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9-002-S-GroundWaterFlow
31 Aug 2020 | | Contributor(s):: Jeremy Cristman, Kenneth Luther, Michael Karls
The goals of this project are to compare a conceptual one-dimensional groundwater flow model to observations made in a laboratory setting, and to discuss the differences. We derive the initial groundwater flow equation, and guide students through a solution. We describe the laboratory set up and...
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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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2017-Sim, Sy Yi, Sie Long Kek, and Kim Gaik Tay - Optimal control of a coupled tanks system with model-reality differences.
25 Mar 2020 | | Contributor(s):: Brian Winkel
2017-SimEtAl-OptControl-CoupledTanksSystemSim, Sy Yi, Sie Long Kek, and Kim Gaik Tay. 2017. Optimal control of a coupled tanks system with model-reality differences. AIP Conference Proceedings. 1872, 020012.See https://aip.scitation.org/doi/10.1063/1.4996669 ...
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5-025-S-SaltCompatments
19 Jul 2019 | | Contributor(s):: Brian Winkel
Model a phenomena in which salt mixtures from two tanks are mixed using several strategies.
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2019-Yagodich, Dina - 1-042-Kool-Aid Modeling Video
24 Feb 2019 | | Contributor(s):: Dina Yagodich
This is a video which can be used with students after they have worked on the Modeling Scenario 1-042-KoolAid. Dina Yagodich, Frederick Community College, Frederick MD USA produced the video in support of her students who thoroughly enjoyed doing this Modeling Scenario.This video is only...
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7-040-S-TankInterruptMixing
22 Aug 2018 | | Contributor(s):: Norman Loney
We present a differential equation model for the interrupted mixing of a tank with salt water. We offer two solution strategies (1) two step approach and (2) Laplace Transforms.
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2012-Levermore. David - First-Order Ordinary Differential Equations II: Graphical Methods and Applications
01 Dec 2017 | | Contributor(s):: Brian Winkel
Levermore. David. 21012. First-Order Ordinary Differential Equations II: Graphical Methods and Applications. University of Maryland. Notes. 23 pp.5. First-Order Equations: General Theory5.1. Well-Posed Problems 25.2. Existence and Uniqueness 36. First-Order Equations:...
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2012-Deboeck, Pascal R. , Jody S. Nicholson, C. S. Bergeman, Kristopher J. Preacher - From Modeling Long-Term Growth to Short-Term Fluctuations: Differential Equation Modeling is the Language of Change.
21 Sep 2017 | | Contributor(s):: Brian Winkel
Deboeck, Pascal R. , Jody S. Nicholson, C. S. Bergeman, Kristopher J. Preacher. 2012. From Modeling Long-Term Growth to Short-Term Fluctuations: Differential Equation Modeling is the Language of Change. Preprint from the 202 Proceedings of the International Meeting of the Psychometric...
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2017-University of Michigan - Math 216 Demonstrations
12 Sep 2017 | | Contributor(s):: Brian Winkel
Math 216 Demonstrations. https://instruct.math.lsa.umich.edu/lecturedemos/ma216/docs/ . Accessed 11 September 2017.This site contains many, many applications with good presentation and analysis as well as Matlab files to illustrate the concepts. For example modeling a swinging door with...
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2012-Unknown - Applied Differential Equations. Notes
11 Sep 2017 | | Contributor(s):: Brian Winkel
2012-Applied Differential Equations. Notes. 34 pp.Set of notes on solution strategies for first order differential equations with attention to detail in solutions and several models: tank mixing problems, mortgage, escape velocityKeywords: differential equation, model, first order, tank...
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2017-Unknown - Calculus for Engineers II-Sample Problems on mathematical modeling with differential equations
10 Sep 2017 | | Contributor(s):: Brian Winkel
Calculus for Engineers II-Sample Problems on mathematical modeling with differential equations. https://www.maths.tcd.ie/~manuela/Sample_1.pdf . Accessed 10 September 2017.Five modeling activities involved with emptying various tanks, projectile motion with resistance, and population growth...
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2013-Slavik, Antonin - Mixing Problems with Many Tanks.
10 Sep 2017 | | Contributor(s):: Brian Winkel
Slavik, Antonin. 2013. Mixing Problems with Many Tanks. Mathematics Monthly. 120: 806-821.See https://www.tandfonline.com/doi/abs/10.4169/amer.math.monthly.120.09.806 .Discusses many tank configurations, circular, cascading, in a row, etc. and the attendant matrix...
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2017-Nichols, David - Review of Mixing Problems
10 Sep 2017 | | Contributor(s):: Brian Winkel
Nichols, David. Review of Mixing Problems. 5 pp.Examples of tank mixing problems and solutions with attention to formulation and solution strategies.Keywords: differential equation, mixing, tank, model
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2017-Unknown - Ten DE Application Problems
10 Sep 2017 | | Contributor(s):: Brian Winkel
Ten Application Problems of Differential EquationA list of 10 applications anonymous list with these instructions, “For each problem, set up a differential equation modeling the situation. Be sure to define your variables, state the units being used, and determine the initial condition....
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2011-Shibberu, Yosi - MA211 Differential Equations. Class Notes
09 Sep 2017 | | Contributor(s):: Brian Winkel
Shibberu, Yosi. 2011. MA211 Differential Equations. Class Notes. PowerPoint. 426 slides. https://www.rose-hulman.edu/~shibberu/MA211/Slides.pdf . Accessed 1 September 2017This is a very good set of course slides and the Table of Contents is given here. Since this is a mathematics...
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1999-Hanin, Leonid G. - Which tank empties first? Preprint.
09 Sep 2017 | | Contributor(s):: Brian Winkel
Hanin, Leonid G. 1999. Which tank empties first? The American Mathematical Monthly. 106(10): 943-947. Preprint.See https://www.tandfonline.com/doi/abs/10.1080/00029890.1999.12005143 .From the opening of the paper, “Suppose that water towers like those shown in...
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2009-Recktenwald, G. - Tank Draining Exercise.
09 Sep 2017 | | Contributor(s):: Brian Winkel
Recktenwald, G. 2009. Tank Draining Exercise.See http://eet.cecs.pdx.edu/expt/tankdrain/pdf/tankDrainingLabExercise_Fall09.pdf . 16 pp. Accessed 7 September 2017.As part of an experience Engineering in Everyday Things this paper describe deep mathematics, including differential...
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2017-Gustafson, G. B. - Differential Equations Course Materials
08 Sep 2017 | | Contributor(s):: Brian Winkel
This material is from a wealth of other material authored by Grant B. Gustafson in the Mathematics Department at the University of Utah. See http://www.math.utah.edu/~gustafso/ for up to date information on his productivity! One could spend hours looking through here for examples,...
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2009-Martinez-Luaces - Modelling Applications Inverse Modelling
07 Sep 2017 | | Contributor(s):: Brian Winkel
Martinez-Luaces, Victor. 2009. Modelling, applications and inverse modelling: innovations in differential equations courses. Seventh Southern Right Delta Conference. pp. 159-170.Abstract: Differential equations and Laplace transform are widely used to solve problems concerned with...
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2014-Blomhøj, M. , T. H. Kjeldsen, and J. Ottesen - Compartment models
07 Sep 2017 | | Contributor(s):: Brian Winkel
Blomhøj, M. , T. H. Kjeldsen, and J. Ottesen. 2014. Compartment models. See http://www4.ncsu.edu/~msolufse/Compartmentmodels.pdf . Accessed 7 September 2017.From the first paragraph, “Background: It is important to master the ability to develop models....