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5-002-T-PhasePortraitForRelationshipDynamics
15 Aug 2019 | Modeling Scenarios | Contributor(s): Karen Bliss
The different possible dynamics of a two-person romantic relationship are modeled -- as a linear two dimensional system of equations -- and analyzed. Students are guided to explore how the mathematical model of one relationship type can be obtained by modifying the mathematical model of another....
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1-068-T-WaterBottleCooling
14 Aug 2019 | Modeling Scenarios | Contributor(s): Karen Bliss
This modeling scenario involves Newton's Law of Cooling and should be appropriate in the first week or even the first day of an introductory differential equations course. The scenario uses an Inquiry Based Learning approach to walk the students through the creation and understanding of a...
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3-067-S-RLCSeriesCircuit
28 Apr 2019 | Modeling Scenarios | Contributor(s): Karen Bliss
In this validation-oriented setup, the second order linear ordinary differential governing equation of a small signal RLC series AC circuit is solved analytically, and the results are compared with the data acquired from analyzing the numerical model (using Multisim).
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3-067-T-RLCSeriesCircuit
28 Apr 2019 | Modeling Scenarios | Contributor(s): Karen Bliss
In this validation-oriented setup, the second order linear ordinary differential governing equation of a small signal RLC series AC circuit is solved analytically, and the results are compared with the data acquired from analyzing the numerical model (using Multisim).
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1-077-T-RLMSimSeriesCircuit
03 Mar 2019 | Modeling Scenarios | Contributor(s): Karen Bliss
In this validation-oriented setup, the first order linear ordinary differential equation governing a small signal RL series AC circuit is solved analytically and the results are compared with the data acquired from analyzing the numerical model (using Multisim) of the circuit. This is compared...
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1986-Cooke-Linear And Logistic Harvesting Models-Math Modeling Journal
09 Dec 2018 | Potential Scenario Ideas | Contributor(s): Karen Bliss
Cook, K. L. and M. Witten. 1986. One-dimensional linear and logistic harvesting models. Mathematical Modeling. 7: 301-340.Abstract: Some of the results in the literature on simple one-dimensional, density dependent, discrete and continuous models-with and without harvesting-are reviewed. Both...
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1-054-T-GrowthInFarmland
14 Aug 2018 | Modeling Scenarios | Contributor(s): Karen Bliss
An enriching project developing a model from data with missing temporal information is described. Students fit functions to the data that leads to the creation of a differential equations model, which they then are required to analyze in multiple ways. Different fits, modeling approaches, and...
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5-026-T-Evictions
12 Aug 2018 | Modeling Scenarios | Contributor(s): Karen Bliss
In this project, students develop two SIS models to study eviction trends in a population of non-homeowner households using an actual eviction rate. (The Eviction Lab at Princeton University has developed a nationwide database of evictions based on 83 million eviction records.) As the first...
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LeakingBucket: Differential Equations in Engineering
03 Mar 2018 | Potential Scenario Ideas | Contributor(s): Karen Bliss
Differential Equations in Engineering: The Leaking Bucket. Laboratory Experiment. 4 pp.From the Text:7.1 Laboratory ObjectiveThe objective of this laboratory is to learn about first order differential equations and theirapplication to a leaking bucket. 7.2 Educational ObjectivesAfter...
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2003-RasmussenKeynes-LinesOfEigenVectorsSolutionsToSytemsOfLinearDifferentialEquations
03 Mar 2018 | Potential Scenario Ideas | Contributor(s): Karen Bliss
Rasmussen, Chris and Michael Keynes. 2003. Lines of Eigenvectors and Solutions to Systems of Linear Differential Equations. PRIMUS. 13(4): 308-320.Abstract: The purpose of this paper is to describe an instructional sequence where students invent a method for locating lines of...
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1988-Strogatz-LoveAffairsAndDifferentialEquations
26 Nov 2017 | Potential Scenario Ideas | Contributor(s): Karen Bliss
Strogatz, Steven H. 1988. Love Affairs and Differential Equations. Mathematics Magazine. 61(7): 35.This is a system of differential equations to describe the love between Shakespeare’s Romeo and Juliet.Keywords: differential equation, system, linear, parameters
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2015-Easton-Mathematical models of health focusing on diabetes
11 Sep 2017 | Potential Scenario Ideas | Contributor(s): Karen Bliss
Easton, Jonathan. 2015. Mathematical models of health focusing on diabetes: Delay differential equations and data mining. Doctoral thesis, 186 pp. Northumbria University. http://nrl.northumbria.ac.uk/23582/ . Accessed 10 September 2017.This is an exhaustive study with very good...
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2013-Slavik-Mixing Problems with Many Tanks
10 Sep 2017 | Potential Scenario Ideas | Contributor(s): Karen Bliss
Slavik, Antonin. 2013. Mixing Problems with Many Tanks. Mathematics Monthly. 120: 806-821.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,...
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BobbingObjectInWater
09 Sep 2017 | Potential Scenario Ideas | Contributor(s): Karen Bliss
Introduction to Second Order Linear Equations- Bobbing Object in Water. 2 pp.This is a nice treatment of developing a model of a bobbing object in water from first principles with some nice additional questions which would make a nice Modeling Scenario.Keywords: buoyancy, bobbing, water,...
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Finio-Linear Non Linear Springs Tutorial
06 Sep 2017 | Potential Scenario Ideas | Contributor(s): Karen Bliss
Finio, Ben. Science Buddies – Linear & Nonlinear Springs Tutorial. https://www.sciencebuddies.org/science-fair-projects/references/linear-nonlinear-springs-tutorial#introduction . Accessed 5 September 2017.This tutorial provides a basic summary of linear and nonlinear...
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1-091-T-Slopefields
04 Sep 2017 | Modeling Scenarios | Contributor(s): Karen Bliss
Students will gain experience writing differential equations to model various population scenarios, they will create slope fields to view the solution curves using software, and they will discuss the behavior of the solution curves. In this activity, students are introduced to the concepts of...
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1-073-T-WaterExitBottle
17 Apr 2017 | Modeling Scenarios | Contributor(s): Karen Bliss
We offer an experiment in which data is collected to ascertain a parameter in the differential equation formulation of Torricelli's Law for water flow out of a cylindrical container. Source: Farmer, T and F. Gass. 1992. Physical demonstration in the calculus classroom. The College...
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3-040-T-FirstPassageTime
07 Apr 2017 | Modeling Scenarios | Contributor(s): Karen Bliss
We apply the notions of dampedness to second order, linear, constant coefficient, homogeneous differential equations used to model a spring mass dashpot system and introduce the notion of first passage time with several applications.
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3-002-T-ModelsMotivatingSecondOrder
30 Mar 2017 | Modeling Scenarios | Contributor(s): Karen Bliss
We introduce several basic, but substantial, approaches to modeling the motion of a spring mass system using a standard second order, linear, constant coefficient differential equation obtained from Newton's Second Law of Motion and a Free Body Diagram. We do this using a set of data...
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Informed Conjecturing in a Modeling Context Differential Equations
29 Mar 2017 | Articles and Publications | Contributor(s): Karen Bliss
We examine two differential equations, (1) first order exponential growth or decay and (2) second order, linear, constant coefficient differential equations, and show the advantage of learning differential equations in a modeling context for informed conjectures of their solution. We follow with...