## Tags: Mathematica

### All Categories (1-20 of 49)

1. 28 Jul 2020 | | Contributor(s):: Therese Shelton

In this modeling activity, students examine the spring-mass-dashpot 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....

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

In this modeling activity, students examine the spring-mass-dashpot 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...

4. 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.

5. 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.

6. 04 Jul 2020 | | Contributor(s):: Brian Winkel

We offer a short Mathematica file in which we demonstrate the step by step commands for solving a second order, linear, constant coefficient, ordinary differential equation using Laplace Transforms and then we condense the entire set of instructions into one line of code - hence the name one liner.

7. 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...

8. 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...

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. 08 Aug 2019 | | Contributor(s):: Eric Stachura

This scenario takes students through the development of an invasive species partial differential equation model. Basic models are discussed first, which lead students to eventually develop their own model which takes into account dispersion. Students will explore various Mathematica modules...

11. 31 Mar 2019 | | Contributor(s):: Mitaxi Mehta

Differential equations and Laplace transforms are an integral part of control problems in engineering systems. However a clear explanation of the relationship of Laplace transforms with the differential equation formalism is difficult to find for coupled differential equations. Here we describe...

12. 15 Sep 2018 | | Contributor(s):: Arati Nanda Pati

We offer students a simulation experience or data from a simulation and ask them to model the simulation using several approaches andusing EXCEL spreadsheet. In this particular modeling scenario, we know the exact solution and want to see how various models predict our expectations. We have used...

13. 24 Apr 2018 | | Contributor(s):: Michael Karls

The goal of this project is to set up and numerically solve a first-order nonlinear ordinary differential equation (ODE) system of three equations in three unknowns that models beer bubbles that form at the bottom of a glass and rise to the top.  The system solution is then used to verify...

14. 18 Jan 2018 | | Contributor(s):: Michael Karls

Incorporating a Modeling First Approach into a Traditional ODE Course by Mike Karls. Ball State University.A talk given at the AMS Special Session on Modeling in Differential Equations - High School, Two-Year College, Four-Year Institution at Joint Mathematics Meetings, San Diego CA, 9-13 January...

15. 10 Sep 2017 | | Contributor(s):: Brian Winkel

Kerckhove, Michael.  2012. From Population Dynamics to Partial Differential Equations. The Mathematica Journal. 14: 1-18.Abstract: Differential equation models for population dynamics are now standard fare in single-variable calculus. Building on these ordinary differential equation (ODE)...

16. 08 Sep 2017 | | Contributor(s):: Brian Winkel

Fay, T. 2001.The Pendulum Equation.  Int. J. Math. Educ. Sci. Technology.  33(4): 505-519.Abstract:We investigate the pendulum equation q’’(t) + l2 sin(q) = 0 and two approximations for it. On the one hand, we suggest that the third and fifth-order Taylor series...

17. 27 Nov 2016 | | Contributor(s):: Brian Winkel

We offer three mixing problems, of increasing order of difficulty, in which salt is coming into a tank of water and upon instantaneous mixing is leaving the tank.

18. 22 Feb 2016 | | Contributor(s):: Brian Winkel

We offer a student posting at the Differential Equations and Fourier Series group found on FaceBook to illustrate the different technologies in use.  We believe what follows illustrates the different technologies faculty and students can use and their preferences for many different reasons....

19. 06 Jun 2015 | | Contributor(s):: Brian Winkel

The Laplace Transform is a mathematical construct that has proven very useful in both solving and understanding differential equations. We introduce it and show its power here. This is done in a Mathematica notebook with pdf provided.

20. 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...