
9002SGroundWaterFlow
31 Aug 2020   Contributor(s):: Jeremy Cristman, Kenneth Luther, Michael Karls
The goals of this project are to compare a conceptual onedimensional 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...

2018Blomhøj, 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...

2017Sim, Sy Yi, Sie Long Kek, and Kim Gaik Tay  Optimal control of a coupled tanks system with modelreality differences.
25 Mar 2020   Contributor(s):: Brian Winkel
2017SimEtAlOptControlCoupledTanksSystemSim, Sy Yi, Sie Long Kek, and Kim Gaik Tay. 2017. Optimal control of a coupled tanks system with modelreality differences. AIP Conference Proceedings. 1872, 020012.See https://aip.scitation.org/doi/10.1063/1.4996669 ...

5025SSaltCompatments
19 Jul 2019   Contributor(s):: Brian Winkel
Model a phenomena in which salt mixtures from two tanks are mixed using several strategies.

2019Yagodich, Dina  1042KoolAid 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 1042KoolAid. 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...

7040STankInterruptMixing
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.

2012Levermore. David  FirstOrder Ordinary Differential Equations II: Graphical Methods and Applications
01 Dec 2017   Contributor(s):: Brian Winkel
Levermore. David. 21012. FirstOrder Ordinary Differential Equations II: Graphical Methods and Applications. University of Maryland. Notes. 23 pp.5. FirstOrder Equations: General Theory5.1. WellPosed Problems 25.2. Existence and Uniqueness 36. FirstOrder Equations:...

2012Deboeck, Pascal R. , Jody S. Nicholson, C. S. Bergeman, Kristopher J. Preacher  From Modeling LongTerm Growth to ShortTerm 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 LongTerm Growth to ShortTerm Fluctuations: Differential Equation Modeling is the Language of Change. Preprint from the 202 Proceedings of the International Meeting of the Psychometric...

2017University 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...

2012Unknown  Applied Differential Equations. Notes
11 Sep 2017   Contributor(s):: Brian Winkel
2012Applied 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...

2017Unknown  Calculus for Engineers IISample Problems on mathematical modeling with differential equations
10 Sep 2017   Contributor(s):: Brian Winkel
Calculus for Engineers IISample 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...

2013Slavik, Antonin  Mixing Problems with Many Tanks.
10 Sep 2017   Contributor(s):: Brian Winkel
Slavik, Antonin. 2013. Mixing Problems with Many Tanks. Mathematics Monthly. 120: 806821.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...

2017Nichols, 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

2017Unknown  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....

2011Shibberu, 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.rosehulman.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...

1999Hanin, 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): 943947. 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...

2009Recktenwald, 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...

2017Gustafson, 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,...

2009MartinezLuaces  Modelling Applications Inverse Modelling
07 Sep 2017   Contributor(s):: Brian Winkel
MartinezLuaces, Victor. 2009. Modelling, applications and inverse modelling: innovations in differential equations courses. Seventh Southern Right Delta Conference. pp. 159170.Abstract: Differential equations and Laplace transform are widely used to solve problems concerned with...

2014Blomhøj, 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....