are in a hotel. Each day, each person has a random chance of 50% of leaving the hotel. No new people enter the hotel. Before you run the...

    Keywords: simulationlogisticexponential decayfitting

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    6-067-LotkaVolterra-ModelingScenario
    This modeling scenario guides students through the process of fitting the Lotka-Volterra model of two differential equations to a real time series observational data. Students use the capabilities...

    Keywords: time seriesdatacompetitionLotka-Volterramodel fittingpredictiongauseRexperimental

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    An Introduction to Statistical Learning: with Applications in R
    This book provides an introduction to statistical learning methods and is aimed for upper level undergraduate students, masters students and Ph.D. students in the non-mathematical sciences.

    Keywords: linear regressiontextbookclassificationcourseclustering coefficientR programming languagestatistical learningmachine learninglogistic regressionresamplingmodel selectionGeneralized additive modelsdecision treesprincipal components analysisMOOCResources @ QUBES - Teaching & Reference

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    2014-Do-Lee-A Differential Equation Model for the Dynamics of Youth Gambling
    We examine the dynamics of gambling among young people aged 16–24 years, how prevalence rates of at-risk gambling and problem gambling change as adolescents enter young adulthood, and prevention...

    Keywords: reproductive numberGamblingepidemicsensitivity indexyouth gambling

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    2014-Wang-EtAl-Estimating Mixed-Effects Differential Equation Models
    When multiple replicates of measurements are available for the dynamic process, it is of great interest to estimate mixed-effects in the ODE model for the process. We propose a semiparametric...

    Keywords: pharmacokineticsdynamic modelssmoothingsplinemixed-effects modelsHiV combination therapy

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    2012-Transtrum-Qiu-Optimal experiment selection for parameter estimation in biological differential equation models
    We explore the question to what extent parameters can be efficiently estimated by appropriate experimental selection.

    Keywords: experimental designsystems biologyAssociation & Data Fittingreaction ratesdecay rates

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    2008-Huet-Deffuant-Differential Equation Models Derived from an Individual-Based Model Can Help to Understand Emergent Effects
    We study a model of primacy effect on individual's attitude. Typically, when receiving a strong negative feature first, the individual keeps a negative attitude whatever the number of moderate...

    Keywords: agent-based modelprimacy effectinformation filteringaggregated modelcollectiveinteractionsdouble-modelling

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    2007-Ramsay-Hooker-Campbell-Cao-Parameter estimation for differential equations-a generalized smoothing approach
    We propose a new method for estimating parameters in models that are defined by a system of non-linear differential equations.

    Keywords: estimating equationfunctional data analysisGauss–Newton methodparameter cascadeprofiled estimationdynamic system

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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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    1967-Israelsson- Johnsson-Circumnutations In Helianthus Annuus
    A theory is given for circumnutations in plants, especially hypocotyls of Helianthus annuus, which were used as experimental material.

    Keywords: plantoscillationdelaycircumnutationturning

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    2018-Robert_Phair-Differential_equation_methods_for_simulation_of_GFP_kinetics_in_non–steady_state_experiments
    Here, we derive new tracer kinetic analytical methods for non–steady state biological systems by constructing mechanistic nonlinear differential equation models of the underlying cell biological...

    Keywords: protein quality controlkineticsCellssteady statechemical kineticsfluouresencephotoactivationinytracellular

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    2018-Weber_Theers_Surmann_Ligges_Weihs-Sensitivity Analysis_of_Ordinary_Differential_Equation_Models
    This report will focus on the sensitivity analysis of ordinary differential equation (ODE) models since they can be used to model so-called Low Frequency Oscillations (LFOs).

    Keywords: sensitivityregressionparameter estimationsystemlow frequency oscillationsoscillations

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