
Secrets of the Mathematical Contest in Modeling
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...

Approximating cosine and sine functions numerically
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...

Two competing populations: simulations with differential equations
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...

Population Modeling
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....

Modeling Falling Bodies
01 Mar 2018  Articles and Publications  Contributor(s):: Hans Rudolf Schneebeli
Modelling falling bodies is discussed using a computer algebra systemcalculator 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,...

Modeling Contaminant Flow in the Puget Sound  Senior Thesis
01 Jun 2017  Articles and Publications  Contributor(s):: Jordan Christopher Trinka
In this paper, we mathematically model contaminant flow in a twodimensional domain of the Puget Sound using a finite element numerical solution to the advectiondiffusion equation coupled with a finite difference numerical solution to the NavierStokes equations. We offer two models of...

Excel Advanced Solver for Partial Differential Equations
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@excelworks.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...

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

Let's Do It: Using Modeling in the Classroom
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): 2627.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...

Informed Conjecturing in a Modeling Context Differential Equations
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...

What Goes Up Must Come Down
02 Mar 2017  Articles and Publications  Contributor(s):: Brian Winkel
Brauer, F. 1999. What Goes Up Must Come Down. American Mathematical Monthly. 108(5): 437440.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...

Beyond Newton's law of cooling – estimation of time since death
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): 765774.Article Abstract: The estimate of the time since death and, thus, the time of death is strictly that, an...

Vertical Projection in a Resisting Medium: Revelations on Observations of Mersenne
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): 499505.Article Abstract: This article, inspired by a 17thcentury woodcut, validates empirical observations of Marin Mersenne...

Differential Equation Models in Sociology
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: 159174.Article Abstract: The use of differential equations models to study social processes has been increasing rapidly. There are, however,...

Analysis of logistic growth models
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. 2:2346. 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,...

Mathematical analysis of delay differential equation models of HIV1 infection
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 HIV1 infection. Mathematical Biosciences. 179: 73–94.Article Abstract: Models of HIV1 infection that include intracellular delays are more accurate representations of the biology...

PredatorPrey Model of Guerrilla Warfare
01 Mar 2017  Articles and Publications  Contributor(s):: Brian Winkel
Intriligator, Michael D. and Dagobert L. Brito. 1988. A PredatorPrey Model of Guerrilla Warfare. Synthese. 76(2): 235244. 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...

Terminal velocity of a shuttlecock in vertical fall
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): 511513.Article Abstract: We have performed a straightforward vertical fall experiment for a case where the effects of air resistance are important and...

Sustainability in a differential equations course: a case study of Easter Island
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): 545553.Article Abstract: Easter Island is a fascinating example of resource depletion and population collapse,...

Curve fitting guide
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....