
1084TGoingViral
31 Aug 2019  Modeling Scenarios
Students employ randomization in order to create a simulation of the spread of a viral disease in a population (the classroom). Students then use qualitative analysis of the expected behavior of the virus to devise a logistic differential equation. Finally, students solve the...

1084SGoingViral
31 Aug 2019  Modeling Scenarios
Students employ randomization in order to create a simulation of the spread of a viral disease in a population (the classroom). Students then use qualitative analysis of the expected behavior of the virus to devise a logistic differential equation. Finally, students solve the...

3064TGearTrain
31 Aug 2019  Modeling Scenarios
In this scenario students will model an inputoutput mechanical system of gears with a second order, nonhomogeneous, ordinary differential equation with constant coefficients. The model incorporates friction and moments of inertia of the gear train components. Students should have some...

3150TItsABlastFurnace
13 Aug 2019  Modeling Scenarios
This project uses the steadystate heat equation to model the temperature distribution in an industrial furnace used for metal production, for example, a blast furnace.The heat flow is assumed to be steadystate, so that only an elementary ordinary differential equation (ODE) is needed, and...

3150SItsABlastFurnace
13 Aug 2019  Modeling Scenarios
This project uses the steadystate heat equation to model the temperature distribution in an industrial furnace used for metal production, for example, a blast furnace.The heat flow is assumed to be steadystate, so that only an elementary ordinary differential equation (ODE) is needed, and...

1076TClimateBifurcation
08 Aug 2019  Modeling Scenarios
In this paper we present (for educational purposes) simple zero and one dimensional models for the mean temperature of the Earth. These models can exhibit bifurcations from the present Earth climate to an ice age or a ``Venus type of climate.'' The models are accompanied by Matlab...

3067TRLCSeriesCircuit
28 Apr 2019  Modeling Scenarios
In this validationoriented setup, the second order linear ordinary differential governing equation of a small signal RLC series AC circuit is solved analytically, and the results are compared with the data acquired from analyzing the numerical model (using Multisim).

SCUDEM and COMAP MCM/ICM Talk at University of Nebraska  Lincoln
22 Apr 2019  CompetitionsSCUDEM
Elizabeth Carlson, holder of NSF Graduate Research Fellowship at the University of Nebraska  Lincoln, Lincoln NE USA, gave a talk in the spring 2018 to the mathematics club at her school on Math Modeling Competitions. Enjoy!

5090TSolidParticleErosion
27 Mar 2019  Modeling Scenarios
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 material from a more ductile surface. Examination of the solution will yield a formula for the...

5005TextTStiffDifferentialEquations
05 Mar 2019  Technique Narratives
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 possess that make it difficult to solve numerically with standard methods, and it is a...

5005TextSStiffDifferentialEquations
05 Mar 2019  Technique Narratives
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 possess that make it difficult to solve numerically with standard methods, and it is a...

AMS Special Session on Using Modeling to Motivate the Study of Differential Equations  JMM 2019, Baltimore MD USA
20 Jan 2019  Presentations
We offer the presentation for AMS Special Session on Using Modeling to Motivate the Study of Differential Equations, I in Room 336, BCC, 19 January 2019, 8:00 AM 11:50 AM held at the Joint Mathematics Meetings 2019, Baltimore MD USAAs we assemble them the presentations are...

2015YrogovchenkoModelingAlcoholConsumption  PowerPoint
16 Dec 2018  Potential Scenario Ideas
Article Review and AnnotationRagovchenko, Yuriy. 2015. Dull, dizzy, or dead: Models of Alcohol Consumption in Undergraduate Teaching. Presented in Brno NORWAY. 7 December 201. Power Point Presentation.This PowerPoint presentation has lots of basic data on laws, levels of alcohol, and...

3009TBallDropInWater
16 Dec 2018  Modeling Scenarios
We conduct an analysis of a falling ball in liquid to determine its terminal velocity and to ascertain just what radius ball for a given mass density is necessary to attain a designated terminal velocity.

3009TBallDropInWater
16 Dec 2018  Modeling Scenarios
We conduct an analysis of a falling ball in liquid to determine its terminal velocity and to ascertain just what radius ball for a given mass density is necessary to attain a designated terminal velocity.

1063TThreeHoleColumn
15 Dec 2018  Modeling Scenarios
We consider a column of water with three holes or spigots through which water can exit and ask students to model the height of the column of water over time.

2004PhoebusReilyTheParachuteProblem
09 Dec 2018  Potential Scenario Ideas
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
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...

Secrets of the Mathematical Contest in Modeling
13 Nov 2018  Articles and Publications
Published in 2009, Dr. Kelly Cline, Carroll College, Helena MT USA, discusses his evolving personal strategy for modeling competitions from young student participant to mature faculty coach. Dr. Cline gives many practical hints and "secrets," all based on thoughtful reflection from his...

1102SCancerGrowth
29 Jul 2018  Modeling Scenarios
This scenario guides students in the use of differential equation models to predict cancer growth and optimize treatment outcomes. Several classical models for cancer growth are studied, including exponential, power law, Bertalanffy, logistic, and Gompertz. They examine the behaviors of the...