
6029STumorGrowth
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...

Engineering Design Optimization using Calculus Level Methods: A Casebook Approach (Manual)
Collections 
20 Mar 2021 
Posted by Phil B Brubaker
https://simiode.org/members/5865/collections/calculuslevelprogramminglanguageandapps

Phil B Brubaker
My HistoryI attended Oregon State U. and majored 3 years in Electrical Engineering. Then I switched to a Math major for my final years and graduated with a B.S. in Math (1967). Developed...
https://simiode.org/members/5865

Mohammad Golchian
https://simiode.org/members/5667

Sushil Kumar
I am Associate professor of mathematics at S. V. National Institute of Technology SuratIndia
https://simiode.org/members/5565

2020Shelton, Therese  Remote Teaching Module  Car Suspensions
28 Jul 2020   Contributor(s):: Therese Shelton
In this modeling activity, students examine the springmassdashpot 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....

3105SFrequencyResponse
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.

3034SCarSuspensions
14 Jul 2020   Contributor(s):: Therese Shelton, Brian Winkel
We examine the springmassdashpot 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.

3027SBobbingDropping
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.

2020Winkel, Brian  Remote Teaching Module  Spring Design to Meet Specs at Minimum Costs
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 springmass using...

1088SRoomTemperature
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...

1136SMarriageAge
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 firstorder ordinary differential equations (which...

2020Winkel, Brian  Remote Teaching Module  Modeling the Spread of Oil Slick
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...

2020Winkel, Brian  Remote Teaching Module  Modeling a Falling Column of Water
07 Jun 2020   Contributor(s):: Brian Winkel
{xhub:include type="stylesheet" filename="pages/resource.css"}{xhub:include type="stylesheet" filename="pages/scudemaccordion.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...

1128SRocketFlight
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.

3026SSpringInverseProblem
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.

3031SSpringCost
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.

5010SDNADegradation
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...

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

5010SMatrixExponential
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...