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    Linking Intermediate Disturbance Hypothesis to Traditional Ecological Knowledge and Conservation
    Traditional Ecological Knowledge is based on deep understanding of systems from observations made over hundreds to thousands of years. This resource connects Traditional Ecological Knowledge to...

    Keywords: climate changeenvironmental justiceintermediate disturbance hypothesisTraditional ecological knowledge

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    HSI - Student Research Journal - Vol.1 Issue 1 - Fall 2020
    The Headwaters Research Experience students have produced some fascinating research throughout our 10-week program. We encourage all to read their reports in our Vol. 1 - Issue 1 - Fall 2020...
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    Going from student to medical doctor. The pathway to medicine with Abel Edossa and Dr. Oluwatoyin Weaver
    In this "lunch with a Scientist" episode, we interviewed a medical student and medical doctor to help us understand the path to medicine. Becoming a medical doctor is a very daunting task but with...

    Keywords: medicine

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    Climate Change Module (Project EDDIE)
    Students explore how climate is changing from the recent record. Produced by Project EDDIE.

    Keywords: climate dataclimate changevolcanoes and climateclimate trends

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    Cladistic Analysis Lesson Using Bats
    Phylogenetic analysis can be a challenging concept to grasp for undergraduate biology students. This cladistic analysis lesson utilizes the amazingly diverse Order Chiroptera as a model to...

    Keywords: batsphylogeny and classificationVertebrate Morphologycladistic analysisbat evolution

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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.

    Keywords: Maternal-Fetal interfaceheat equationConservation of Energytheat fluxEuler's forward methodcentral differenceskin burnhyperthermiathermal conductivitylayers

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    7-011-CoupledSystemLaplace-ModelingScenario
    Differential equations and Laplace transforms are an integral part of control problems in engineering systems. We consider a baby warming device.

    Keywords: transfer functionpolycarbonatebaby heatercoupled systemheating

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    7-006-LaplaceTransformBirth-TechniqueNarrative
    We present a way of introducing the Laplace Transform as the continuous analogue of a power series expression of a function.

    Keywords: Transformationspower series

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    5-030-LinNonHomoSystemSol-TechniqueNarrative
    We offer strategies for solving linear systems of nonhomogeneous differential equations using a conjectured solution strategy for a system of constant coefficient, linear, n

    Keywords: strategiesdiscovery learningeigenvectorseigenvalue

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    5-012-LinearSystemConjecture-TechniqueNarrative
    Students go from the solution for y'(t) = k*y(t) to a natural extension to the solution conjecture of a system of two constant coefficient, homogeneous, linear differential equations introducing...

    Keywords: discovery learningconjecturesolutionsubstitution

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    7-005-OverViewLaplaceTransforms-TechniqueNarrative
    This is a specialized overview of Laplace Transform application to solving differential equations in Mathematica.

    Keywords: integrationLaplace transformInverse Laplace transofrmintegration by parts

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    5-010-MatrixExponential-TechniqueNarrative
    The matrix exponential is a powerful computational and conceptual tool for analyzing systems of linear, constant coefficient, ordinary differential equations (ODE's). This narrative offers a quick...

    Keywords: matrix esponentialPutzer's Algorithmdiagonalizationeigenvalueseigenvectors

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    5-005-StiffDifferentialEquations-TechniqueNarrative
    This material introduces the topic of ``stiffness'' for a system of ordinary differential equations (ODE's), through a series of examples. Stiffness is a property that a system of ODE's may...

    Keywords: Euler's methodexplicit methodsimplicit methodsstiffsitffnessstiff differential equationinstability

    383

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    3-090-ChebyshevPolynomialSolution-TechniqueNarrative
    The Chebyshev equation is presented as a vehicle to view series solutions techniques for linear, second order homogeneous differential equations with non-constant coefficients.

    Keywords: series soluotionpolynomial solutionsChebyshev polynomialsChebyshev differential equations

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    2-005-LinearizeItAll-TechniqueNarrative
    Linear approximations are often used to simplify nonlinear ordinary differential equations (ODEs) for ease in analysis. The resulting linear approximation produces an ODE where closed form...

    Keywords: computationerrorTorricelli's Lawdata fittinglinear approximation

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    2-001-NumericalMethodsComparisons-TechniqueNarrative
    This material teaches the basics of numerical methods for first order differential equations by following graphical and numerical approaches. We discuss the order of accuracy of the methods and...

    Keywords: Euler's methodimproved Euler's methodRK3 methodsRK4 methodsorder of accuracyabsolute errorCPU time

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    1-030-RandomPerturbation-TechniqueNarrative
    After a brief historical view of this problem, we will demonstrate the derivation of first order linear differential equations with random perturbations.

    Keywords: random perturbationBrownian motionLangevin equationRiemann-Steiltjes integralWiener processIto's calculus

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    1-010-AtmosphericCO2Bifurcation-TechniqueNarrative
    Students are introduced to the concept of a bifurcation in a first-order ordinary differential equation (ODE) through a modeling scenario involving atmospheric carbon dioxide whish is taken as a...

    Keywords: carbon dioxideSurface Atmosphere Exchangebifurcationfold bifurcationsaddle node

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    1-009-Bifurcation-TechniqueNarrative
    We lead students to investigate first-order differential equations that contain unknown parameters. Students discover what happens to the qualitative behavior of solutions to these equations as...

    Keywords: bifurcationqualitative behaviorbifurcation diagram

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    8-002-TrigSumRepresentation-TechniqueNarrative
    Students discover how to represent functions as sums of trigonometric functions and the value of such representations in many fields. This is an introduction to the study of Fourier Series.

    Keywords: estimationTrigonometryTrigonometric Functionssum of square errorsfinite sumFourier seriesFouriere sumspectrumapproximatiopn

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