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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. 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...

5. 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...

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. 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...

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. 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...

10. 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...

11. 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...

12. 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...

13. 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...

14. 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...

15. 24 Jun 2015 | Potential Scenario Ideas

Zhao, D. I. 2011. Differential Equation Models for  Systems Biology:  A Survey. Computational Analysis and Modeling, Lousiana Tech University, Ruston LA USA.  30 pp. http://www.advancedcomputing.cn/sys_bio_review.pdf . Accessed 22 June 2015.Abstract:  In this paper, we will...

16. 23 Jun 2015 | Articles and Publications

Nagy, Gabriel. 2015. Ordinary Differential Equations. Mathematics Department, Michigan State University, East Lansing MI USA. 333 pp. http://users.math.msu.edu/users/gnagy/teaching/ode.pdf . Accessed 22 June 2015.This text is free and downloadable. The coverage is formal with proofs of...

17. 06 Jun 2015 | Technique Narratives

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.

18. 05 Jun 2015 | Modeling Scenarios

We offer data on the position of a mass at the end of a spring over time where the spring mass configuration has additional damping due to taped flat index cards at the bottom of the mass. The general modeling of a spring mass configuration and the estimation of parameters form the core of this...

19. 04 Jun 2015 | Modeling Scenarios

We build on  a model (Torricelli's Law ) for the height of a falling column of water with a small hole in the container at the bottom of the column of water. We use data from one video of a falling column of water and the resulting Torricelli's Law model to estimate a parameter in...

20. 04 Jun 2015 | Modeling Scenarios

We build the infinite set of first order differential equations for modeling a stochastic process, the so-called birth and death equations. We will only need to use integrating factor solution strategy or DSolve in Mathematica for success.  We work to build our model of random events which...