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

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.

FirstOrderModels
03 Mar 2018   Contributor(s):: Unknown
Modeling with First Order EquationsMathematical models characterize physical systems, often using differential equations.Model Construction: Translating physical situation into mathematical terms. Clearly state physical principlesbelieved to govern process. Differential equation is a mathematical...

2012DeboeckEtAlModeling LongTerm Growth to ShortTerm Fluctuations
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. Prepring from the 202 Proceedings of the International Meeting of the Psychometric...

2012Applied Differential Equations
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 mixing,...

2013SlavikMixing Problems with Many Tanks
10 Sep 2017   Contributor(s):: Brian Winkel
Slavik, Antonin. 2013. Mixing Problems with Many Tanks. Mathematics Monthly. 120: 806821.Discusses many tank configurations, circular, cascading, in a row, etc. and the attendant matrix representation of the linear mixing model of differential equations. Keywords: tank, circula,...

Joyner  Mixing Problems
10 Sep 2017   Contributor(s):: Brian Winkel
Joyner, David. Mixing Problems in ODEs. Notes. 4 pp. https://www.usna.edu/Users/math/wdj/_files/documents/teach/sm212/DiffyQ/demixing.pdf . Accessed 10 September 2017.Here is what this material is about,“Suppose that we have two chemical substances where one is soluable in the other, such...

Chapter Nine – Mathematical Models with Differential Equations.
10 Sep 2017   Contributor(s):: Brian Winkel
Chapter Nine – Mathematical Models with Differential Equations. From unknown text. pp. 582622. http://higheredbcs.wiley.com/legacy/college/anton/0470183454/add_materials/mathematical_modeling_with_diff_equations.pdfThis is a rich chapter from unknown text with rich text and...

Nichols 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

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. You...

2011ShibberuDEClassNotes
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 2017 This is a very good set of course slides and the Table of Contents is given here. Since this is a mathematics...

1999HaninWhichTankEmptiesFirst
09 Sep 2017   Contributor(s):: Brian Winkel
Hanin, Leonid G. 1999. Which tank empties first? The American Mathematical Monthly. 106(10): 943947. Preprint.From the opening of the paper, “Suppose that water towers like those shown in Figure 1 are initially filled with water and have the same volume, height, and...

2009RecktenwaldTankDrainingExercise
09 Sep 2017   Contributor(s):: Brian Winkel
Recktenwald, G. 2009. Tank Draining Exercise. 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 equations...

Gustafson2250 Systems Differential Equations Applications
08 Sep 2017   Contributor(s):: Brian Winkel
Gustafson, G. B. Systems of Differential Equations, Chapter 11. 69 pp.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...

2009MartinezLuacesModelling 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...

2014BlomhojEtAlCompartmentModels
07 Sep 2017   Contributor(s):: Brian Winkel
Blomhøj, M. , T. H. Kjeldsen, and J. Ottesen. 2014. Compartment models. 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. Modeling of...

2012WoodsModelingConcentrationInTank
05 Sep 2017   Contributor(s):: Brian Winkel
Woods, Christian. 2012. Modeling concentration of a solution. https://www.math.ucsd.edu/~c1woods/teaching/tankproblem.pdf . Accessed 4 September 2017.These are teaching notes from when the author was a graduate student TA in 2012.This is a nice exposition of a tank mixing...

1998ClausMcGahanModeling Projects In DE Course
05 Sep 2017   Contributor(s):: Brian Winkel
ClausMcGahan, Elly. 1998. Modeling Projets in a Differential Equations Course. PRIMUS: Problems, Resources, and Issues in Mathematics Undergraduate Studies. 8(2): 137149Abstract: Much has been said about the benefits of using projects in teaching the calculus sequence. Here we dis cuss...

1057SFiguringFluidFlow
15 Aug 2017   Contributor(s):: Brian Winkel
We propose three differential equations models for the height of a column of falling water as the water exits a small bore hole at the bottom of the cylinder and ask students to determine which model is the best of the three.

1042SKoolAid
26 Apr 2017   Contributor(s):: Kristin Burney, Lydia Kennedy, Audrey Malagon
We model the amount of drink powder in a second tank of a two tank flow system.