## Resources

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Resource Type (25)

Modeling Scenario(20) Technique Narrative(1) Potential Scenario(3) Article or Presentation(1)

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Differential Equation Type (25)

ODE(25) First(7) Second(13) Linear(13) Nonlinear(5) System(4) Constant Coeff(10) Homogeneous(11) Nonhomogeneous(5)

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Technique (25)

Boundary Value Problems(2) Eigen Methods(2) Initial Value Problems(15) Laplace Transform(1) Linear Algebra(1) Numerical Methods(2) Parameter Estimation(6) Qualitative Behavior(1) Separable(3) Separation of Variables(2) Substitution Methods(1) Other(1)

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Qualitative Analysis (25)

Equilibrium(3) Stability(2) Phase Plane(3) Graphical analysis(13) Eigenvalue analysis(2) Parameters(14) Other(2)

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Application Area (25)

Economics(1) Engineering(6) Life Sciences(3) Mathematics(4) Modeling (general)(20) Physics(18)

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Course (25)

Calculus 2(4) Calculus 3 (multivariable)(1) Differential Equations(25) Modeling(24)

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Course Level (25)

Introductory(25) Upper Level(23) High School(17)

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Lesson Length (25)

Portion of one class period(9) One class period(10) Multiple class periods(2) Other(5)

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Technology (25)

Excel(4) Maple(1) Mathematica(19) MatLab(1) Python(1) R(1) Desmos(1) None(3) Other(4)

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Approach (25)

Directed(3) Guided(20) Discussion(1) Develop model(1) Other(3)

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Skills (25)

Data collection(5) Data analysis(10) Statistics(1) Other(14)

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Key Scientific Process Skills (20)

Reviewing prior research(1) Asking a question(20) Formulating hypotheses(17) Designing/conducting experiments(3) Predicting outcomes(9) Gathering data/making observations(5) Analyzing data(9) Interpreting results/data(10) Displaying/modeling results/data(10) Communicating results(10) Translating into mathematics(1)

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Assessment Type (21)

Homework(16) Give an oral presentation(1) Informal in-class report(1) Written assignment: Essay(1) Written assignment: Report(19)

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Pedagogical Approaches (20)

Guided inquiry/investigation(20)

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Vision and Change Core Competencies - Ability (20)

Create and develop models(19) Use quantitative reasoning(16) Design simulations(3) Tap into interdisciplinary study(2)

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Principles of How People Learn (21)

Motivates student to learn material(20) Focuses student on the material to be learned(18)

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Bloom's Cognitive Level (20)

Foundational: factual knowledge & comprehension(2) Application & Analysis(20)

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Includes clear efforts on Issues (0)

###### Applied Filters

Modeling Scenario

##### 1-155-CruiseControl-ModelingScenario

In this project we illustrate the design of a proportional-integral-derivative (PID) cruise control algorithm for an automobile. PID control is one of the most common techniques in control engineering.Modeling Scenario

##### 3-027-BobbingDropping-ModelingScenario

We present two exercises in which we ask students to model (1) falling object experiencing terminal velocity and (2) bobbing block of wood in liquid. We model the motion using Newton's Second Law of Motion and Archimedes' Principle.Modeling Scenario

##### 5-014-TwoSpringMass-ModelingScenario

We ask students to build a Free Body Diagram for a vertical two mass situation in which the two masses are held fixed at the tip and at the bottom. The mass holds the springs together at the join of the two springs in between.Modeling Scenario

##### 1-128-RocketFlight-ModelingScenario

We offer an opportunity to build a mathematical model using Newton's Second Law of Motion and a Free Body Diagram to analyze the forces acting on the rocket of changing mass in its upward flight under power and then without power followed by its...Modeling Scenario

##### 6-012-RiverCrossing-ModelingScenario

Students develop a model of a river crossing in a boat with thrust using Newton's Second Law of Motion from a Free Body Diagram they construct. The model is thence a system of one second order linear and a second order nonlinear differential...Potential Scenario

##### 2015-Doust-Saraj-The logistic modeling population having harvesting factor

The present paper deals with the logistic equation having harvesting factor, which is studied in two cases constant and non-constant.Modeling Scenario

##### 3-065-UpDown-ModelingScenario

We model the height of a launched object which is subject to resistance proportional to velocity during its flight. We ask questions about the motion as well, e.g., highest point or apex and terminal velocity.Modeling Scenario

##### 3-009-BallDropInWater-ModelingScenario

We conduct an analysis of a falling ball in liquid to determine its terminal velocity and to ascertain just what radius ball for a given mass density is necessary to attain a designated terminal velocity.Modeling Scenario

##### 3-013-WhiffleBallFall-ModelingScenario

We are given data on the time and position of a whiffle ball as it falls to the ground. We attempt to model the falling ball and we confront the different resistance terms and models.Modeling Scenario

##### 4-020-AnIEDBlast-ModelingScenario

These three exercises offer students a chance to model with second order ordinary differential equations, how they might incorporate a spring-mass system into a larger model, and how they can use the model to determine the results of a dynamical...Modeling Scenario

##### 3-080-PendulumModeling-ModelingScenario

We lead students through building model for several pendulum configurations in motion and ask students to compare results.Modeling Scenario

##### 1-012-Sublimation-Modeling Scenario

We offer data on the sublimation of dry ice (carbon dioxide) collected in a classroom setting so that students can model the rate of change in the mass of a small solid carbon dioxide block with a differential equation model, solve the...Article or Presentation

##### 2020-TeachingModule-GeometricBehaviorOfLinearSysteModeling

This module concentrates on the geometric properties of a system of 2 linear, homogeneous first order differential equations in 2 variables as dictated by the corresponding eigenvalues. Students should be familiar with using eigenvalues.Modeling Scenario

##### 3-002-ModelsMotivatingSecondOrder-ModelingScenario

Ordinary differential equations involve second derivatives and second derivatives appear in many contexts, chief among them are the study of forces and resulting motion. This is principally because of Newton's Second Law of Motion.Modeling Scenario