SIMIODE

Articles and Publications feed

1. Secrets of the Mathematical Contest in Modeling

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   13 Nov 2018 | Articles and Publications | Contributor(s):: Kelly Cline

   Published in 2009, Dr. Kelly Cline, Carroll College, Helena MT USA, discusses his evolving personal strategy for modeling competitions from young student participant to mature faculty coach. Dr. Cline gives many practical hints and "secrets," all based on thoughtful reflection from his...

2. Approximating cosine and sine functions numerically

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   01 Mar 2018 | Articles and Publications | Contributor(s):: Hans Rudolf Schneebeli

   Abstract:How can function values ​​for sine or cosine be quickly and reliably numerically estimated?  We consider equal circular motions on the unit circle in the complex plane and find sine and cosine as solutions of a differential equation. The two functions can be numerically...

3. Two competing populations: simulations with differential equations

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   01 Mar 2018 | Articles and Publications | Contributor(s):: Hans Rudolf Schneebeli, Claudio Marsan

   Abstract: Suppose two populations are competing with each other. How can they then develop? We offer insights with simulation calculations. In the model is the evolution of the biomass of the two populations described with differential equations. A fundamental building block is the logistic...

4. Population Modeling

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   01 Mar 2018 | Articles and Publications | Contributor(s):: Hans Rudolf Schneebeli, Claudio Marsan

   This paper offers many problems inolving a single population model while introducing several specific models. Both numerical methods and qualitative anlyses are offered.The paper is in German and is entitled, "Populationsmodelle: Eine Einführung in Differentialgleichungen."Hans R....

5. Modeling Falling Bodies

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   01 Mar 2018 | Articles and Publications | Contributor(s):: Hans Rudolf Schneebeli

   Modelling falling bodies is discussed using a computer algebra system-calculator and introducing various traditional and elementary methods from calculus as well as  numerics for dealing with the resulting ordinary differential equations.This article is in German under the title,...

6. Modeling Contaminant Flow in the Puget Sound - Senior Thesis

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   01 Jun 2017 | Articles and Publications | Contributor(s):: Jordan Christopher Trinka

   In this paper, we mathematically model contaminant flow in a two-dimensional domain of the Puget Sound using a finite element numerical solution to the advection-diffusion equation coupled with a finite difference numerical solution to the Navier-Stokes equations. We offer two models of...

7. Excel Advanced Solver for Partial Differential Equations

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   25 May 2017 | Articles and Publications | Contributor(s):: Chahid Ghaddar

   We offer an illustration of PDASOLVE() an Excel Advanced Solver for Partial Differential Equations by Chahid Ghaddar of ExcelWorks (cghaddar@excel-works.com ) along with two articles concerning use of the software. ExcelWorks is in the greater Boston MA USA area and one may read about the author...

8. A Particular Solutions Formula For Inhomogeneous Arbitrary Order Linear Ordinary Differential Equations

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   24 May 2017 | Articles and Publications | Contributor(s):: CLAUDE MICHAEL CASSANO

   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...

9. Let's Do It: Using Modeling in the Classroom

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   14 May 2017 | Articles and Publications | Contributor(s):: Brian Winkel

    Winkel, B. J. 2017. Let's Do It: Using Modeling in the Classroom. MAA FOCUS.  37(2): 26-27.In this article the author, Brian Winkel, Director of SIMIODE, attempts to make the case for modeling in the differential equations classroom by giving both rationale and examples.The entire...

10. Informed Conjecturing in a Modeling Context Differential Equations

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    29 Mar 2017 | Articles and Publications | Contributor(s):: Brian Winkel

    We examine two differential equations, (1) first order exponential growth or decay and (2) second order, linear, constant coefficient differential equations, and show the advantage of learning differential equations in a modeling context for informed conjectures of their solution. We follow with...

11. What Goes Up Must Come Down

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    02 Mar 2017 | Articles and Publications | Contributor(s):: Brian Winkel

    Brauer, F. 1999. What Goes Up Must Come Down. American Mathematical Monthly. 108(5): 437-440.Article Abstract: NONEThis paper is a wonderfully general analysis of the following, “It is natural to ask whether a particle propelled upwards takes longer to fall to earth from its maximum height...

