## Resources

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Resource Type (115)

Modeling Scenario(49) Technique Narrative(2) Potential Scenario(54) Article or Presentation(4) Free Online Textbook(5) General Resource(1)

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Differential Equation Type (115)

ODE(109) PDE(4) Difference(13) Delay(7) Integral(1) First(42) Second(22) Higher(2) Linear(32) Nonlinear(44) System(58) Constant Coeff(14) Homogeneous(21) Nonhomogeneous(16) Other(1)

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Technique (115)

Boundary Value Problems(5) Eigen Methods(4) Initial Value Problems(96) Integrating Factor(2) Laplace Transform(2) Linear Algebra(1) Matrices(2) Numerical Methods(15) Parameter Estimation(35) Qualitative Behavior(26) Separable(10) Separation of Variables(8) Theory (general)(1) Other(8)

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Qualitative Analysis (115)

Equilibrium(79) Stability(55) Attractor(2) Phase Plane(18) Graphical analysis(43) Eigenvalue analysis(5) Parameters(68) Other(7)

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Application Area (115)

Chemistry(6) Economics(11) Engineering(12) Humanities(1) Life Sciences(52) Mathematics(60) Modeling (general)(92) Physics(27) Social Sciences(18)

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Course (115)

Calculus 2(18) Differential Equations(112) Modeling(108) Other(1)

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Introductory(112) Upper Level(109) Graduate(1) High School(53) Other(3)

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Lesson Length (115)

Portion of one class period(21) One class period(28) Multiple class periods(5) One term (semester or quarter)(2) One year(1) Other(63)

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Technology (115)

Excel(11) Maple(6) Mathematica(22) MatLab(12) Octave(1) Python(1) SAGE(2) None(10) Other(69)

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Approach (115)

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Skills (115)

Data collection(19) Data analysis(44) Programming(2) Statistics(1) Other(68)

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Key Scientific Process Skills (51)

Reviewing prior research(5) Asking a question(48) Formulating hypotheses(49) Designing/conducting experiments(13) Predicting outcomes(19) Gathering data/making observations(18) Analyzing data(20) Interpreting results/data(21) Displaying/modeling results/data(21) Communicating results(20) Translating into mathematics(2)

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Assessment Type (50)

Homework(47) Solve problem(s)(2) Written assignment: Report(45)

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Pedagogical Approaches (45)

Collaborative Work(1) Computer Model(2) Guided inquiry/investigation(42)

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Vision and Change Core Competencies - Ability (52)

Create and develop models(51) Use quantitative reasoning(46) Design simulations(13) Tap into interdisciplinary study(9) Communicate and collaborate with mathematics community(3) Communicate and collaborate with other disciplines(7) Understand the relationship between material and society(1)

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Principles of How People Learn (52)

Motivates student to learn material(50) Focuses student on the material to be learned(49) Develops supportive community of learners(3) Leverages differences among learners(1) Reveals prior knowledge(1)

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Bloom's Cognitive Level (47)

Foundational: factual knowledge & comprehension(4) Application & Analysis(46) Synthesis/Evaluation/Creation(2)

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Includes clear efforts on Issues (1)

Equity(1)

###### Applied Filters

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

##### 3-101-SpringMassFirstTry-NoResistance-ModelingScenario

Students build a model based on their perceptions of what the solution should look like for a simple spring mass system with no damping.Modeling Scenario

##### 3-102-SpringMassDamped-ModelingScenario

Students build a model based on their perceptions of what the solution should look like for a simple spring mass system with damping.Modeling Scenario

##### 3-140-TwoSpringsOneMassFixedEnds-ModelingScenario

Students build a model of a two spring, single mass with fixed end configuration and then plot solutions to experience the motion.Modeling Scenario

##### 3-031-SpringCost-ModelingScenario

We assume students are familiar with overdamping and underdamping of a spring-mass-dashpot system. Students will apply this knowledge to model the interplay between spring constant, tolerance, and cost.Modeling Scenario

##### 1-118-SolowEconomicGrowth-ModelingScenario

Students construct and analyze the celebrated Solow-Swan model of economic growth theory. The project is divided into three sequential parts to teach students to understand, develop, and analyze a simple nonlinear model of economic dynamics.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

##### 4-050-ResonanceBeats-ModelingScenario

We study what can happen when a pure oscillator (no damper) is driven by a forced vibration function which has the same or close to the same natural frequency as the system it is driving.Modeling Scenario

##### 3-034-CarSuspension-ModelingScenario

We examine the spring-mass-dashpot that is part of a car suspension, how the ride is related to parameter values, and the effect of changing the angle of installation. We model a ``quarter car'', meaning a single wheel.Free Online Textbook

##### 2015-H_Sayama-Intro to Modeling and Analysis of Complex Systems

Introduces students to mathematical/computational modeling and analysis developed in the emerging interdisciplinary field of Complex Systems Science.Modeling Scenario

##### 3-001-SpringMassDataAnalysis-ModelingScenario

We offer data on position of a mass at end of spring over time where the spring mass configuration has damping due to taped flat index cards at the bottom of the mass. Modeling of a spring mass configuration and estimation of parameters are the core.Modeling Scenario

##### 3-090-OneSpringMass-ModelingScenario

We lead students through building a mathematical model for a single mass (bob)-spring system that is hanging vertically. We also lead the students, using data that they collect together with their model to approximate the value of the spring...Technique Narrative

##### 1-010-AtmosphericCO2Bifurcation-TechniqueNarrative

Students are introduced to the concept of a bifurcation in a first-order ordinary differential equation (ODE) through a modeling scenario involving atmospheric carbon dioxide whish is taken as a parameter and temperature is a function of time.Potential Scenario

##### 2000-Idels-Wang-Harvesting Fisheries Management Strategies With Modified Effort Function

This study concludes that a control parameter beta (the magnitude of the effect of the fish population size on the fishing effort function E), changes not only the rate at which the population goes to equilibrium, but also the equilibrium values.Modeling Scenario