
1082TMirrorMirror
21 Aug 2019  Modeling Scenarios
This project models the ``Foucault Knife Edge Test,'' an optical test commonly used by amateur astronomers who make their own mirrors for reflecting telescopes. The goal of the test is to estimate the shape of the surface of a mirror from optical reflection data. The model results in a...

1082SMirrorMirror
21 Aug 2019  Modeling Scenarios
This project models the ``Foucault Knife Edge Test,'' an optical test commonly used by amateur astronomers who make their own mirrors for reflecting telescopes. The goal of the test is to estimate the shape of the surface of a mirror from optical reflection data. The model results in a...

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...

1003TTextIntroNumericalMethods
10 Jan 2019  Technique Narratives
We develop elementary approaches to numerically solving first order differential equations with Euler's Method and Improved Euler's Method. We ask students to develop these geometrically and to compute numeric solutions and compare them to the analytic solutions for a number of different...

1003STextIntroNumericalMethods
10 Jan 2019  Technique Narratives
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.

6024TDronePackageDelivery
18 Sep 2018  Modeling Scenarios
In this scenario, students will begin by carefully reading through the problem statement and uncovering which information is useful. Students will derive a system of first order differential equations which describe the flight path of a drone delivering a package. Techniques used to derive the...

6024SDronePackageDelivery
18 Sep 2018  Modeling Scenarios
In this scenario, students will begin by carefully reading through the problem statement and uncovering which information is useful. Students will derive a system of differential equations which describe the flight path of a drone delivering a package. Techniques used to derive the analytical...

2001TextSNumericalMethodsComparisons
18 Aug 2018  Technique Narratives
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...

2001TextTNumericalMethodsComparisons
18 Aug 2018  Technique Narratives
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...

9001TextTSkinBurnModelNumericalMethods
18 Aug 2018  Technique Narratives
The heat equation is an important partial differential equation (PDE) which describes the distribution of heat in a given region over time. Here we learn to solve a heat equation numerically. It is difficult to study the behavior of temperature in problems with interfaces analytically so...

9001TextSSkinBurnModelNumericalMethods
18 Aug 2018  Technique Narratives
The heat equation is an important partial differential equation (PDE) which describes the distribution of heat in a given region over time. Here we learn to solve a heat equation numerically. It is difficult to study the behavior of temperature in problems with interfaces analytically so...

6070TBeerBubbles
24 Apr 2018  Modeling Scenarios
The goal of this project is to set up and numerically solve a firstorder nonlinear ordinary differential equation (ODE) system of three equations in three unknowns that models beer bubbles that form at the bottom of a glass and rise to the top. The system solution is then used to verify...

The Logistic Differential Equation
03 Mar 2018  Potential Scenario Ideas
The Logistic Differential Equation. Notes. 7 pp.Goals from the notes:• MATH: To analyze the behavior of solutions of an ordinary differential equation geometrically .• MATH: To analyze stability behavior of equilibria of an ordinary differential equation geometricallyand...

2007Bellomo EtAlLectureNotesMathModelingInAppliedScience
03 Mar 2018  Potential Scenario Ideas
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...

2015DiosEtAlHowEngineersDealWithMathematicsSolvingDifferentialEquations
28 Nov 2017  Potential Scenario Ideas
Dios, Araceli Queiruga. Ascensión Hernández Encinas, Jesús Martín Vaquero, Ángel Martín del Rey, Juan José Bullón Pérez, and Gerardo Rodríguez Sánchez. 2015. How Engineers deal with Mathematics solving...

2009WilsonDifferential Equation Models for Forecasting Highway Traffic Flow
23 Sep 2017  Potential Scenario Ideas
Wilson, R. Eddie. 2009. Differential Equation Models for Forecasting Highway Traffic FlowPresentation at Conference on Traffic Modelling. The Open University, Milton Keynes, UK. 31 March. 32 slides. This talk builds the mathematical model for traffic flow and addresses the issues of...

2017KruegerParameter Estimation Methods in Microbioloogy
21 Sep 2017  Potential Scenario Ideas
Krueger, Justin M. 2017. Parameter Estimation Methods for Ordinary Differential Equation Models with Applications to Microbiology. PhD Thesis. 109 pp.Abstract: The compositions of inhost microbial communities (microbiota) play a significant role in host health, and a better understanding of the...

2005HowardModeling with Differential Equations
10 Sep 2017  Potential Scenario Ideas
Howard P. 2005. Modeling with ODE. Notes. 48 pp.Great exposition and lots of Modeling Scenarios almost laid out completely as exercises.From the textOverviewA wide variety of natural phenomena such as projectile motion, the flow of electric current, and the progression of chemical reactions are...

2005LieIntro to Math Modelling ODEs and Heat Equation
10 Sep 2017  Potential Scenario Ideas
2005 Lie, Knut–Andreas. Introduction to Mathematical Modelling: Ordinary Differential Equations and Heat Equations SINTEF ICT, Dept. Applied Mathematics PowerPoint slide. 45 slides. www.uio.no/studier/emner/matnat/ifi/INF2340/v05/foiler/sim02.pdf . Accessed 9...