## Tags: ordinary

### Modeling Scenarios (1-20 of 42)

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. 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.

3. 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.

4. 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.

5. 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...

6. 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...

7. 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.

8. 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.

9. 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.

10. 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...

11. 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...

12. 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...

13. 22 Aug 2018 | | Contributor(s):: Norman Loney

We present a differential equation model for the temperature of a mercury thermometer which is sitting in a stream of water whose temperature oscillates. We suggest a solving strategy which uses Laplace Transforms.

14. 30 May 2018 | | Contributor(s):: Ryan Edmund Miller, Stanley F Florkowski

Students will transform, solve, and interpret Susceptible Infected Recovered (SIR) models using systems of differential equation models. The project is progressively divided into three parts to understand, to apply, and to develop SIR models. Part one focuses on understanding and interpreting SIR...

15. 25 Jun 2016 | | Contributor(s):: Troy Henderson

We offer raw data collected from a webcam and a thermometer for evaluating the strength of steeping tea.  We ask students to build a mathematical model using the data to predict how long the tea should steep before essentially reaching saturation.

16. 22 Jun 2016 | | Contributor(s):: Troy Henderson

We offer raw data collected from two thermometers used in the smoking process of Southern barbecue.  One thermometer measures the temperature inside of the smoke chamber and the other measures the internal temperature of the meat.  This data can be used to model and predict the amount...

17. 06 Jun 2015 | | Contributor(s):: Karen Bliss

Adapted from 1-11-Kinetics, SIMIODE modeling scenario.  We help students see the connection between college level chemistry course work and their differential equations coursework.  We do this through modeling kinetics, or rates of chemical reaction. We study zeroth, first, and...

18. 04 Jun 2015 | | Contributor(s):: Brian Winkel

We build the infinite set of first order differential equations for modeling a stochastic process, the so-called birth and death equations. We will only need to use integrating factor solution strategy or DSolve in Mathematica for success.  We work to build our model of random events which...

19. 04 Jun 2015 | | Contributor(s):: Brian Winkel

We provide data (in EXCEL and Mathematica files) on evaporation of 91% isopropyl alcohol in six different Petri dishes and one conical funnel and on evaporation of water in one Petri dish. We  ask students to develop a mathematical model for the rate of evaporation for the alcohol mixture...

20. 04 Jun 2015 | | Contributor(s):: Brian Winkel

Students build three different models for levels of salt in a tank of water and at each stage the level of complexity increases with attention to nuances necessary for success.