
1124SWorldPopulation
30 May 2020  Modeling Scenarios  Contributor(s): Jessica Libertini
We build models of world population using data to estimate growth rate.CZECH LANGUAGE VERSION We have placed in Supporting Docs a Czech version of this Student Modeling Scenario. Name will be xySTitleStudentVersionCzech.

3031SSpringCost
28 May 2020  Modeling Scenarios
This is a situation where the student is a young tech staff member in a company and is charged with anlyzing costs for a spring to meet certain specifications.

Transient and Steady State response in RC or RL circuits
16 Apr 2020  Presentations  Contributor(s): Jessica Libertini
Transient and Steady State response in RC or RL circuits . PowerPoint Slides. 54 Slides, This is a presentation to help understand the concepts of Transient and Steady State response in RC or RL circuits . There is detailed technical material and graphs to richly illustrate the clear...

1999McCartneyCareyModelingTrafficFlow
05 Apr 2020  Potential Scenario Ideas  Contributor(s): Jessica Libertini
1999McCartneyCareyModelingTrafficFlowMcCartney, Mark and Malachy Carey. 1999. Modelling Traffic Flow: Solving and Interpreting Differential Equations. Teaching Mathematics and its Applications: An International Journal of the IMA. 18(3):...

1092SDashItAll
01 Sep 2019  Modeling Scenarios  Contributor(s): Jessica Libertini
This project uses very basic physics, Newton's Second Law of Motion, to model the motion of a sprinter running down a track. The model is driven by data from the world record race of Usain Bolt in the 2008 Beijing Olympic games. In particular, we derive the classic HillKeller model for a...

Ice Coverage in the Arctic Climate over time
17 Aug 2019  Articles and Publications  Contributor(s): Jessica Libertini
In this paper, entitled Ice Coverage in the Arctic Climate, from two students, Angie Dimopulos and Kelcey Heaney, and their professor, Dr. Wisam Bukaita, ice coverage in the Arctic is modeled over time. We present their abstract here and include the paper itself.ABSTRACT The Arctic plays a...

1001dSHotelPopulationDecay
03 Jul 2019  Modeling Scenarios  Contributor(s): Jessica Libertini
We offer students an opportunity to create a simulation model a hotel population with clients checking in and checking out according to two different disciplines as well as a number of different starting populations in the hotel.

5005TextSStiffDifferentialEquations
05 Mar 2019  Technique Narratives  Contributor(s): Jessica Libertini
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...

1003STextIntroNumericalMethods
10 Jan 2019  Technique Narratives  Contributor(s): Jessica Libertini
We ask students to develop two numerical methods for solving first order differential equations geometrically and to compute numeric solutions and compare them to the analytic solutions for a number of different step sizes.

1138SInnerEarDrugDelivery
20 Aug 2018  Modeling Scenarios  Contributor(s): Jessica Libertini
Hearing loss is difficult to treat due to the inner ear location and structure. Drawing from this challenging case, this scenario guides students to transform a treatment protocol into a mathematical model. Students engage in preclinical studies to examine local drug delivery to the cochlea. The...

2001TextSNumericalMethodsComparisons
18 Aug 2018  Technique Narratives  Contributor(s): Jessica Libertini
It is not always possible to solve a differential equation analytically.This material makes an effort to teach the basics of numerical methods for first order differential equations by following graphical and numerical approaches. Here we also discuss the order of accuracy of the methods and...

1081STumorGrowth
09 Jun 2018  Modeling Scenarios  Contributor(s): Jessica Libertini
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...

FirstOrderModels
03 Mar 2018  Potential Scenario Ideas  Contributor(s): Jessica Libertini
Modeling with First Order EquationsMathematical models characterize physical systems, often using differential equations.Model Construction: Translating physical situation into mathematical terms. Clearly state physical principlesbelieved to govern process. Differential equation is a mathematical...

LeakingBucket: Differential Equations in Engineering
03 Mar 2018  Potential Scenario Ideas  Contributor(s): Jessica Libertini
Differential Equations in Engineering: The Leaking Bucket. Laboratory Experiment. 4 pp.From the Text:7.1 Laboratory ObjectiveThe objective of this laboratory is to learn about first order differential equations and theirapplication to a leaking bucket. 7.2 Educational ObjectivesAfter...

Mike Karls  Incorporating a Modeling First Approach into a Traditional ODE Course
18 Jan 2018  Presentations
Incorporating a Modeling First Approach into a Traditional ODE Course by Mike Karls. Ball State University.A talk given at the AMS Special Session on Modeling in Differential Equations  High School, TwoYear College, FourYear Institution at Joint Mathematics Meetings, San Diego CA, 913 January...

2012LevermoreOrdinaryDifferentialEquationsGraphical MethodsApplications
01 Dec 2017  Potential Scenario Ideas  Contributor(s): Jessica Libertini
Levermore. David. 21012. FirstOrder Ordinary Differential Equations II: Graphical Methods and Applications. University of Maryland. Notes. 23 pp/5. FirstOrder Equations: General Theory5.1. WellPosed Problems 25.2. Existence and Uniqueness 36. FirstOrder Equations: Graphical Methods6.1....

2015EndaleApplicationsOfODEsToRealWorldSystems
26 Nov 2017  Potential Scenario Ideas  Contributor(s): Jessica Libertini
2015. Endale, Mersha Amdie. Some application of first order differential equations to real world system. Masters Thesis. Haramaya University.We quote from the opening by the author,“The subject of differential equations is important part of mathematics for understanding the physical...

2009MallettFetbrandtDifferential Equations Class Notes
11 Sep 2017  Potential Scenario Ideas  Contributor(s): Jessica Libertini
Mallett, Travis and Josh Fetbrandt. Differential Equations Class Notes. Washington State University.From the Dear Reader opening page of these notes,“These notes were written by two students (Travis Mallett and Josh Fetbrandt) at Washington State University in Fall 2009 and are intended to...

2012Applied Differential Equations
11 Sep 2017  Potential Scenario Ideas  Contributor(s): Jessica Libertini
2012Applied Differential Equations. Notes. 34 pp.Set of notes on solution strategies for first order differential equations with attention to detail in solutions and several models: tank mixing problems, mortgage, escape velocityKeywords: differential equation, model, first order, tank mixing,...

2012BourneModeling fish stocks
10 Sep 2017  Potential Scenario Ideas  Contributor(s): Jessica Libertini
Bourne, Murray. 2012. BourneModeling fish stocks. https://www.intmath.com/blog/mathematics/modelingfishstocks7377 . Accessed 10 September 2017.Discusses many models of harvesting and consequences.Keywords: logistic, harvest, differential equation, model, first order, fish, fish...