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...
23 Jan 2022 | | Contributor(s):: Erich McAlister
Pitch velocity is one of the most fascinating statistics in baseball, as documented in the 2015 documentary Fastball. Modern measurements of pitch velocity are taken as the maximum velocity achieved at any point between the pitcher's hand and home plate. However, the velocity of the ball...
21 Jan 2022 | | Contributor(s):: Jacob Paul Duncan
Most projectile motion and free fall models are based on the assumption that gravity is the only force acting on the object. Here we develop, solve, and analyze a second order nonhomogeneous differential equation model for free fall which incorporates air resistance. Students will solve the model...
14 Jan 2022 | | Contributor(s):: Bonnie Moon
In this lab students will collect data on their spring mass systems and compare their empirical models to their theoretical ones—giving them an opportunity to actually test a model against data. Before this lab, students should have modeled spring-mass systems and solved second-order...
18 Oct 2021 | | Contributor(s):: Maila Hallare, Charles Lamb
This activity analyzes the spread of a technological innovation using the Bass Model from Economics. The equation is a first-order, two-parameter separable equation and the solution has a characteristic S-shaped curve or sigmoid curve. The students derive the solution to the model, use least...
20 Sep 2021 | | Contributor(s):: Arati Nanda Pati
In this modeling scenario, we offer students simulation experience from a given data set which represents the heart death rate during the period 2000 - 2010 using several approaches to include exponential decay, difference equation, differential equation, and parameter estimation using EXCEL. We...
25 Aug 2021 | | Contributor(s):: Joshua Goldwyn
In this activity students will study a linear, first order, one-dimensional ordinary differential equation (ODE) and learn how it can be used to understand basics of neural dynamics. The modeling framework is known in the mathematical neuroscience literature as the ``integrate-and-fire''...
07 Aug 2021 | | Contributor(s):: Iordanka Panayotova, Maila Hallare
This modeling scenario guides students through the process of fitting the Lotka-Volterra model of two differential equations to a real time series observational data. Students use the capabilities of R and R studio, an integrated development environment for R, and the gauseR package, a collection...
04 Aug 2021 | | Contributor(s):: Allison Leigh Lewis
This modeling scenario guides a student familiar with single ordinary differential equation (ODE) models towards the development of a more complex system of two ODEs for describing the evolution of tumor growth over time. Students should have prior experience with solving ODEs using the separable...
Optimum Matched Filter Design (Transfer Function)
22 Mar 2021 |
Posted by Phil B Brubaker
2021-Sanft, Rebecca, and Anne Walter - Exploring Mathematical Modeling in Biology Through Case Studies and Experimental Activities
20 Jan 2021 | | Contributor(s):: Rebecca Sanft, Anne Walter
Exploring Mathematical Modeling in Biology Through Case Studies and Experimental Activities, written collaboratively by a mathematician and biologist, provides supporting materials for a course taken simultaneously by students majoring in the mathematical sciences and those in the life sciences....
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.
2020-Harwood, Corban - Remote Teaching Module: Introduction to Modeling
28 Jul 2020 | | Contributor(s):: Corban Harwood
We place here and in the Supporting Documents all the materials in support of the SIMIODE Remote Teaching Module.Introduction to ModelingThis Remote Teaching Module introduces modeling with first order differential equations and motivates students to fully engage in the solution and...
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 x-y-S-Title-StudentVersion-Czech.
29 May 2020 | | Contributor(s):: Brian Winkel
We are given data on the position of a mass in an oscillating spring mass system and we seek to discover approaches to estimating an unknown parameter.
21 Apr 2020 | | Contributor(s):: Brian Winkel
We ask students to use the system of first order linear differential equations given in a source paper and estimates of the data from laboratory procedures from a plot to estimate the parameters and complete the modeling process. Then we seek to compare the results of the final model with...
14 Apr 2020 | | Contributor(s):: Erdi KARA
We will explore a model which describes the process of entry into marriage by an individual. In the model, rate of change in the fraction of the cohort already married will be investigated along with two governing assumptions; social pressure experienced by unmarried individual increases as...
2018-Weber, Frank, Stefan Theers, Dirk Surmann, Uwe Ligges, and Claus Weihs - Sensitivity Analysis of Ordinary Differential Equation Models
06 Apr 2020 | | Contributor(s):: Brian Winkel
Weber, Frank, Stefan Theers, Dirk Surmann, Uwe Ligges, and Claus Weihs. 2018. Sensitivity Analysis of Ordinary Differential Equation Models.See https://d-nb.info/1160443556/34 .Introduction The goal of sensitivity analysis is to examine how sensitive a mathematical model...
2019-Hu,Yueqin and Raymond Treinen - A one-step method for modelling longitudinal data with differential equations.
06 Apr 2020 | | Contributor(s):: Brian Winkel
Hu,Yueqin and Raymond Treinen. 2019. A one-step method for modelling longitudinal data with differential equations. British Journal of Mathematical and Statistical Psychology. 72: 38–60See https://bpspsychub.onlinelibrary.wiley.com/doi/abs/10.1111/bmsp.12135...
2007-Helfgott, Michel and Edith Seier - Some Mathematical and Statistical Aspects of Enzyme Kinetics.
05 Apr 2020 | | Contributor(s):: Brian Winkel
2007-HelfgottSeier-MathStatAspectsOfEnzymeKineticsHelfgott, Michel and Edith Seier. 2007. Some Mathematical and Statistical Aspects of Enzyme Kinetics. The Journal of Online Mathematics and Its Applications. Volume 7, October 2007, Article ID...