
1097SSwimmingPool
08 Aug 2021   Contributor(s):: Barbara ZubikKowal
This project involves the dynamics of chlorine concentration during regular swimming pool maintenance cycles. Students will have the opportunity to use both analytic and numerical methods. On the analytical side, students will solve one of the model equations, describing the first stage of a...

3011SEulerBallThrowing
19 Aug 2019   Contributor(s):: Chris McCarthy
If a tennis ball is thrown through the air it will eventually hit the ground due to gravity. Using Euler's method, write a short script (Python, Matlab, R, etc.) to find the trajectory of the ball which will maximize the distance the ball lands from the thrower taking into account air...

1005TextSNavigatingNumericalMethods
31 Mar 2019   Contributor(s):: Corban Harwood
This technique narrative guides a discoverybased approach to learning the basics of numerical methods for first order differential equations, by following the graphical and analytical perspectives of the forward Euler method and second order Taylor method. These methods are motivated by velocity...

5005TextSStiffDifferentialEquations
05 Mar 2019   Contributor(s):: Kurt Bryan
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...

2001TextSNumericalMethodsComparisons
18 Aug 2018   Contributor(s):: Swarn Singh
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...

2018Schneebeli, Hans R.  Approximating cosine and sine functions numerically
01 Mar 2018   Contributor(s):: Hans Rudolf Schneebeli
Abstract:How can function values for sine or cosine be quickly and reliably numerically estimated? We consider equal circular motions on the unit circle in the complex plane and find sine and cosine as solutions of a differential equation. The two functions can be numerically...

2018Schneebeli,Hans R.  Modeling Falling Bodies
01 Mar 2018   Contributor(s):: Hans Rudolf Schneebeli
Modelling falling bodies is discussed using a computer algebra systemcalculator and introducing various traditional and elementary methods from calculus as well as numerics for dealing with the resulting ordinary differential equations.This article is in German under the title,...

2010Keesom, No'am , Trisha Macrae, Anjuli Uhlig, and Richard Wang  Fishing for Answers: Investigating Sustainable Harvesting Rate.
12 Sep 2017   Contributor(s):: Brian Winkel
Keesom, No’am , Trisha Macrae, Anjuli Uhlig, and Richard Wang. 2010. Fishing for Answers: Investigating Sustainable Harvesting Rate. Paper 11 pp.Abstract: The purpose of this report is to determine and propose a model by which an optimal harvesting frequency can be...

2005Lie, Knut–Andreas  Introduction to Mathematical Modelling: Ordinary Differential Equations and Heat Equations
10 Sep 2017   Contributor(s):: Brian Winkel
Lie, Knut–Andreas. 2005. 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 September...

2013Gonze, Didier  Numerical methods for Ordinary Differential Equations. Notes.
09 Sep 2017   Contributor(s):: Brian Winkel
Gonze, Didier. 2013. Numerical methods for Ordinary Differential Equations. Notes. 15 pp.See http://homepages.ulb.ac.be/~dgonze/TEACHING/numerics.pdf. Accessed 8 September 2017.The paper begins,“Differential equations can describe nearly all systems undergoing change....

1024SMalariaControl
06 May 2016   Contributor(s):: David Culver
This project offers students a chance to make policy recommendations based on the analysis of models using both linear (exponential decay) and nonlinear (logistic growth) differential equations. The scenario is based on the deployment of the United States Army's 62nd Engineer Battalion to...