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1. 12 Sep 2019 | Technique Narratives

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...

2. 12 Sep 2019 | Technique Narratives

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...

3. 21 Aug 2019 | Modeling Scenarios

This project models the ``Foucault Knife Edge Test,'' an optical test commonly used by amateur astronomers who make their own mirrors for reflecting telescopes. The goal of the test is to estimate the shape of the surface of a mirror from optical reflection data. The model results in a...

4. 25 Mar 2019 | Modeling Scenarios

This scenario models the loss of employees and the employer's attempt to retain them through stock options. It most naturally is solved with a first-order linear decay model with two populations. This is intended for introductory students and is paired well with exponential growth/decay...

5. 09 Dec 2018 | Potential Scenario Ideas

Bonin, C.R.B. Et al. 2017. Mathematical modeling based on ordinary differential equations: A promising approach to vaccinology. Human Vaccines and Immunotherapy. 13(2): 484–489.Abtract: New contributions that aim to accelerate the development or to improve the efficacy and safety of...

6. 18 Aug 2018 | Technique Narratives

It is not always possible to solve a differential equation analytically.This material makes an effort to teach the basics of numerical methods for first order differential equations by following graphical and numerical approaches. Here we also discuss the order of accuracy of the methods and...

7. 18 Aug 2018 | Technique Narratives

It is not always possible to solve a differential equation analytically.This material makes an effort to teach the basics of numerical methods for first order differential equations by following graphical and numerical approaches. Here we also discuss the order of accuracy of the methods and...

8. 30 May 2018 | Modeling Scenarios

Students will transform, solve, and interpret Susceptible Infected Recovered (SIR) models using systems of differential equation models. The project is progressively divided into three parts to understand, to apply, and to develop SIR models. Part one focuses on understanding and interpreting...

9. 30 May 2018 | Modeling Scenarios

Students will transform, solve, and interpret Susceptible Infected Recovered (SIR) models using systems of differential equation models. The project is progressively divided into three parts to understand, to apply, and to develop SIR models. Part one focuses on understanding and interpreting...

10. 24 Apr 2018 | Modeling Scenarios

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...

11. 03 Mar 2018 | Potential Scenario Ideas

Camporesi, Roberto. 2016. A fresh look at linear ordinary differential equations with constant coefficients. Revisiting theimpulsive response method using factorization. Int. J. Math. Educ. Sci. Technol. 47(1): 82-99Summary: We present an approach to the impulsive response method for solving...

12. 03 Mar 2018 | Potential Scenario Ideas

Rasmussen, Chris and  Michael Keynes. 2003. Lines of Eigenvectors and Solutions to Systems of Linear Differential Equations.  PRIMUS. 13(4): 308-320.Abstract: The purpose of this paper is to describe an instructional sequence where students invent a method for locating lines of...

13. 18 Jan 2018 | Presentations

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...

14. 10 Sep 2017 | Potential Scenario Ideas

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)...

15. 08 Sep 2017 | Potential Scenario Ideas

Nokkaew, A. Et Al. Estimation of Algae Growth Model Parameters by a Double Layer Genetic Algorithm. WSEAS TRANSACTIONS on COMPUTERS. 11(11): 377-386. http://www.wseas.org/multimedia/journals/computers/2012/56-122.pdf . Accessed 7 September 2017.ABSTRACT: This paper presents a double layer...

16. 08 Sep 2017 | Potential Scenario Ideas

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. 24 May 2017 | Articles and Publications

A particular solution for any nonhomogeneous linear second, third, and fourth order ordinary differential equation is generally determined. Applying what was determined thus; and following by example a particular solution formula for arbitrary order is obtained. Finding a particular solutions to...

18. 10 Jan 2017 | Articles and Publications

Our goal is to give a very simple, effective and intuitive algorithm for the solution of initial value problem of ordinary differential equations of first order and higher order with  constant, variable or nonlinear coefficients and systems of these ordinary differential equations. We find...

19. 22 Jun 2016 | Modeling Scenarios

We offer raw data collected from two thermometers used in the smoking process of Southern barbecue.  One thermometer measures the temperature inside of the smoke chamber and the other measures the internal temperature of the meat.  This data can be used to model and predict the amount...

20. 22 Feb 2016 | Articles and Publications

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....