12. Beyond Newton's law of cooling – estimation of time since death

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    02 Mar 2017 | Articles and Publications | Contributor(s):: Brian Winkel

    Leinbach, Carl. 2011. Beyond Newton’s law of cooling – estimation of time since death. International Journal of Mathematical Education in Science and Technology. 42(6): 765-774.Article Abstract: The estimate of the time since death and, thus, the time of death is strictly that, an...

13. Vertical Projection in a Resisting Medium: Revelations on Observations of Mersenne

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    02 Mar 2017 | Articles and Publications | Contributor(s):: Brian Winkel

    Groetsch, C. W. and S. A. Yost. 2014. Vertical Projection in a Resisting Medium: Revelations on Observations of Mersenne. The American Mathematical Monthly. 21(6): 499-505.Article Abstract: This article, inspired by a 17th-century woodcut, validates empirical observations of Marin Mersenne...

14. Differential Equation Models in Sociology

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    02 Mar 2017 | Articles and Publications | Contributor(s):: Brian Winkel

    Nielsen, Francois and Rachel A. Rosenfeld. 1981. Substantive Interpretations of Differential Equation Models. American Sociological Review. 46: 159-174.Article Abstract: The use of differential equations models to study social processes has been increasing rapidly. There are, however,...

15. Analysis of logistic growth models

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    02 Mar 2017 | Articles and Publications | Contributor(s):: Brian Winkel

    Tsoularis, A. 2001. Analysis of logistic growth models. Research Letters in the Information and Mathematical Sciences. 2:23-46. Full article available at http://mro.massey.ac.nz/handle/10179/4341 .Article Abstract: A variety of growth curves have been developed to model both unpredated,...

16. Mathematical analysis of delay differential equation models of HIV-1 infection

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    02 Mar 2017 | Articles and Publications | Contributor(s):: Brian Winkel

    Nelson, Patrick W. and Alan S. Perelson. 2002. Mathematical analysis of delay differential equation models of HIV-1 infection. Mathematical Biosciences. 179: 73–94.Article Abstract: Models of HIV-1 infection that include intracellular delays are more accurate representations of the biology...

17. Predator-Prey Model of Guerrilla Warfare

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    01 Mar 2017 | Articles and Publications | Contributor(s):: Brian Winkel

    Intriligator, Michael D. and Dagobert L. Brito. 1988. A Predator-Prey Model of Guerrilla Warfare. Synthese. 76(2): 235-244. Special issue: Formal Analysis in International Relations.Excerpt from Article Abstract: “The purpose of this paper is to analyze guerrilla warfare by means of a...

18. Terminal velocity of a shuttlecock in vertical fall

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    01 Mar 2017 | Articles and Publications | Contributor(s):: Brian Winkel

    Peastrel, M., R. Lynch, and A. Armenti, Jr. 1980. Terminal velocity of a shuttlecock in vertical fall. American Journal of Physics. 48(7): 511-513.Article Abstract: We have performed a straightforward vertical fall experiment for a case where the effects of air resistance are important and...

19. Sustainability in a differential equations course: a case study of Easter Island

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    01 Mar 2017 | Articles and Publications | Contributor(s):: Brian Winkel

    Koss, Lorelei. 2011. Sustainability in a differential equations course: a case study of Easter Island. International Journal of Mathematical Education in Science and Technology. 42(4): 545-553.Article Abstract: Easter Island is a fascinating example of resource depletion and population collapse,...

20. Curve fitting guide

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    01 Mar 2017 | Articles and Publications | Contributor(s):: Brian Winkel

    Fitting Models to Biological Data Using Linear and Nonlinear Regression: A Practical Guide to Curve FittingMotulsky, Harvey and Arthur Christopoulos. 2001. Fitting Models to Biological Data Using Linear and Nonlinear Regression: A Practical Guide to Curve Fitting. La Jolla CA: GraphPad Software....