Tags: initial condition

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  1. 1-190-S-IntroClass

    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...

  2. 3-092-S-WirelessPower

    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 second-order differential equations with constant coefficients. One of the equations is homogeneous while the other one is non-homogeneous. The application is called wireless power transmission...

  3. 1-150-S-CancerTherapy

    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...

  4. 3-076-S-CircuitBuilding

    27 Jul 2021 | | Contributor(s):: Chiu Choi

    In this project students will establish a mathematical model for an electric circuit as a second-order ordinary differential equation with constant coefficients. They will derive the initial conditions for this differential equation by using circuit laws. They will obtain its closed-form solution...

  5. Engineering Design Optimization using Calculus Level Methods: A Casebook Approach (Manual)

    Collections | 20 Mar 2021 | Posted by Phil B Brubaker


  6. 9-002-S-GroundWaterFlow

    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...

  7. 9-020-S-HeatDiffusion

    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...

  8. 7-040-S-TankInterruptMixing

    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.

  9. 1-039-S-StochasticPopModels

    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...

  10. 1-032-S-WordPropagation

    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.

  11. 1-001pgf-S-BirthDeathImmigration

    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. 

  12. 1-034-S-FishMixing

    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 student-designed restocking and fishing plan in a lake. The mixture is of two species of fish, one being the current sole...

  13. 1-013-S-Sleuthing

    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...

  14. 1-031-S-CoolIt

    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...

  15. 1-006-S-FinancingSavingsAndLoans

    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...