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9-030-S-WaterHammer
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 initial-boundary value problem that describes the time evolution of...
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5-076-S-LanchesterLaws
27 Jul 2021 | | Contributor(s):: Blain Patterson
Lanchester's laws are used to calculate the relative strengths of military forces. The Lanchester equations are differential equations describing the time dependence of two armies' strengths A and B as a function of time, with the function depending only on A and B. In this project, you...
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2021-Bryan, Kurt - SIMIODE Textbook Code Materials Arranged by Software
04 Jul 2021 | | Contributor(s):: Kurt Bryan
SIMIODE Textbook ResourcesPreambleThe various scripts and routines below are preliminary versions that support the exercises and projects throughout the book, especially those that involve data or large symbolic or numerical computations (they will be "official" in late August...
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SIMIODE EXPO 2021 - Minicourse M-R1 - Glenn Ledder - An Epidemiological Model for COVID-19
21 Feb 2021 | | Contributor(s):: Glenn Ledder
SIMIODE EXPO 2021 - Minicourse M-R1 - Glenn Ledder - An Epidemiological Model for COVID-19Glenn Ledder, University of Nebraska, Lincoln NE USAThis was a presentation made at the SIMIODE EXPO 2021 - see program.Abstract: We develop a model for COVID-19 population dynamics by...
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2018-Blomhøj, M. , T.H. Kjeldsen, and J. Ottesen. 2018. Compartment models. Lecture Notes.
01 Apr 2020 | | Contributor(s):: Brian Winkel
M. Blomhøj, T.H. Kjeldsen, and J. Ottesen. 2018. Compartment models. Lecture Notes 47 pp. Chapter 1 - Compartment ModelsBackground: It is important to master the ability to develop models. Modeling of dynamical systems plays a very important role in...
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9-020-S-HeatDiffusion
14 Oct 2019 | | Contributor(s):: Kimberly Spayd, James Puckett
This project guides students through experimental, analytical, and numerical techniques for understanding the heat (diffusion) equation with nonhomogeneous boundary conditions. In particular, students collect data and model a physical scenario in which heat energy diffuses through a long, thin...
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5-002-S-PhasePortraitForRelationshipDynamics
15 Aug 2019 | | Contributor(s):: Lawrence C Udeigwe
The different possible dynamics of a two-person romantic relationship are modeled -- as a linear two dimensional system of equations -- and analyzed. Students are guided to explore how the mathematical model of one relationship type can be obtained by modifying the mathematical model of another....
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1-001d-S-HotelPopulationDecay
03 Jul 2019 | | Contributor(s):: Dina Yagodich
We offer students an opportunity to create a simulation model a hotel population with clients checking in and checking out according to two different disciplines as well as a number of different starting populations in the hotel.
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7-011-Text-S-CoupledSystemLaplace
31 Mar 2019 | | Contributor(s):: Mitaxi Pranlal Mehta
Differential equations and Laplace transforms are an integral part of control problems in engineering systems. However a clear explanation of the relationship of Laplace transforms with the differential equation formalism is difficult to find for coupled differential equations. Here we describe...
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1-143-S-PopulationModelVariationsMATLAB
17 Feb 2019 | | Contributor(s):: Bill Skerbitz
Students will walk through a detailed derivation and review of basic population models (exponential and logistic) to create and understand variations of those models while learning some basic MATLAB functions for working with differential equations. They will also work with other utilities...
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3-043-S-BallisticModeling-SpongeDart
20 Nov 2018 | | Contributor(s):: Jean Marie Linhart, Peter Howard
The goal of this project is for students to develop, analyze, and compare three different models for the flight of a sponge dart moving under the influences of gravity and air resistance. The first two models are based respectively on the common simplifying assumptions of no air resistance and...
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9-001-Text-S-SkinBurnModelNumericalMethods
18 Aug 2018 | | Contributor(s):: Suruchi Singh
The heat equation is an important partial differential equation (PDE) which describes the distribution of heat in a given region over time. Here we learn to solve a heat equation numerically. It is difficult to study the behavior of temperature in problems with interfaces analytically so...
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6-070-S-BeerBubbles
24 Apr 2018 | | Contributor(s):: Michael Karls
The goal of this project is to set up and numerically solve a first-order nonlinear ordinary differential equation (ODE) system of three equations in three unknowns that models beer bubbles that form at the bottom of a glass and rise to the top. The system solution is then used to verify...
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2002-de Pillis, L. G. and A. E. Radunskaya - Parameter Estimation for Tumor-Immune ODE System. Slides.
21 Sep 2017 | | Contributor(s):: Brian Winkel
de Pillis, L. G. and A. E. Radunskaya. 2002. Parameter Estimation for Tumor-Immune ODE System, 24 slides. See https://pages.pomona.edu/~aer04747/TumorModule/parameter_estimation.pdf . This is a very thorough and complete introduction to estimating parameters for a simple differential...
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2011-Wentworth, Corinne, Masami Fujiwara, and Jay Walton - Optimal harvesting models for fishery populations.
12 Sep 2017 | | Contributor(s):: Brian Winkel
Wentworth, Corinne, Masami Fujiwara, and Jay Walton. 2011. Optimal harvesting models for fishery populations. REU paper. 17 pp.Abstract. Fishery management is the consideration of the ecological effects of harvesting. Fisherman work to provide fish for a growing human population...
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2011-Harwood, Kenny - Modeling a RLC Circuit's Current with Differential Equations
12 Sep 2017 | | Contributor(s):: Brian Winkel
Harwood, Kenny. 2011. Modeling a RLC Circuit’s Current with Differential Equations. Paper. 17 pp.Abstract The world of electricity and light have only within the past century been explained in mathematical terms yet still remain a mystery to the human race. R. Buckminster Fuller said;...
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2001-Knisley, Jeff and Lyndell Kerley - Using data to motivate the models used in introductory differential equations.
11 Sep 2017 | | Contributor(s):: Brian Winkel
Knisley, Jeff and Lyndell Kerley. 2001. Using data to motivate the models used in introductory differential equations. PRIMUS. 11(2): 111-123.See https://www.tandfonline.com/doi/abs/10.1080/10511970108965983 .Abstract: Although data is often used to estimate parameters for models in...
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2011-Nguyen, Olivia and Xiaoyu Shi - Modeling the absorption, circulation, and metabolism of tirapazamine
11 Sep 2017 | | Contributor(s):: Brian Winkel
Nguyen, Olivia and Xiaoyu Shi. 2011. Modeling the absorption, circulation, and metabolism of tirapazamine.http://www.isn.ucsd.edu/courses/beng221/problems/2011/project02.pdf . Accessed 10 Sept 2017.This apparently is a student project and it develops the kinetic model, uses...
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2005-Howard P. - Modeling with ODE. Notes.
10 Sep 2017 | | Contributor(s):: Brian Winkel
Howard P. 2005. Modeling with ODE. Notes. 48 pp.See https://www.math.tamu.edu/~phoward/m412/modode.pdf .Great exposition and lots of Modeling Scenarios almost laid out completely as exercises.From the textOverviewA wide variety of natural phenomena such as projectile motion,...
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2017-MBW- Predator-Prey Models With Delay And Prey Harvesting
10 Sep 2017 | | Contributor(s):: Brian Winkel
MBW- Predator-Prey Models With Delay And Prey Harvesting. https://mathbio.colorado.edu/index.php/MBW:Predator-prey_models_with_delay_and_prey_harvesting . Accessed 10 September 2017.This is a very nice exposition, no problems or data offered, of a biological system and is part of a larger...