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    Translocation of Nutrients in the Phloem: Poiseuille's Equation
    This module introduces the Poiseuille equation in the context of understanding nutrient flow in plant cells. It is intended for an introductory biology audience.

    Keywords: plant physiologycalculushyperbolic equationsrates of change

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    Fragile States: A Case Study Exploring Genetics, Molecular Biology, and Biochemistry Through the Lens of Fragile X Syndrome
    This case aims to strengthen students’ understanding of molecular biology concepts through study of Fragile X Syndrome (FXS). Students begin by learning the cause and phenotypes of FXS and...

    Keywords: gene regulationtranscriptiontranslationFragile X syndrometriplet repeat expansionsex linkagemetabolic pathway

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    2009-Noakes-Sleigh-Mathematical models for assessing the role of airflow on the risk of airborne infection in hospital wards
    Understanding the risk of airborne transmission can provide important information for designing safe healthcare environments with an appropriate level of environmental control for mitigating risks.

    Keywords: infectioncompartmenthospitalventilationairbornesthochasticWells–Riley

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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...

    Keywords: resistanceprojectile motionprojectilefluidMersenne

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    3-069-HeatInBar-ModelingScenario
    The temperature distribution along a uniform slender bar due to conduction and convection is investigated through experimental, analytical, and numerical approaches.

    Keywords: heat transferexperimentconductionconvectionboundary conditionsfinite volume method

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    Waking up Anna - Adaptations and Conversion to Mol*
    This case focuses on understanding the molecular basis of Anna's sleeping disorder and its treatment. The adaptations addressed question clarity and reformatting to use Mol*.

    Keywords: sleepmolecular visualization and analysisPDBMolecular Case StudyGABAMolCaseNetMol*MolStarProtein visualizationFlumazenil

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    Waking up Anna
    This case focuses on understanding the molecular basis of Anna's sleeping disorder and its treatment.

    Keywords: sleepmolecular visualization and analysisPDBMolecular Case StudyGABA

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    2008-Duran-Caginalp-Parameter optimization for differential equations in asset price forecasting
    The optimization procedure is used in conjunction with daily market prices (MPs) and net asset values to determine the parameters for which the AFDE yield the best fit for the previous n days.

    Keywords: financeinverse problemnumerical nonlinear optimizationasset flowfinancial market dynamicsmarket return prediction algorithm

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    Tension in Blood Vessels: LaPlace's Equation
    This module introduces Laplace's equation in the context of understanding tension in the walls of blood vessels. It is intended for an introductory biology audience.

    Keywords: linear equationsOpenStaxAnimal Physiology

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    Science “Fails”: A Bank of Historical Examples for Learning From Failure in Science
    Learning from failure is critically important to the processes of scientific inquiry, discovery, and invention. However, students are not routinely taught how to reflect on, learn from, and...

    Keywords: metacognitionScience process skillsLearning from failurepower and privilegestudent wellbeing

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    1999-PS_Crooke-S_Hota_JJ_Martini-JR_Hochkiss-A Mathematical Model for Carbon Dioxide Exchange
    A mathematical model is presented to study the effect of Tracheal Gas Insufflation (TGI) on the alveolar ventilation during passive, mechanical ventilation.

    Keywords: mechanical ventilationventilationcarbon dioxide exchangetracheal gas insufflationalveolar ventilationshunttwo-compartment model

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    1975-DH_Griffel-Teaching the formation and solution of differential equations
    This paper raises many interesting questions about teaching the formation (and solution) of differential equations, i.e. modeling with differential equations.

    Keywords: parasitesTopographypopulationepidemictraffic flowsocial interactionsfish weightarms race

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    1-029-ConeToCubeFlow-ModelingScenario
    An inverted right circular cone with a hole at the bottom is suspended above an open-topped cube which also has a hole in the center of the bottom. The cone is filled with water and we model...

    Keywords: waterflowTorricelli's Lawconecube

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    Agent-Based Modeling Course Materials
    Materials created for an upper level ABM course. Prerequisite: Students have taken either (a) another modeling course, or (b) the introductory computer science sequence.

    Keywords: agent-based modelingindividual-based modelingcourse materials

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    1-026-Evaporation-ModelingScenario
    We provide data on evaporation of 91% isopropyl alcohol in six different Petri dishes and one conical funnel and on evaporation of water in one Petri dish. We ask students to develop a...

    Keywords: evaporationconealcoholPetri dish

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    2017-David_Morin-Oscillations
    So needless to say, an understanding of oscillations is required for an understanding of waves.

    Keywords: dampingfrequency responseresonanceoscillationbeatsunderdampingharmonic oscillatorsover dampingcritical damping

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    2007-Zenker-Rubin-Clermont-From inverse problems in mathematical physiology to quantitative differential diagnoses
    The improved capacity to acquire quantitative data in a clinical setting has generally failed to improve outcomes in acutely ill patients, suggesting a need for advances in computer-supported data...

    Keywords: physiologyinverse problem

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    5-090-SolidParticleErosion-ModelingScenario
    By applying Newton's second law, and making a collection of reasonable assumptions, students will derive a system of differential equations that model the path of a rigid particle as it gouges...

    Keywords: classical mechanicssolid mechanicsNewton's Laws of Motionrigid bodyplasticitypittingductile surface

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    2000-deOlivera-Delfino-Costa-Leite-Pinhole Water Flow From Cylindrical Bottles
    The water flowing from the first bottle feeds the second one located below it. The same concepts of mass and energy conservation now lead to a non-trivial differential equation for the lowest...

    Keywords: Torricelli's LawConservation of EnergytConservation of MassBernoulli’s Theorem

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    1-074-BottleWaterFlow-ModelingScenario
    We offer an experiment in which data is collected to ascertain a parameter in the differential equation formulation of Torricelli's Law for water flow.

    Keywords: bwaterTorricelli's Lawbottle

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