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    Potential Scenario
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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.
    estimating equationfunctional data analysisGauss–Newton methodparameter cascadeprofiled estimationdynamic system
    Potential Scenario
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    2017-Bruce_Emerson-Wonderful World of Differential Equations
    This is a terrific set of noted with models and applications woven into the material at every opportunity and data as well. This is introductory differential equations with attention to detail and motivation.
    Newton's Second Law of MotionNewton's Law of CoolingreactionsPoiseuille’s Lawstopping distancerate of changeproblemsmodeling opportunities
    Potential Scenario
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    2017-Andras_Domokos-Differential Equations - Theory and Applications – Notes
    This is a terrific set of notes with models and applications woven into the material at every opportunity and data as well. This is introductory differential equations with attention to detail and motivation.
    Newton's Second Law of MotionNewton's Law of Coolingbiochemical reactionsPoiseuille’s Lawstopping distance
    Potential Scenario
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    2014-Niemann-Miklos-Simple Method for Estimation of Parameters in First Order Systems
    A simple method for estimation of parameters in first order systems with time delays is presented in this paper.
    delaytime delystep response
    Potential Scenario
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    2012-Campbell-EtAl-Parameter estimation in differential equation models with constrained states
    We introduce a method to estimate parameters and states from a differential equation model while enforcing interpretability constraints such as monotone or non‐negative states.
    chemical engineeringsmoothing-based relaxation method
    Potential Scenario
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    2003-Givens-Bonfima-Direct observation of normal modes in coupled oscillators
    We propose a simple and inexpensive method to directly observe each normal mode of a system of coupled oscillators, as well as to measure its corresponding frequency, without performing Fourier analysis or using expensive apparatus.
    frequencyresonancecoupled oscillator
    Potential Scenario
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    2015-Zhang-EtAl-On the Selection of ODE Models with Application to Predator-Prey Dynamical Models
    We propose a computationally inexpensive approach that employs statistical estimation of the full model, followed by a combination of a least squares approximation (LSA) and the adaptive Lasso.
    least-squares approximationSpline modelingMonte Carlo simulationsvariable selectionadaptive LASSO
    Potential Scenario
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    2018-Adeniji-EtAl-InverseProblemHolling-TannerModel
    We consider the inverse problem of parameter identification of nonlinear system of ODEs for a specific case of complete information about solution of the Holling-Tanner model for finite number of points for the finite time interval.
    goal functionabsolute error curvesinvers methodholling-Tanner model
    Potential Scenario
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    2017-Justin_Krueger-Parameter Estimation Methods for Ordinary Differential Equation Models with Applications to Microbiology
    We demonstrate the feasibility of principal differential analysis using simulation studies and then apply the method to intestinal and vaginal microbiota data.
    microbiologyLotka Volterrramicrobiota
    Potential Scenario
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    2016-Roberto_Camporesi-A fresh look at linear ordinary differential equations with constant coefficients
    We present an approach to the impulsive response method for solving linear constant-coefficient ordinary differential equations of any order based on the factorization of the differential operator.
    impulseGreen functionsinstructional exposition
    Potential Scenario
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    2009-Peter-Howard-Modeling With ODE
    This is a set of class notes rich in examples and ideas for modeling. There is some MatLab code in support of some of the activities.
    ratescompetitionpopulationepidemicpendulumcarbon datingreaction chemistrymechanicsplanetary motiondrag racingHamilton’s methodvariational method
    Potential Scenario
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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 method to estimate mixed-effects ODE models.
    pharmacokineticsdynamic modelssmoothingsplinemixed-effects modelsHiV combination therapy
    Potential Scenario
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    1998-K_H_Louie_Clark-P_C_D_Newton-Analysis of differential equation models in biology-clover meristem populations
    A simple differential equation model (dynamical system) for clover, based on meristem numbers, is outlined and analysed mathematically.
    sensitivity analysisstability analysissteady statesgrowing pointsbudsmeristems
    Free Online Textbook
    138

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    2017-Russell+Herman-A_First_Course_in_Differential_Equations_for_Scientists_and_Engineers
    This is a self-published text book with excellent coverage and solid mathematics and theory to support applications.
    textbookengineeringapplications
    Potential Scenario
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    2018-Joseph-EtAl-A Nonlinear differential equation model of Asthma effect of environmental pollution using LHAM
    In this paper, we investigated a nonlinear differential equation mathematical model to study the spread of asthma in the environmental pollutants from industry and mainly from tobacco smoke from smokers in different type of population.
    asthmatobacco smokeLiao’s Homotopy analysis Method (environmental pollutants
    Potential Scenario
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    2017-Jean-Roux-Mathematical Models in Air Quality Problems
    Presents many models with analysis in air quality control. Starts with chemical kinetics models and builds complexity to PDE models.
    air pollution effects on forest ecosystemsfinite volume methodboundary layerchemical kineticsfinite differenceemissionsdepositionsadvection
    Potential Scenario
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    2016-Wilkie-EtAl-Using ODEs to Explore Cancer-Immune Dynamics and Tumor Dormancy
    Here we present a general method using ordinary differential equations (ODEs) to model and analyze cancer-immune interactions, and in particular, immune-induced tumor dormancy.
    cancertumor-inhibiting cytotoxic actiontumor-promoting inflammationimmune-induced tumor dormancytumor growth dynamics
    Potential Scenario
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    2001-Smith-Moore-The SIR Model for Spread of Disease
    A multiple part tour of SIR Models freely available with Maple, Mathematics, and MatLab support files at MAA site.
    epidemicSIR modelEuler's methodherd immunityHong Kong flu
    Potential Scenario
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    1987-Claude-Marmasse-Studies on differential equations of enzyme kinetics-Biomolecular scheme
    The integral curve is compared with the solutions given by the two classical approximations to the problem: it is shown that the steady-state approximation is to be preferred to the rapid equilibrium theory as a general method.
    steady-state modelisoclinesenzyme kinetics
    Potential Scenario
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    2017-CW_Groetsch-Hammer and Feather - Some Calculus of Mass and Fall Time
    Does a heavy object fall faster than a lighter one? In 1971 NASA astronaut Dave Scott, Commander of the Apollo 15 lunar mission, used a hammer and a falcon feather on the surface of the moon to give a dramatic illustration that this is not so.
    gravityfree falllinear resistancequadratic resistancehammerfeatherMoon resistanceGalileo