## Resources

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Resource Type (71)

Modeling Scenario(45) Potential Scenario(20) Article or Presentation(4) Free Online Textbook(2)

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Differential Equation Type (71)

ODE(69) PDE(3) Difference(2) First(21) Second(50) Higher(1) Linear(37) Nonlinear(11) System(18) Constant Coeff(24) Homogeneous(20) Nonhomogeneous(24) Other(1)

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Technique (71)

Boundary Value Problems(5) Eigen Methods(1) Initial Value Problems(56) Integrating Factor(2) Linear Algebra(2) Matrices(1) Numerical Methods(8) Parameter Estimation(32) Qualitative Behavior(5) Separable(4) Separation of Variables(6) Undetermined Coefficients(1) Other(2)

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Qualitative Analysis (71)

Equilibrium(2) Stability(3) Phase Plane(2) Graphical analysis(27) Eigenvalue analysis(3) Parameters(46) Other(9)

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Application Area (71)

Chemistry(3) Engineering(14) Life Sciences(8) Mathematics(24) Modeling (general)(59) Physics(57) Social Sciences(1)

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Course (71)

Calculus 2(21) Calculus 3 (multivariable)(1) Differential Equations(70) Modeling(68)

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Course Level (71)

Introductory(69) Upper Level(65) Graduate(1) High School(48) Other(1)

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Lesson Length (71)

Portion of one class period(28) One class period(16) Multiple class periods(3) One term (semester or quarter)(1) Other(25)

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Technology (71)

Excel(5) Maple(1) Mathematica(34) MatLab(2) Octave(1) Python(2) SAGE(1) Desmos(1) None(4) Other(32)

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Approach (71)

Guided(44) Open-ended(2) Develop model(2) Other(25)

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Skills (71)

Data collection(15) Data analysis(39) Programming(1) Statistics(3) Other(32)

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Key Scientific Process Skills (44)

Reviewing prior research(3) Asking a question(43) Formulating hypotheses(40) Designing/conducting experiments(10) Predicting outcomes(17) Gathering data/making observations(10) Analyzing data(21) Interpreting results/data(22) Displaying/modeling results/data(24) Communicating results(21)

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Assessment Type (45)

Homework(39) Written assignment: Essay(1) Written assignment: Report(42)

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Pedagogical Approaches (39)

Case Study(1) Computer Model(2) Physical Model(1) Guided inquiry/investigation(36)

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Vision and Change Core Competencies - Ability (43)

Create and develop models(43) Use quantitative reasoning(38) Design simulations(10) Tap into interdisciplinary study(6) Communicate and collaborate with other disciplines(3)

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Principles of How People Learn (43)

Motivates student to learn material(41) Focuses student on the material to be learned(38) Leverages differences among learners(1) Reveals prior knowledge(2) Requires student to do the bulk of the work(3)

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Bloom's Cognitive Level (43)

Foundational: factual knowledge & comprehension(2) Application & Analysis(43) Synthesis/Evaluation/Creation(1)

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Includes clear efforts on Issues (0)

###### Applied Filters

Modeling Scenario

##### 3-043-BallisticModeling-SpongeDart-ModelingScenario

The goal of this project is for students to develop, analyze, and compare three different models for the flight of a sponge dart moving under the influences of gravity and air resistance.Potential Scenario

##### 2002-Chai-Optimal initial angle to fire a projectile

Assume a projectile is fired without air resistance and lands at a height y above its initial vertical position. What is the optimal initial angle of firing to maximize the horizontal distance traveled by the projectile?”Modeling Scenario

##### 3-033-S-TimeUpTimeDown-ModelingScenario

We seek to compare for the time a projectile takes to go vertically up with the time it takes to return to its starting position.Potential Scenario

##### 1987-MS_Greenwood-Using videotapes to study underdamped motion of a pendulum

Using a video camera to study the effects of air resistance acting on pendulum bob, ping-pong ball, styrofoam spheres, and brass spheres.Potential Scenario

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

This is an article from the author’s homepage. The work contains fundamental and basic background and derivation of the differential equation models for a number of phenomena.Modeling Scenario

##### 1-145-FastPitch-ModelingScenario

We consider the problem of comparing pitch velocities using measurement methods in different eras of baseball.Modeling Scenario

##### 3-015-StyrofoamBallFall-ModelingScenario

We are given data on a falling Styrofoam ball and we seek to model this motion.Modeling Scenario

##### 3-095-ShotInWater-ModelingScenario

This project uses Newton's Second Law of Motion in conjunction with a quadratic model for the resistance experienced by a bullet moving through water to analyze a classic action movie scene.Modeling Scenario

##### 1-105-AnimalFall-ModelingScenario

This project uses Newton's Second Law of Motion to model a falling animal with a resistance term proportional to cross sectional area of the animal, presumed to be spherical in shape.Potential Scenario

##### 1980-Peastrel-Lynch-Armenti-Terminal velocity of a shuttlecock in vertical fall

We have performed a straightforward vertical fall experiment for a case where the effects of air resistance are important and directly measurable.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

##### 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

##### 3-065-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.Article or Presentation

##### 1980-Peastrel-Lynch-Armenti-Terminal_velocity_of_a_shuttlecock_in_vertical_fall

This paper offers a set of data on a falling shuttlecock (the moving object in badminton) in air. How the authors collected the data is described fully and can be replicated easily by modern equipment.Modeling Scenario