## Tags: ordinary

### Resources (1-20 of 64)

1. 04 Aug 2021 | | Contributor(s):: Allison Leigh Lewis

This modeling scenario guides a student familiar with single ordinary differential equation (ODE) models towards the development of a more complex system of two ODEs for describing the evolution of tumor growth over time. Students should have prior experience with solving ODEs using the separable...

2. 28 Jul 2020 | | Contributor(s):: Therese Shelton

In this modeling activity, students examine the spring-mass-dashpot that is part of a car suspension. We model a "quarter car'', meaning a single wheel, and compare effects of different masses, spring constants, damping coefficients, and the angle at which the assembly is installed....

3. 22 Jul 2020 | | Contributor(s):: Brian Winkel

We describe the frequency response to a second order differential equation with a driving function as the maximum steady state solution amplitude and perform some analyses in this regard.

4. 14 Jul 2020 | | Contributor(s):: Therese Shelton, Brian Winkel

We examine the spring-mass-dashpot that is part of a car suspension, how the ride is related to parameter values, and the effect of changing the angle of installation. We model a "quarter car'', meaning a single wheel.

5. 10 Jul 2020 | | Contributor(s):: Brian Winkel

We present two exercises from a differential equations text in which we ask students to model (1) falling object experiencing terminal velocity and (2) bobbing block of wood in liquid. We model the motion using Newton's Second Law of Motion and Archimedes' Principle.

6. 16 Jun 2020 | | Contributor(s):: Brian Winkel

We place here all the materials in support of the SIMIODE Remote Teaching Module - Spring Design to Meet Specs at Minimum Costs. This  Module is about second order, linear, ordinary differential equations.The class lesson starts with building a model of a spring-mass using...

7. 15 Jun 2020 | | Contributor(s):: Tracy Weyand

Students will analyze temperature variations in a room using Newton's Cooling Law. In this model, the only influence on the indoor temperature is the (oscillating) outdoor temperature (as we assume the heating/cooling system is broken). The main goal of this project is for students to set up...

8. 11 Jun 2020 | | Contributor(s):: Tracy Weyand

Students will build and analyze a model of the fraction of people who are married (for the first time) by a certain age. This model comes from a paper by Hernes and, in this project, is compared to another model used by Coale.These models are first-order ordinary differential equations (which...

9. 10 Jun 2020 | | Contributor(s):: Brian Winkel

We place here and in the Supporting Docs all the materials in support of the SIMIODE Remote Teaching Module - Modeling the Spread of Oil Slick.This module contains1)  (Below and separate file in Supporting Docs) A brief Teaching Guide with an overview of the content and...

10. 07 Jun 2020 | | Contributor(s):: Brian Winkel

{xhub:include type="stylesheet" filename="pages/resource.css"}{xhub:include type="stylesheet" filename="pages/scudem-accordion.css"}We place here and in the Supporting Docs all the materials in support of the SIMIODE Remote Teaching Module - Modeling the Falling Column of Water.This module...

11. 04 Jun 2020 | | Contributor(s):: Brian Winkel

We offer an opportunity to build a mathematical model using Newton's Second Law of Motion and a Free Body Diagram to analyze the forces acting on the rocket of changing mass in its upward flight under power and then without power followed by its fall to earth.

12. 29 May 2020 | | Contributor(s):: Brian Winkel

We are given data on the position of a mass in an oscillating spring mass system and we seek to discover approaches to estimating an unknown parameter.

13. 28 May 2020 | | Contributor(s):: Brian Winkel

This is a situation where we are charged with analyzing costs for a spring to meet certain specifications.

14. 21 Apr 2020 | | Contributor(s):: Brian Winkel

We ask students to use the system of first order linear differential equations given in a source paper and estimates of the data from laboratory procedures from a plot to estimate the parameters and complete the modeling process. Then we seek to compare the results of the final model with...

15. 04 Apr 2020 | | Contributor(s):: Brian Winkel

Bonin, Carla Rezende Barbosa, Guilherme Cortes Fernandes,  Rodrigo Weber dos Santos, and Marcelo Loboscoa. 2016. Mathematical modeling based on ordinary differential equations: A promising approach to vaccinology.  Hum Vaccin Immunother. 13(2):...

16. 12 Sep 2019 | | Contributor(s):: Kurt Bryan

The matrix exponential is a powerful computational and conceptual tool for analyzing systems of linear, constant coefficient, ordinary differential equations (ODE's). This narrative offers a quick introduction to the technique, with examples and exercises. It also includes an introduction to...

17. 01 Sep 2019 | | Contributor(s):: Kurt Bryan

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 Hill-Keller model for a...

18. 13 Aug 2019 | | Contributor(s):: Kurt Bryan

This project uses the steady-state 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 steady-state, so that only an elementary ordinary differential equation (ODE) is needed, and...

19. 21 Jun 2019 | | Contributor(s):: X. M. Huang

Article Review and Annotation2014-Huang-ODE Model Application in Prediction Control PopulationHuang X. M. 2014.  Ordinary Differential Equation Model and its Application in the Prediction Control of Population. Applied Mechanics and Materials. 631-632: 714-717.Abstract: Ordinary...

20. 31 Mar 2019 | | Contributor(s):: Mitaxi Pranlal Mehta

Differential equations and Laplace transforms are an integral part of control problems in engineering systems. However a clear explanation of the relationship of Laplace transforms with the differential equation formalism is difficult to find for coupled differential equations. Here we describe...