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    Potential Scenario
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    2017-Alex_Honchar-Neural Networks For Solving Differential Equations
    In this post I want to show how I applied simple feed-forward NNs to different differential equations with increasing complexity: ODEs, second order ODEs, and, finally, PDEs.
    neural networksCybenko theoremdiffusion equationfluid dynamics
    Modeling Scenario
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    406

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    3-060-DataToDifferentialEquation-ModelingScenario
    Students use knowledge of second-order linear differential equations in conjunction with physical intuition of spring-mass systems to estimate the damping coefficient and spring constant from data.
    Association & Data Fittingmassspring-mass systemspring\total distancenumerical differentiation
    Free Online Textbook
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    2015-Eric_Sullivan-Numerical Methods_An_Inquiry-Based_Approach_with_Python
    This is an OER effort on the part of Eric Sullivan to explore the joy of numerical methods. He has provided several versions.
    pythonnumerical analysisNumerical Methods
    Free Online Textbook
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    2015-Dan_Sloughte-Notes on Diffy Qs Differential Equations for Engineers
    This is a calculus book with the last chapter devoted to ordinary differential equations topics. The effort begins with a study of numerical methods and goes through traditional technique strategies.
    Numerical Methodspendulumtext
    Modeling Scenario
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    4-065-GasInjection-ModelingScenario
    Students use programs (or create their own code) based on exponential box-scheme approximations for solving systems of nonlinear differential equations that contain small parameters for the highest derivative terms or singularities in boundary...
    Prandtl-Blasius equationsboundary layergas injectionesponential box schemeuniform convergenceFORTRAN
    Free Online Textbook
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    70

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    2009-Eriksson- Estep-Hansho-Johnson-Computational Differential Equations
    Differential Equations and Advanced Computational Differential Equations, presents a unified approach to computational mathematical modeling using differential equations based on a principle of a fusion of mathematics and computation.
    Galerkin
    Potential Scenario
    138

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    58

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    1994-Paul_Davis-Asking Good Questions about Differential Equations
    A general essay about the Rule of Three – numerical, algebraic, and graphical perspectives + modeling with one illustration about Irish population.
    questionspopulationnumericalphysical contextgraphicalalgebraicIreland
    Technique Narrative
    401

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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
    Modeling Scenario
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    9-030-WaterHammer-ModelingScenario
    We develop and apply a numerical algorithm that solves a system of two nonlinear partial differential equations (PDEs) that describes the time evolution of the water hammer phenomenon.
    Stock and Flow modelhyperbolic equationsfinite differenceswater hammerhydrodynamicscompressibilitywave celerity
    Technique Narrative
    256

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    265

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    1-015-DimensionlessVariables-TechniqueNarrative
    This material introduces the idea of ``rescaling'' for ordinary differential equations (ODE's) by the use of dimensionless variables. In practice this is an extremely common and useful prelude to the analysis and solution of ODE's.
    linearizationdimensional analysistime scalescalingdimensionless variablesspatial scale
    Modeling Scenario
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    366

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    1

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    3-104-BungeeJumping-ModelingScenario
    In this project, students design a bungee jumping cord (cross-sectional area and length) that will keep jumpers safe. Students communicate their recommendations as a letter to a client interested in starting a bungee jumping business.
    designfallingmassspring\bungeeelesticityrecommendationconsult
    Free Online Textbook
    1452

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    2011-Steven_Desjardins-Remi_Vaillancourt-Ordinary_Differential_Equations_Laplace_Transforms_and_Numerical_Methods_for_Engineers
    This text is packed with worked out presentations, problems, and exercises (with solutions) and MatLab code. There is sufficient detail and attention to topics to more than address interests/needs in an introductory course.
    modelingtextbookmatlabengineeringLaplace transform
    Modeling Scenario
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    9-012-PDEGuitarTuning-ModelingScenario
    We lead students through a derivation of a partial differential equation which models the motion of a string held at both ends, a case of the one-dimensional wave equation, and then play it on Mathematica.
    extensionsine wavesfrequencyguitardampingFourierstringtuning
    Potential Scenario
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    2008-Ahmed_Mohameden-Solving initial-value second order ordinary differential equations on an Excel spreadsheet
    This paper presents a friendly method of solving initial-value second order differential equations (DEs) analytically on a MS Excel© workbook.
    ExcelSpreadsheet
    Free Online Textbook
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    2014-Jeffrey_Chasnov-Lecture_Notes_on_Introduction_to_Differential_Equations
    The differential equations text is 128 pages and develops and motivates the theory of the material nicely, with links to YouTube lectures to assist.
    differential equationsbiologytextbook
    Technique Narrative
    221

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    348

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    1-060-RegularPerturbation-TechniqueNarrative
    This paper presents an introduction to a set of analytical approximations referred to as regular perturbation. This is a particular mathematical tool within the broader set of perturbation methods.
    perturbationregular perturbationasymptotic expansionsanalytical approximationBernoulli equation
    Potential Scenario
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    2006-TK_Kar-Controllability and optimal harvesting of a prey–predator model incorporating a prey refuge
    This paper deals with a prey–predator model incorporating a prey refuge and harvesting of the predator species.
    survivalpredator-preyharvestrefugePontryagin’s maximal principlehidingoptimal harvest
    Potential Scenario
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    1999-Peter_Deuflhard-Differential Equations in Technology and Medicine
    It deals with a variety of challenging real life problems selected from clinical cancer therapy, communication technology, polymer production, and pharmaceutical drug design.
    cancerdesigntumordrugpolymertherapy
    Potential Scenario
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    1989-Protopopescu-Santoro-Dockery-Combat modeling with partial differential equations
    We propose an extension of the classical modeling of combat via Lanchester equations to include one-dimensional spatial effects.
    combatLanchester
    Technique Narrative
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    189

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    1-003-IntroNumericalMethods-TechniqueNarrative
    We develop elementary approaches to numerically solving first order differential equations with Euler's Method, Improved Euler's Method and develop these geometrically to compute numeric solutions and compare them to analytic solutions.
    analytic solutionEuler's methodimproved Euler's method