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1-190-S-IntroClass
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...
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1-102C-S-CancerGrowth
19 Jan 2022 | | Contributor(s):: Jennie D'Ambroise, Jue Wang
This module is designed for Calculus I class and guides students in the use of differential equation models to predict cancer growth and study treatment outcomes. Several classical models for cancer growth are presented including exponential, power law, Bertalanffy, logistic, and Gompertz....
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1-160-S-HeartDeathRate
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...
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1-150-S-CancerTherapy
03 Aug 2021 | | Contributor(s):: Maila Hallare, Iordanka Panayotova
This activity builds upon elementary models on population growth. In particular, we compare two different treatment models of cancer therapy where in one, surgery happens before therapy and in the other, surgery happens after therapy.Activities will help students appreciate the importance of...
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SIMIODE EXPO 2021 - Minicourse M-R1 - Brian Winkel - Introduction to Differential Equations of Stochastic Processes
11 Feb 2021 | | Contributor(s):: Brian Winkel
SIMIODE EXPO 2021 - Minicourse M-R1 - Brian Winkel - Introduction to Differential Equations of Stochastic ProcessesBrian Winkel, Director SIMIODE, Cornwall NY USAThis was a presentation made at the SIMIODE EXPO 2021 - see program.Abstract: We describe efforts to...
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2013-Evans, Michael - Growth and Decay. Calculus Module 13
22 Mar 2020 | | Contributor(s):: Brian Winkel
2013-Evans-GrowthDecay3e-EdServicesAustraliaEvans, Michael. 2013. Growth and Decay. Calculus Module 13. Supporting Australian Mathematics Project. Education Services Australia: South Victoria AUSTRALIASee https://www.amsi.org.au/ESA_Senior_Years/PDF/GrowthDecay3e.pdf...
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1-062-S-BacterialGrowth
15 Sep 2018 | | Contributor(s):: Arati Nanda Pati
We offer students a simulation experience or data from a simulation and ask them to model the simulation using several approaches andusing EXCEL spreadsheet. In this particular modeling scenario, we know the exact solution and want to see how various models predict our expectations. We have used...
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1-102-S-CancerGrowth
29 Jul 2018 | | Contributor(s):: Jue Wang
This scenario guides students in the use of differential equation models to predict cancer growth and optimize treatment outcomes. Several classical models for cancer growth are studied, including exponential, power law, Bertalanffy, logistic, and Gompertz. They examine the behaviors of the...
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2018-Schneebeli, Hans R. - Population Modeling
01 Mar 2018 | | 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...
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1-024-S-MalariaControl
06 May 2016 | | Contributor(s):: David Culver
This project offers students a chance to make policy recommendations based on the analysis of models using both linear (exponential decay) and non-linear (logistic growth) differential equations. The scenario is based on the deployment of the United States Army's 62nd Engineer Battalion to...
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1-032-S-WordPropagation
07 Apr 2016 | | Contributor(s):: Rachelle DeCoste, Rachel Bayless
This activity is a gentle introduction to modeling via differential equations. The students will model the rate at which the word jumbo has propagated through English language texts over time.
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1991-Watson, Jane M. - Building probability models in a differential equations course
26 Jun 2015 | | Contributor(s):: Jane M. Watson
Watson, Jane M. 1991. Building probability models in a differential equations course. International Journal of Mathematical Education in Science and Technology. 22(4): 507-517.See https://www.tandfonline.com/doi/abs/10.1080/0020739910220402 .Article Abstract: An application is...
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2011-Leinbach, Carl - Beyond Newton's law of cooling – estimation of time since death.
20 Jun 2015 | | Contributor(s):: Carl Leinbach
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): 765-774.See - https://www.tandfonline.com/doi/abs/10.1080/0020739X.2011.592613 . The...
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7-008-S-MachineReplacement
04 Jun 2015 | | Contributor(s):: Brian Winkel
Students build an differential equation model using a convolution for machine replacement strategies for two different machine failure models: (1) exponentially distributed failure (student exercise) and (2) fixed time replacement. We discuss all the necessary probability notions which...
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1-002-S-Tossing
11 May 2015 | | Contributor(s):: Brian Winkel
We offer students simulation experience or data from a simulation and ask them to model the simulation using several approaches, to include exponential decay fit, difference equation, and differential equation.We add a Hand Out Working Version which can be used in class authored by Rachel ...