
7011TextSCoupledSystemLaplace
31 Mar 2019  Technique Narratives  Contributor(s): Mitaxi Mehta
Differential equations and Laplace transforms are an integral part of control problems in engineering systems. However a clear explanation of the relationship of Laplace transforms with the differential equation formalism is difficult to find for coupled differential equations. Here we describe...

1143SPopulationModelVariationsMATLAB
17 Feb 2019  Modeling Scenarios  Contributor(s): Bill Skerbitz
Students will walk through a detailed derivation and review of basic population models (exponential and logistic) to create and understand variations of those models while learning some basic MATLAB functions for working with differential equations. They will also work with other utilities...

2008WillHansenExamplesOfODEsInPhysics
09 Dec 2018  Potential Scenario Ideas  Contributor(s): Brian Winkel
WittHansen, Ole. 2008. Examples of the Differential equations of Physics. www.olewitthansen.dk. Contents1. The dependence of pressure with altitude.............................................................................. 12. Radioaktive chains of decay...

2004PhoebusReilyTheParachuteProblem
09 Dec 2018  Potential Scenario Ideas  Contributor(s): Brian Winkel
Phoebus, Ronald and Cole Reilly. 2004, Differential Equations and the Parachute Problem. Presentation 10 May 2004. https://mse.redwoods.edu/darnold/math55/DEproj/sp04/coleron/presentation.pdf .Abstract: The parachute problem is a classical first semester differential equations problem...

1987RodinMurthyComparativeEvalOfMathModelingBooks
09 Dec 2018  Potential Scenario Ideas  Contributor(s): Brian Winkel
Murthy, D. N. P. and E. Y. Rodin. 1987. A comparative evaluation of books on mathematical modeling. Mathematical Modeling. 9(1): 1728.Abstract: In this paper we present a comparative evaluation of books on mathematical modelling that have appeared in the last 1.5 years.While dated this gives...

6019SEnablingEpidemicExploration
17 Sep 2018  Modeling Scenarios  Contributor(s): Brian Winkel
We offer several strategies for estimating parameters in models of epidemics, one using a MichaelisMenten saturation infected rate.

6003SSchoolFluEpidemic
28 Aug 2018  Modeling Scenarios  Contributor(s): Darrell Weldon Pepper
We offer a model of the spread of flu in a school dormitory and are asked to find when the flu levels reach their peak and explain long term behavior of the spread of the flu.

1108SPoissonProcess
27 Aug 2018  Modeling Scenarios  Contributor(s): Mehdi HakimHashemi
In this project students learn to derive the probability density function (pdf) of the Poisson distribution and the cumulative distribution (cdf) of the waiting time. They will use them to solve problems in stochastic processes.

1032SDigoxinElimination
17 Aug 2018  Modeling Scenarios  Contributor(s): Therese Shelton
We model the concentration of digoxin eliminated from the human body at a rate proportional to the concentration. This is a ``firstorder reaction'' in the language of pharmacokinetics  the study of how drugs move in the body. This activity can be used to introduce compartmentalized...

Kaabar, Mohammed2018A Friendly Introduction to Differential Equations
29 Jul 2018  Free Online Texts  Contributor(s): Mohammed K A Kaabar
In this book, there are five chapters: The Laplace Transform, Systems of Homogeneous Linear Differential Equations (HLDE), Methods of First and Higher Orders Differential Equations, Extended Methods of First and Higher Orders Differential Equations, and Applications of Differential Equations. In...

1081STumorGrowth
09 Jun 2018  Modeling Scenarios  Contributor(s): Ryan Miller, Randy Boucher
Students will transform, solve, and interpret a tumor growth scenario using nonlinear differential equation models. Two population growth models (Gompertz and logistic) are applied to model tumor growth. Students use technology to solve the Gompertz model and answer a series of questions...

6018SExploringSIRModel
30 May 2018  Modeling Scenarios  Contributor(s): Stanley Florkowski, Ryan Miller
Students will transform, solve, and interpret Susceptible Infected Recovered (SIR) models using systems of differential equation models. The project is progressively divided into three parts to understand, to apply, and to develop SIR models. Part one focuses on understanding and interpreting...

