SIMIODE - What's New:

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10 Jan 2021 | Contributor(s):: Brian Winkel

Winkel, B. J. and M. Naylor. 2010. Biangular Coordinates Redux - The Joy of Discoveries in a New Kind of Geometry. The College Mathematics Journal. 41(1): 29-41.Creating Bipolar or Biangular Plots. Years ago I co-authored a paper with Mike Taylor (now of NORWAY) on Bipolar or Biangular plots,...

Ice Coverage in the Arctic Climate over time

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17 Aug 2019 | Contributor(s):: Wisam Victor Yossif Bukaita, Kelcey Meaney, Angie Dimopulos

In this paper, entitled Ice Coverage in the Arctic Climate, from two students, Angie Dimopulos and Kelcey Heaney, and their professor, Dr. Wisam Bukaita, ice coverage in the Arctic is modeled over time. We present their abstract here and include the paper itself.ABSTRACT The Arctic plays a...

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...

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 approximated...

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...

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....

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,...

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...

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...

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...

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...

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...

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

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