
1190SIntroClass
05 Mar 2022   Contributor(s):: Bill Skerbitz
Students are led step by step through the development of introductory ideas in mathematical modeling with differential equations. They will encounter the fundamental ideas underlying unlimited population growth (exponential models), limited population growth (logistic models), and a coupled...

3092SWirelessPower
04 Aug 2021   Contributor(s):: Maila Hallare, Iordanka Panayotova
This activity presents an engineering application that is modelled by a coupled system of two linear secondorder differential equations with constant coefficients. One of the equations is homogeneous while the other one is nonhomogeneous. The application is called wireless power transmission...

1150SCancerTherapy
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...

3076SCircuitBuilding
27 Jul 2021   Contributor(s):: Chiu Choi
In this project students will establish a mathematical model for an electric circuit as a secondorder ordinary differential equation with constant coefficients. They will derive the initial conditions for this differential equation by using circuit laws. They will obtain its closedform solution...

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

9002SGroundWaterFlow
31 Aug 2020   Contributor(s):: Jeremy Cristman, Kenneth Luther, Michael Karls
The goals of this project are to compare a conceptual onedimensional 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...

9020SHeatDiffusion
14 Oct 2019   Contributor(s):: Kimberly Spayd, James Puckett
This project guides students through experimental, analytical, and numerical techniques for understanding the heat (diffusion) equation with nonhomogeneous boundary conditions. In particular, students collect data and model a physical scenario in which heat energy diffuses through a long, thin...

7040STankInterruptMixing
22 Aug 2018   Contributor(s):: Norman Loney
We present a differential equation model for the interrupted mixing of a tank with salt water. We offer two solution strategies (1) two step approach and (2) Laplace Transforms.

1039SStochasticPopModels
11 Sep 2016   Contributor(s):: Dan Flath
We offer students the opportunity to develop several strategies for creating a population model using some simple probabilistic assumptions. These assumptions lead to a system of differential equations for the probability that a system is in state (or population size) n at time t. We go further...

1032SWordPropagation
07 Apr 2016   Contributor(s):: Rachelle DeCoste, Rachel Bayless
This activity is a gentle introduction to modeling via differential equations. The students will model the rate at which the word jumbo has propagated through English language texts over time.

1001pgfSBirthDeathImmigration
09 Feb 2016   Contributor(s):: Chris McCarthy
We develop a mathematical model of a death and immigration process using m&m's as a stochastic process with the help of probability generating functions.

1034SFishMixing
24 Dec 2015   Contributor(s):: Eric Sullivan, Elizabeth Anne Carlson
This activity gives students a chance to build the underlying differential equation and/or difference equation for a mixing problem using tangible objects (fish) and a studentdesigned restocking and fishing plan in a lake. The mixture is of two species of fish, one being the current sole...

1013SSleuthing
03 Jun 2015   Contributor(s):: Brian Winkel
We present several situations in which differential equation models serve to aid in sleuthing and general investigations. One involves initial speed given information about constant deceleration and distance to stop in traffic incident; one involves modeling a steel ball launched vertically and...

1031SCoolIt
02 Jun 2015   Contributor(s):: Brian Winkel
We offer data on the temperature of water in a beaker which resides in a room of constant temperature and also in an environment of nonconstant temperature. Students are encouraged to consider both empirical and analytic modeling approaches. We offer additional data sets in Excel spreadsheets...

1006SFinancingSavingsAndLoans
31 May 2015   Contributor(s):: Brian Winkel
We describe two situations (Pa) one in which we are saving for a purpose and (2) one in which we are borrowing for a purpose. In the first case we ask for discrete and continuous model of the situation and in the second case we ask that the results of the model be used to examine some...