## Resources

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Resource Type (166)

Modeling Scenario(98) Technique Narrative(4) Potential Scenario(47) Article or Presentation(10) Free Online Textbook(6) General Resource(1)

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Differential Equation Type (166)

ODE(158) PDE(5) Difference(7) Delay(2) First(64) Second(78) Higher(4) Linear(92) Nonlinear(35) System(58) Constant Coeff(75) Homogeneous(48) Nonhomogeneous(40) Other(2)

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Technique (166)

Boundary Value Problems(14) Eigen Methods(7) Exact Equations(1) Initial Value Problems(127) Integrating Factor(5) Laplace Transform(8) Linear Algebra(8) Matrices(7) Numerical Methods(21) Parameter Estimation(60) Qualitative Behavior(11) Separable(16) Separation of Variables(18) Series(1) Substitution Methods(2) Theory (general)(1) Undetermined Coefficients(1) Variation of Parameters(2) Other(9)

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Qualitative Analysis (166)

Equilibrium(17) Stability(14) Phase Plane(6) Graphical analysis(62) Eigenvalue analysis(8) Parameters(100) Other(33)

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Application Area (166)

Chemistry(16) Economics(8) Engineering(42) Life Sciences(42) Mathematics(61) Modeling (general)(132) Physics(78) Social Sciences(10) Other(1)

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Course (166)

Precalculus(1) Calculus 1(1) Calculus 2(45) Calculus 3 (multivariable)(3) Differential Equations(165) Modeling(152)

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Skills (166)

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Reviewing prior research(6) Asking a question(96) Formulating hypotheses(85) Designing/conducting experiments(15) Predicting outcomes(30) Gathering data/making observations(20) Analyzing data(37) Interpreting results/data(39) Displaying/modeling results/data(40) Communicating results(34) Translating into mathematics(4)

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Assessment Type (102)

Assessment of student groups/teams(1) Homework(90) Solve problem(s)(2) Written assignment: Essay(1) Written assignment: Report(92)

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Pedagogical Approaches (93)

Case Study(1) Collaborative Work(1) Computer Model(3) Guided inquiry/investigation(89)

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Vision and Change Core Competencies - Ability (102)

Create and develop models(97) Use quantitative reasoning(90) Design simulations(23) Tap into interdisciplinary study(14) Communicate and collaborate with mathematics community(5) Communicate and collaborate with other disciplines(10) Understand the relationship between material and society(3)

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Principles of How People Learn (105)

Motivates student to learn material(100) Focuses student on the material to be learned(94) Develops supportive community of learners(6) Leverages differences among learners(4) Reveals prior knowledge(2) Requires student to do the bulk of the work(5)

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Bloom's Cognitive Level (100)

Foundational: factual knowledge & comprehension(12) Application & Analysis(94) Synthesis/Evaluation/Creation(6)

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Includes clear efforts on Issues (0)

###### Applied Filters

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

##### 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...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

##### 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

##### 3-060-DataToDifferentialEquation-ModelingScenario

Students use knowledge of second-order linear differential equations in conjunction with physical intuition of spring-mass systems to estimate the damping coefficient and spring constant from data.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

##### 3-001-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

##### 3-010-EnergyInSpringMassSystem-ModlingScenario

As a way to synthesize the effects of damping and forcing terms, this activity is meant to encourage students to explore how different forcing terms will change the total energy in a mass-spring system.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.Modeling Scenario

##### 3-040-FirstPassageTime-ModelingScenario

We apply the notions of dampedness to second order, linear, constant coefficient, homogeneous differential equations used to model a spring mass dashpot system and introduce the notion of first passage time through 0 value with several applications.Modeling Scenario

##### 3-091-SpringModeling-ModelingScenario

In this lab students will collect data on their spring mass systems and compare their empirical models to their theoretical onesâ€”giving them an opportunity to actually test a model against data.Modeling Scenario

##### 4-035-ParEstSteadyState-ModelingScenario

Students estimate parameters in a second order, linear, ordinary differential equations through analysis of the steady state solution. By applying a driver we can collect data in terms of the parameters and estimate these parametersModeling 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