## Resources

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Resource Type (13)

Modeling Scenario(7) Technique Narrative(1) Potential Scenario(4) Article or Presentation(1)

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Differential Equation Type (13)

ODE(8) PDE(3) First(3) Second(4) Linear(4) Nonlinear(3) System(2) Constant Coeff(2) Nonhomogeneous(3) Other(2)

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Technique (13)

Boundary Value Problems(3) Initial Value Problems(8) Numerical Methods(2) Parameter Estimation(4) Qualitative Behavior(1) Separable(1) Series(1) Other(2)

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Qualitative Analysis (13)

Graphical analysis(8) Eigenvalue analysis(1) Parameters(7) Other(3)

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Application Area (13)

Engineering(3) Humanities(1) Life Sciences(2) Mathematics(4) Modeling (general)(9) Physics(7)

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Course (13)

Calculus 2(4) Calculus 3 (multivariable)(1) Differential Equations(12) Modeling(11)

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Course Level (13)

Introductory(12) Upper Level(13) High School(7)

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Lesson Length (13)

Portion of one class period(2) One class period(4) Multiple class periods(2) Other(5)

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Technology (13)

Excel(1) Mathematica(5) None(1) Other(6)

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Approach (13)

Directed(1) Guided(7) Open-ended(1) Other(5)

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Skills (13)

Data collection(1) Data analysis(9) Other(4)

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Key Scientific Process Skills (8)

Asking a question(8) Formulating hypotheses(7) Designing/conducting experiments(2) Predicting outcomes(2) Gathering data/making observations(1) Analyzing data(1) Interpreting results/data(2) Displaying/modeling results/data(4) Communicating results(3)

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Assessment Type (8)

Homework(8) Written assignment: One minute paper(1) Written assignment: Report(5)

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Pedagogical Approaches (7)

Case Study(1) Computer Model(1) Guided inquiry/investigation(6)

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Vision and Change Core Competencies - Ability (7)

Create and develop models(6) Use quantitative reasoning(7) Design simulations(2) Tap into interdisciplinary study(1)

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Principles of How People Learn (8)

Motivates student to learn material(8) Focuses student on the material to be learned(7) Reveals prior knowledge(1)

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Bloom's Cognitive Level (8)

Foundational: factual knowledge & comprehension(1) Application & Analysis(7)

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Includes clear efforts on Issues (0)

###### Applied Filters

Technique Narrative

##### 8-002-TrigSumRepresentation-TechniqueNarrative

Students discover how to represent functions as sums of trigonometric functions and the value of such representations in many fields. This is an introduction to the study of Fourier Series.Modeling Scenario

##### 9-012-PDEGuitarTuning-ModelingScenario

We lead students through a derivation of a partial differential equation which models the motion of a string held at both ends, a case of the one-dimensional wave equation, and then play it on Mathematica.Potential Scenario

##### 2011-W_Wood-Squigonometry

The differential equations used to define a unit circle, namely xâ€™(t) = - y(t), yâ€™(t) = x(t), x(0) = 1, y(0) = 0 are generalized to produce interesting functions which satisfy trig like identities.Article or Presentation

##### 2008-Brian_Winkel-Fourier_Series-Optimization_Opportunity

We discuss the introduction of Fourier series as an immediate application of optimization of a function of more than one variable.Potential Scenario

##### 2017-David_Morin-Oscillations

So needless to say, an understanding of oscillations is required for an understanding of waves.Modeling Scenario

##### 1-096-OP-AMP-Differentiator-ModelingScenario

The output waveform (function) of a operational amplifier type of differentiator circuit is determined analytically from the first order governing ordinary differential equation and compared with the data acquired from numerical model (using...Potential Scenario

##### 2011-W_Wood-Squigonometry

The differential equations used to define a unit circle, namely xâ€™(t) = - y(t), yâ€™(t) = (t), x(0) = 1, y(0) = 0 are generalized to produce interesting functions which satisfy trig like identities.Potential Scenario

##### 2018-Meredith_Greer-Ella_Livesay-Mathematical Epidemiology Goes to College

In this article we present models that were inspired by two real-life outbreaks at a small residential college campus: H1N1 influenza in 2009 and, surprisingly, mumps in 2016.Modeling Scenario

##### 9-005-InvasiveSpeciesModel-ModelingScenario

This scenario takes students through the development of an invasive species partial differential equation model. Basic models are discussed first, which lead students to eventually develop their own model which takes into account dispersion.Modeling Scenario

##### 4-036-AltitudeDependentGravity-ModelingScenario

When projectiles are way above Earth's surface gravity's changes become important when dealing with projectiles at high altitudes. We lay out an approach for such a case which is a second-order differential equation.Modeling Scenario

##### 9-010-TravelingWave-ModelingScenario

Students are taken through a traveling wave analysis of a porous medium model. While the starting point is a nonlinear partial differential equation model, after a change of variables, students are led quickly to an ordinary differential equation...Modeling Scenario

##### 3-071-WirelessTelegraphy-ModelingScenario

This project has three parts, (1) done at home, (2) and (3) in class. In (1) we recall how to solve second order differential equations with constant coefficients and simple source functions. In class understand resonance and beats.Modeling Scenario