## Resources

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Resource Type (97)

Modeling Scenario(70) Technique Narrative(1) Potential Scenario(22) Article or Presentation(4)

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Differential Equation Type (97)

ODE(88) PDE(7) Delay(1) First(55) Second(30) Linear(39) Nonlinear(31) System(17) Constant Coeff(19) Homogeneous(28) Nonhomogeneous(17)

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Technique (97)

Boundary Value Problems(6) Eigen Methods(2) Initial Value Problems(82) Integrating Factor(2) Laplace Transform(1) Linear Algebra(1) Matrices(2) Numerical Methods(8) Parameter Estimation(41) Qualitative Behavior(7) Separable(14) Separation of Variables(28) Substitution Methods(1)

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Qualitative Analysis (97)

Equilibrium(6) Stability(1) Phase Plane(7) Graphical analysis(36) Eigenvalue analysis(4) Parameters(60) Other(18)

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Application Area (97)

Chemistry(8) Economics(4) Engineering(17) Life Sciences(19) Mathematics(25) Modeling (general)(87) Physics(69) Social Sciences(4)

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Course (97)

Calculus 1(1) Calculus 2(46) Calculus 3 (multivariable)(1) Differential Equations(96) Modeling(89)

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Course Level (97)

Introductory(96) Upper Level(95) High School(66)

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Lesson Length (97)

Portion of one class period(44) One class period(30) Multiple class periods(6) Other(25)

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Technology (97)

Derive(1) Excel(14) Maple(6) Mathematica(43) MatLab(8) Octave(2) R(1) SAGE(1) Desmos(1) None(6) Other(34)

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Approach (97)

Directed(4) Guided(69) Open-ended(3) Discussion(1) Develop model(1) Other(25)

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Skills (97)

Data collection(26) Data analysis(50) Programming(1) Statistics(1) Other(44)

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Key Scientific Process Skills (71)

Reading research papers(1) Reviewing prior research(4) Asking a question(68) Formulating hypotheses(63) Designing/conducting experiments(16) Predicting outcomes(21) Gathering data/making observations(21) Analyzing data(31) Interpreting results/data(32) Displaying/modeling results/data(32) Communicating results(33) Translating into mathematics(2)

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Assessment Type (71)

Homework(67) Solve problem(s)(1) Written assignment: Essay(1) Written assignment: Report(65) Written assignment: Literature review(1)

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Pedagogical Approaches (63)

Case Study(1) Collaborative Work(2) Computer Model(1) Guided inquiry/investigation(61)

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Vision and Change Core Competencies - Ability (72)

Create and develop models(71) Use quantitative reasoning(65) Design simulations(13) Tap into interdisciplinary study(5) Communicate and collaborate with other disciplines(5)

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Principles of How People Learn (69)

Motivates student to learn material(67) Focuses student on the material to be learned(65) Develops supportive community of learners(1) Leverages differences among learners(1) Reveals prior knowledge(2) Requires student to do the bulk of the work(1)

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Bloom's Cognitive Level (65)

Foundational: factual knowledge & comprehension(3) Application & Analysis(63)

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Includes clear efforts on Issues (1)

Equity(1)

###### Applied Filters

Modeling Scenario

##### 9-002-GroundWaterFlow-ModelingScenario

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.Potential Scenario

##### 2017-Bruce_Emerson-Wonderful World of Differential Equations

This is a terrific set of noted with models and applications woven into the material at every opportunity and data as well. This is introductory differential equations with attention to detail and motivation.Potential Scenario

##### 2017-Andras_Domokos-Differential Equations - Theory and Applications â€“ Notes

This is a terrific set of notes with models and applications woven into the material at every opportunity and data as well. This is introductory differential equations with attention to detail and motivation.Potential Scenario

##### 2015-Goodnow-EtAl-Mathematical Models of Water Clocks

This is a historical tour of water clocks, known as clepsydra a Greek word meaning water thief. These devices were for telling time.Modeling Scenario

##### 1-144-HeatCool-ModelingScenario

We offer an opportunity to build a mathematical model using Newton's Law of Cooling for a closed plastic baggie of liquid inside a liquid container.Potential Scenario

##### 2018-Chris McCarthy-Newtons Law of Cooling

You have hot water (initial temperature ) in a container, say a cup or glass. The temperature in the room is cooler, say a constant degrees Celsius. Come up with a differential equation that models the water's temperature.Modeling Scenario

##### 1-058-WaterClocks-ModelingScenario

We apply Torricelli's Law to the task of building a water clock in which the height of the water in a container falls at a constant rate when the container has a hole in the bottom to let the water flow out.Modeling Scenario

##### 1-064-TorricelliBox-ModelingScenario

The time it takes a column of water to empty and the time it takes the same volume of column of water with a box (various sizes) submerged in the column of water are compared through modeling with Torricelli's Law.Modeling Scenario

##### 1-079-HomeHeating-ModelingScenario

This project concerns using Newton's Law of Cooling to model the heating of a house. In particular, if one is going away for awhile, is it more economical to leave a house at a desired temperature or reheat it upon return?Potential Scenario

##### 1992-Jude_Sommerfeld-More Applied Math Problems on Vessel Draining

From a chemical engineering point of view emptying processing and storage tanks is important and this article considers many issues and shapes of containers. The main interest is in the total time it takes to empty the tank for a collection of...Potential Scenario

##### 2017-Zhang-Wang-Study on public opinion propagation in self media age based on time delay differential model

We establish the Logistic equation, introduce the operator time delay differential equation, and finally establish the improved delay differential equation, which can describe the propagation trend of network news from the self media.Modeling Scenario

##### 1-074-BottleWaterFlow-ModelingScenario

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.Modeling Scenario

##### 1-015-Torricelli-ModelingScenario

We help students develop a model (Torricelli's Law) for the height of a falling column of water with a small hole in the container at the bottom of the column of water through which water exits the column.Potential Scenario

##### 2012-Lensyl-Urbano-The Draining of a Plastic Bottle-Integrating a Physics Experiment into Calculus

I punched a small hole (about 1mm radius) in a one gallon plastic bottle and had my students measure the rate at which water drained.Potential Scenario