## Tags: separable

### All Categories (1-20 of 54)

1. 23 Jan 2022 | | Contributor(s):: Erich McAlister

Pitch velocity is one of the most fascinating statistics in baseball, as documented in the 2015 documentary Fastball. Modern measurements of pitch velocity are taken as the maximum velocity achieved at any point between the pitcher's hand and home plate. However, the velocity of the ball...

2. 22 Aug 2021 | | Contributor(s):: Brody Dylan Johnson, Elodie Pozzi

This project involves the application of Newton's law of cooling to the study of insulated water bottles. Students have the option to conduct experiments with their own bottles outside of class or use data included in the student version. The modeling scenario leads the students through an...

3. 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...

4. 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...

5. 03 Aug 2021 | | Contributor(s):: Maila Hallare, Iordanka Panayotova

This activity builds upon elementary models on population growth. In particular, we compare two different treatment models of cancer therapy where in one, surgery happens before therapy and in the other, surgery happens after therapy.Activities will help students appreciate the importance of...

6. 20 Sep 2020 | | Contributor(s):: Rob Krueger

A simple first order population growth model is presented.  The challenge is to produce a final differential equation which is the result of the difference or ratio of birth and death rates. This ratio is not immediately intuitive.

7. 31 Aug 2020 | | Contributor(s):: Jeremy Cristman, Kenneth Luther, Michael Karls

The goals of this project are to compare a conceptual one-dimensional groundwater flow model to observations made in a laboratory setting, and to discuss the differences. We derive the initial groundwater flow equation, and guide students through a solution. We describe the laboratory set up and...

8. 21 Jul 2020 | | Contributor(s):: Patrice Geary Tiffany

This module uses the scenario:  Ebola Outbreak in West Africa to introduce and apply the technique of separation of variables.   The students first have a warm up to give them background on the scenario, they review topics they need to know for the module, they start the...

9. 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...

10. 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...

11. 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...

12. 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.

13. 02 Sep 2019 | | Contributor(s):: Jeff Pettit

Students perform experiments to model spread of information within a population. Students collect data, determine essential components and parameters and build a mathematical model which can be compared to predicted data, measured data, and modeled data. Part 3 can require students to move from...

14. 03 Jul 2019 | | Contributor(s):: Dina Yagodich

We offer students an opportunity to create a simulation model a hotel population with clients checking in and checking out according to two different disciplines as well as a number of different starting populations in the hotel.

15. 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,...

16. 11 Sep 2017 | | Contributor(s):: Brian Winkel

Mallett, Travis and Josh Fetbrandt. 2009. Differential Equations Class Notes. Washington State University.From the Dear Reader opening page of these notes,“These notes were written by two students (Travis Mallett and Josh Fetbrandt) at Washington State University in Fall 2009 and...

17. 10 Sep 2017 | | Contributor(s):: Brian Winkel

Edelstein-Keshet, Leah. 2009. Chapter 11 – Differential Equations.  See http://ugrad.math.ubc.ca/coursedoc/math103/keshet.notes/chapter11Notes.pdf . Accessed 10 September 2017.Thorough and very readable material on many topics in differential equation, e.g.,...

18. 10 Sep 2017 | | Contributor(s):: Brian Winkel

Del Ciello, Sarah, Jack Clementi, and Nailah Hart. 2010. Modeling Disease – FinalReport. See http://educ.jmu.edu/~strawbem/math_201/final_reports/Clementi_DelCiello_Hart_Final.pdf . Acessed 8 September 2017.Abstract: This paper models the progression of a disease through a...

19. 30 Nov 2016 | | Contributor(s):: Richard Corban Harwood

This modeling scenario guides students to simulate and investigate the spread of the common cold in a residence hall. An example floor plan is given, but the reader is encouraged to use a more relevant example. In groups, students run repeated simulations, collect data, derive a differential...

20. 22 Nov 2016 | | Contributor(s):: Brian Winkel

We examine many different physical situations to determine the time it takes a fixed volume of water to flow out of different shape containers through the same size exit hole at the bottom of the container.