
2022KalmanImproved Approaches to Discrete and Continuous Logistic Growth
18 Mar 2022   Contributor(s):: Brian Winkel
2022. Kalman, Dan, Improved Approaches to Discrete and Continuous Logistic Growth. PRIMUS. Preprint at https://maa.tandfonline.com/doi/abs/10.1080/10511970.2022.2040664#.YjUMVurMI_U . Abstract: In the precalculus curriculum, logistic growth generally appears in either a discrete...

1190SIntroClass
05 Mar 2022   Contributor(s):: Bill Skerbitz
Students are led step by step through the development of introductory ideas in mathematical modeling with differential equations. They will encounter the fundamental ideas underlying unlimited population growth (exponential models), limited population growth (logistic models), and a coupled...

9030SWaterHammer
31 Aug 2021   Contributor(s):: Panagiotis D. Scarlatos
The students will develop and apply a numerical algorithm that solves a system of two nonlinear partial differential equations (PDEs). The equations involved are nonlinear and of hyperbolic type. The problem to be solved is an initialboundary value problem that describes the time evolution of...

6075SLorenzSystemSimulation
27 Aug 2021   Contributor(s):: Vladimir Riabov
The Lorenz system will be examined by students as a simple model of chaotic behavior (also known as strange attractor). MATLAB code has been created to find the numerical solutions of the Lorenz’ system of nonlinear ordinary differential equations using various parameters, as well as to...

1104SInfectionRisk
26 Aug 2021   Contributor(s):: Qingxia Li
This project is designed to examine differences between the exponential and logistic growth models in biology and how to apply these models in solving epidemic questions. This project was designed for an introductory section in Calculus II or a course involving ordinary differential equations,...

4065SGasInjection
14 Aug 2021   Contributor(s):: Vladimir Riabov
Students will use computer programs (or create their own programming code) based on exponential boxscheme approximations for solving systems of nonlinear differential equations that contain small parameters for the highest derivative terms or singularities in boundary conditions. The uniform...

6017SOncolyticViruses
03 Aug 2021   Contributor(s):: Iordanka Panayotova, Maila Hallare
In this project, students explore oncolytic virotherapy using systems of differential equations and numerical simulations. The first activity guides the students in simulating the dynamics between the uninfected cancer cells x(t), the oncolytic virusinfected cancer cells y(t), and the...

2021Brubaker, Phil  Importance of Curve Fitting
26 Mar 2021   Contributor(s):: Phil B Brubaker
Importance of Curve Fitting Curve fitting data to a continuous math function is commonly done for the following reasons:interpolation and/or extrapolation of data;parameter estimation where derivative values are required;ease to ‘picture’ a technical problem...

1139SPlantsVsHerbivores
08 Mar 2021   Contributor(s):: Mary Vanderschoot
In a recent study of plants and herbivores on an island in the North Sea, ecologists made a surprising observation: Instead of more vegetation resulting in more grazers, more vegetation resulted in fewer grazers. Consequently, the ecologists hypothesized that, as the vegetation grew more dense,...

1137SSheepGraze
03 Mar 2021   Contributor(s):: Mary Vanderschoot
One of the most wellknown mathematical models in ecology is the LotkaVolterra predatorprey system of differential equations. Initially, this model was used to analyze interactions between two animal populations. But ecologists discovered that it could also be applied to plant (`prey') and...

6026SFakingGause
30 Oct 2020   Contributor(s):: Brian Winkel
We use a fake or toy data set to permit discovery of the parameters in a two population protozoan model used to study paramecium and yeast competiton in the 1930's studies of G.~F.~Gause in the Soviet Union.

1136SMarriageAge
11 Jun 2020   Contributor(s):: Tracy Weyand
Students will build and analyze a model of the fraction of people who are married (for the first time) by a certain age. This model comes from a paper by Hernes and, in this project, is compared to another model used by Coale.These models are firstorder ordinary differential equations (which...

2020Winkel, Brian  Remote Teaching Module  Modeling a Falling Column of Water
07 Jun 2020   Contributor(s):: Brian Winkel
{xhub:include type="stylesheet" filename="pages/resource.css"}{xhub:include type="stylesheet" filename="pages/scudemaccordion.css"}We place here and in the Supporting Docs all the materials in support of the SIMIODE Remote Teaching Module  Modeling the Falling Column of Water.This module...

1124SWorldPopulation
30 May 2020   Contributor(s):: Lenka Pribylova, Jan Sevcik, Pavel Morcinek, Brian Winkel
We build models of world population using data to estimate growth rate.CZECH LANGUAGE VERSION We have placed in Supporting Docs a Czech version of this Student Modeling Scenario. Name will be xySTitleStudentVersionCzech.

6045SCholeraTranmission
19 Apr 2020   Contributor(s):: Urmi GhoshDastidar
A recent cholera outbreak in Haiti brought public attention to this disease. Cholera, a diarrheal disease, is caused by an intestinal bacterium, and if not addressed in a timely manner may become fatal. During the project described here, the students will learn how to solve and address a...

2018Greer, Meredith and Ella Livesay  Mathematical Epidemiology Goes to College.
01 Apr 2020   Contributor(s):: Brian Winkel
Greer, Meredith and Ella Livesay. 2018. Mathematical Epidemiology Goes to College. Math Horizons. 25(3): 811.See https://scarab.bates.edu/cgi/viewcontent.cgi?article=1113&context=faculty_publications .From Introduction:Every year waves of illnesses sweep...

1977Freedman, H. I. and Paul Waltman  Mathematical models of population interactions with dispersal. I Stability of two habitats with and without a predator
01 Apr 2020   Contributor(s):: Brian Winkel
FREEDMAN, H. I. AND PAUL WALTMAN, 1977. MATHEMATICAL MODELS OF POPULATION INTERACTIONS WITHDISPERSAL. I: STABILITY OF TWO HABITATS WITH AND WITHOUTA PREDATOR. SIAM J. APPL. MATH. 32(3): 631648,See https://epubs.siam.org/doi/abs/10.1137/0132052?mobileUi=0&...

2018Joseph ,G Arul J. and S Balamuralitharan  A Nonlinear differential equation model of Asthma effect of environmental pollution using LHAM
01 Apr 2020   Contributor(s):: Brian Winkel
Joseph ,G Arul J. and S Balamuralitharan. 2018. A Nonlinear differential equation model of Asthma effect of environmental pollution using LHAM. IOP Conf. Series: Journal of Physics: Conf. Series. 1000:...

2007Choisy, M., J.F. Guégan, and P. Rohani Mathematical Modeling of Infectious Diseases Dynamics.
01 Apr 2020   Contributor(s):: Brian Winkel
Choisy, M., J.F. Guégan, and P. Rohani1. 2007. Mathematical Modeling of Infectious Diseases...

2018Brinks, Ralph  IllnessDeath Model in Chronic Disease Epidemiology: Characteristics of a Related, Differential Equation and an Inverse Problem.
29 Mar 2020   Contributor(s):: Brian Winkel
Brinks, Ralph. 2018. IllnessDeath Model in Chronic Disease Epidemiology: Characteristics of a Related, Differential Equation and an Inverse Problem. Computational and Mathematical Methods in Medicine. Volume 2018, Article ID 5091096. 6...