2017RumbosDifferentialEquaitonsANDModelingLectureNotes
03 Mar 2018  Potential Scenario Ideas  Contributor(s): Adolfo J. Rumbos
Rumbos, Adolfo J. 2017. Differential Equations and modeling. Lecture Notes. 129 pp.From the PrefaceDifferential equations are ubiquitous in the sciences. The study of any phenomenon in the physical or biological sciences, in which continuity and differentiability assumptions about the quantities...

2015SivakumarRajendranKineticModelBananaWaste
03 Mar 2018  Potential Scenario Ideas  Contributor(s): Pavithra Sivakumar, Lakshmanan Rajendran
Sivakumar, Pavithra and Lakshmanan Rajendran. 2012. Approximate Analytical Expression of Concentrations in a Kinetic Model for Biogas Generation from Banana Waste. Applied Mathematics. 5(1): 714.Abstract: The initial value problem in a kinetic model for biogas generation from...

Herman, Russell L. 2017. A First Course in Differential Equations for Scientists and Engineers
03 Mar 2018  Free Online Texts  Contributor(s): Russell L. Herman
Herman, Russell L. 2017. A First Course in Differential Equations for Scientists and Engineers. Text book. 369 pp. http://people.uncw.edu/hermanr/mat361/ODEBook/ODE1.pdf . Accessed 2 March 2018.This is a selfpublished text book with excellent coverage and solid mathematics and theory to support...

2007Bellomo EtAlLectureNotesMathModelingInAppliedScience
03 Mar 2018  Potential Scenario Ideas  Contributor(s): Nicola Bellomo
Bellomo, Nicola , Elena De Angelis, and Marcello Delitala. 2007. Lecture Notes on Mathematical Modelling in Applied Sciences, Lecture Notes. 168 pp.From the Opening of the Notes:The Lecture Notes collected in this book refer to a university course delivered at the Politecnico of Torino to...

HohenauerPhysical modelling based on first order ODEs
03 Mar 2018  Potential Scenario Ideas  Contributor(s): W. Hohenauer
Hohenauer, W. Physical modelling based on first order ODEs. Notes. 22 pp.http://www.phox.at/upload/Physical%20modelling%20based%20on%20first%20order%20ODEs%20(v1.3).pdf . Accessed 3 March 2018.Abstract: An introduction in techniques to solve first order ODE´s is given....

Modeling the Opioid Epidemic in the United States
19 Jan 2018  Potential Scenario Ideas  Contributor(s): Brian Winkel, Bill Skerbitz
Bill Skerbitz, Wayzata High School, Plymouth MN USA, passed this along as an idea for a Modeling Scenario."When I met with Bev West, Emerita Ithaca College, Ithaca NY USA, she mentioned that they plan on putting out a special issue of the CODEE journal that is focused on matters of...

Yagodich, Winkel, Skerbitz, Harwood  Panel  Experience with Engaging in Modeling in a Differential
19 Jan 2018  Presentations  Contributor(s): Brian Winkel, Dina Yagodich, Richard Corban Harwood, Bill Skerbitz
Panel  Experience with Engaging in Modeling in a DifferentialBy Dina Yagodich, Frederick Community Colllege; Brian Winkel, SIMIODE; Bill Skerbitz, Wayzata High School; Corban Harwood, George Fox University.A panelgiven at the AMS Special Session on Modeling in Differential Equations...

Rasmussen , C., K. Keene, J. Dunmye, and N. Fortune. 2017. InquiryOriented Differential Equations.
05 Jan 2018  Free Online Texts  Contributor(s): Brian Winkel
Authors: Rasmussen , C., K. Keene, J. Dunmye, and N. Fortune.Date of Publication: 20i7.Title: InquiryOriented Differential Equations.Location: https://iode.wordpress.ncsu.eduAccessed 5 January 2018.This online text with both Student version and Teacher version (for the...