## Resources

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Resource Type (12)

Modeling Scenario(6) Potential Scenario(6)

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Differential Equation Type (12)

ODE(10) First(4) Second(7) Linear(4) Nonlinear(2) System(1) Constant Coeff(3) Homogeneous(2) Nonhomogeneous(4)

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Technique (12)

Initial Value Problems(12) Numerical Methods(2) Parameter Estimation(5) Separable(1) Separation of Variables(2) Undetermined Coefficients(1)

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Qualitative Analysis (12)

Stability(1) Graphical analysis(5) Parameters(6) Other(2)

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Application Area (12)

Engineering(2) Life Sciences(1) Mathematics(6) Modeling (general)(11) Physics(9)

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Course (12)

Calculus 2(6) Differential Equations(12) Modeling(11)

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Course Level (12)

Introductory(12) Upper Level(10) Graduate(1) High School(7)

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Lesson Length (12)

Portion of one class period(4) One class period(3) Multiple class periods(1) Other(6)

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Technology (12)

Mathematica(1) MatLab(2) Python(1) None(4) Other(5)

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Approach (12)

Guided(5) Open-ended(1) Other(6)

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Skills (12)

Data analysis(3) Programming(1) Other(9)

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Key Scientific Process Skills (6)

Asking a question(6) Formulating hypotheses(6) Designing/conducting experiments(2) Predicting outcomes(4) Gathering data/making observations(1) Analyzing data(2) Interpreting results/data(2) Displaying/modeling results/data(3) Communicating results(1)

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Assessment Type (6)

Homework(5) Written assignment: Report(6)

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Pedagogical Approaches (5)

Guided inquiry/investigation(5)

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Vision and Change Core Competencies - Ability (6)

Create and develop models(6) Use quantitative reasoning(5) Design simulations(1) Communicate and collaborate with other disciplines(1)

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Principles of How People Learn (6)

Motivates student to learn material(6) Focuses student on the material to be learned(6)

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Bloom's Cognitive Level (5)

Application & Analysis(5)

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Includes clear efforts on Issues (0)

###### Applied Filters

Modeling Scenario

##### 3-011-EulerBallThrowing-ModelingScenario

If a tennis ball is thrown through the air it will hit the ground due to gravity. Using Euler's method, write a short script (Python, Matlab, R, etc.) to find the trajectory of the ball which will maximize the distance the ball lands from the...Potential Scenario

##### 1999-Long-Weiss-The Velocity Dependence of Aerodynamic Drag A Primer for Mathematicians

This paper is exactly what it says it is, namely, a Primer for Mathematicians. There are ample models, data, attention to such issues as Reynoldsâ€™ numbers, and attention to aerodynamics issues.Potential Scenario

##### 2017-Ole_Witt-Hansen-Examples Of Differential Equations In Physics

This is an article from the authorâ€™s homepage. The work contains fundamental and basic background and derivation of the differential equation models for a number of phenomena.Potential Scenario

##### 2009-Peter-Howard-Modeling With ODE

This is a set of class notes rich in examples and ideas for modeling. There is some MatLab code in support of some of the activities.Potential Scenario

##### 1994-Roland_Minton-A Progression of Projectiles-Examples from Sports

There is a progression of complexity and issues in projectile motion modeling from no resistance, to resistance proportional to velocity, then to velocity squared,Modeling Scenario

##### 1-083-FallingMeteorites-ModelingScenario

After introducing the solution to the ordinary differential equation which models a falling object with drag (first-order, non-linear, separable), students will consider generalizing the model to a falling and disintegrating meteorite. The focus...Potential Scenario

##### 2003-Bohren-Dimensional analysis-falling bodies--fine art of not solving differential equations

Dimensional analysis is a simple, physically transparent and intuitive method for obtaining approximate solutions to physics problems, especially in mechanics.Modeling Scenario

##### 4-039-FallingDarts-ModelingScenario

we develop, solve, and analyze a second order differential equation model for free fall incorporating air resistance. Students solve the model using two methods -- reduction of order and separation of variables, and method of undetermined...Modeling Scenario

##### 3-055-FloatingBox-ModelingScenario

In this scenario, we lead students through the process of building a mathematical model for a floating rectangular box that is bobbing up and down.Potential Scenario

##### 1994-T_Gruszka-A Balloon Experiment in the Classroom

The following experiment involves a balloon, a stopwatch, and a measurement device such as a meter stick,Modeling Scenario

##### 6-070-BeerBubbles-ModelingScenario

The goal of this project is to set up and numerically solve a first-order nonlinear ordinary differential equation (ODE) system of three equations in three unknowns that models beer bubbles that form at the bottom of a glass and rise to the top.Modeling Scenario