Tags: euler

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1. 08 Aug 2021 | | Contributor(s):: Barbara Zubik-Kowal

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...

2. 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...

3. 31 Mar 2019 | | Contributor(s):: Corban Harwood

This technique narrative guides a discovery-based 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...

4. 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...

5. 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...

6. 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...

7. 01 Mar 2018 | | Contributor(s):: Hans Rudolf Schneebeli

Modelling falling bodies is discussed using a computer algebra system-calculator 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,...

8. 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...

9. 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...

10. 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....

11. 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 non-linear (logistic growth) differential equations. The scenario is based on the deployment of the United States Army's 62nd Engineer Battalion to...