## Resources

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Resource Type (749)

Modeling Scenario(293) Technique Narrative(20) Potential Scenario(353) Article or Presentation(51) Free Online Textbook(29) General Resource(3)

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Differential Equation Type (749)

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Technique (749)

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Qualitative Analysis (749)

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Application Area (749)

Chemistry(63) Economics(48) Engineering(100) Humanities(10) Life Sciences(315) Mathematics(408) Modeling (general)(586) Physics(225) Social Sciences(84) Other(5)

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Course (749)

Precalculus(5) Calculus 1(11) Calculus 2(203) Calculus 3 (multivariable)(8) Differential Equations(723) Modeling(686) Other(10)

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Introductory(723) Upper Level(677) Graduate(8) High School(350) Other(12)

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Approach (749)

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Skills (749)

Data collection(102) Data analysis(334) Programming(20) Statistics(14) Other(400)

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Key Scientific Process Skills (312)

Reading research papers(2) Reviewing prior research(23) Asking a question(297) Formulating hypotheses(264) Designing/conducting experiments(55) Predicting outcomes(97) Gathering data/making observations(74) Analyzing data(125) Interpreting results/data(141) Displaying/modeling results/data(139) Communicating results(115) Translating into mathematics(6)

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Assessment Type (313)

Assessment of individual student performance(1) Assessment of student groups/teams(3) Assignment(1) Homework(285) Give an oral presentation(1) Informal in-class report(1) Solve problem(s)(3) Written assignment: One minute paper(1) Written assignment: Essay(4) Written assignment: Report(278) Written assignment: Literature review(1)

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Pedagogical Approaches (275)

Case Study(11) Collaborative Work(9) Computer Model(10) Physical Model(6) Guided inquiry/investigation(252)

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Vision and Change Core Competencies - Ability (308)

Create and develop models(287) Use quantitative reasoning(273) Design simulations(52) Tap into interdisciplinary study(48) Communicate and collaborate with mathematics community(10) Communicate and collaborate with other disciplines(32) Understand the relationship between material and society(3)

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Principles of How People Learn (312)

Motivates student to learn material(301) Focuses student on the material to be learned(287) Develops supportive community of learners(8) Leverages differences among learners(8) Reveals prior knowledge(8) Requires student to do the bulk of the work(8)

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Bloom's Cognitive Level (289)

Foundational: factual knowledge & comprehension(31) Application & Analysis(271) Synthesis/Evaluation/Creation(7)

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Includes clear efforts on Issues (2)

Diversity(1) Equity(2) Inclusion(1) Enhancement of all(1)

###### Applied Filters

Modeling Scenario

##### 3-030-SecondOrderIntro-ModelingScenario

We outline the solution strategies involved in solving second-order, linear, constant coefficient ordinary differential equations, both homogeneous and nonhomogeneous and offer many application and modeling activities.Modeling Scenario

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

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

##### 3-009-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

##### 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

##### 3-010-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.Technique Narrative

##### 8-002-TrigSumRepresentation-TechniqueNarrative

Students discover how to represent functions as sums of trigonometric functions and the value of such representations in many fields. This is an introduction to the study of Fourier Series.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...Potential Scenario

##### 1991-JR_Lobry-P_Flandois-Comparison of Monod's Growth Model Parameters from the Same Data Set

The paper obtains the parameters in Monod's Growth model using a minimization of the sum of square errors with a given data set and obtains confidence intervalsPotential Scenario

##### 2010-Shianga-EtAl-Computational model of the human glucose-insulin regulatory system

A computational model of insulin secretion and glucose metabolism for assisting the diagnosis of diabetes mellitus in clinical research is introduced. ThePotential Scenario

##### 1984-W_Brunner-D__Focht-Deterministic Three-Half-Order Kinetic Model for Microbial Degradation

The kinetics of mineralization of carbonaceous substrates has been explained by a deterministic model which is applicable to either growth or nongrowth conditions in soil.Potential Scenario

##### 2015-Carl_Lutzer-Using Expected Value to Introduce the Laplace Transform

We propose an introduction to the Laplace transform in which Riemann sums are used to approximate the expected net change in a function, assuming that it quantifies a process that can terminate at random.Potential Scenario

##### 2008-Luis_San_AndrÃ©s-Dynamic Response of Second Order Mechanical Systems with Viscous Response Forces

Walk through the cases in context of second order linear constant coefficient differential equation with driving functionModeling Scenario

##### 5-080-SpaceFlightRecolonize-ModelingScenario

This project is a combination of differential equations, multi-variable calculus, and vector calculus with use of technology to model colonization of a new planet. Students solve a system of second order differential equations to model a planetModeling Scenario

##### 5-077-MandMAttritionWarfare-ModelingScenario

Students model attrition between two opposing forces using M&M candies and discover a system of linear differential equations of order one, often called the Lanchester equations.Potential Scenario