## Resources

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Resource Type (180)

Modeling Scenario(102) Technique Narrative(7) Potential Scenario(56) Article or Presentation(10) Free Online Textbook(4) General Resource(1)

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Differential Equation Type (180)

ODE(161) PDE(11) Difference(12) Delay(7) First(66) Second(57) Higher(2) Linear(63) Nonlinear(47) System(56) Constant Coeff(29) Homogeneous(33) Nonhomogeneous(29) Other(4)

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Technique (180)

Boundary Value Problems(15) Eigen Methods(2) Initial Value Problems(135) Integrating Factor(5) Laplace Transform(1) Linear Algebra(2) Matrices(2) Numerical Methods(27) Parameter Estimation(73) Qualitative Behavior(15) Separable(13) Separation of Variables(22) Substitution Methods(2) Theory (general)(1) Undetermined Coefficients(1) Other(13)

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Qualitative Analysis (180)

Equilibrium(14) Stability(14) Phase Plane(10) Graphical analysis(62) Eigenvalue analysis(2) Parameters(106) Other(36)

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Application Area (180)

Chemistry(11) Economics(13) Engineering(31) Humanities(3) Life Sciences(53) Mathematics(70) Modeling (general)(138) Physics(78) Social Sciences(19) Other(1)

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Course (180)

Precalculus(2) Calculus 1(2) Calculus 2(59) Calculus 3 (multivariable)(3) Differential Equations(178) Modeling(170)

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Excel(21) Maple(11) Mathematica(61) MatLab(10) Octave(2) Python(2) R(3) SAGE(1) Desmos(1) None(11) Other(89)

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Approach (180)

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Skills (180)

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Key Scientific Process Skills (106)

Reviewing prior research(8) Asking a question(103) Formulating hypotheses(92) Designing/conducting experiments(15) Predicting outcomes(29) Gathering data/making observations(22) Analyzing data(40) Interpreting results/data(46) Displaying/modeling results/data(46) Communicating results(39) Translating into mathematics(3)

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Assessment Type (109)

Assessment of individual student performance(1) Assessment of student groups/teams(1) Homework(99) Solve problem(s)(3) Written assignment: Essay(2) Written assignment: Report(97)

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Pedagogical Approaches (92)

Case Study(3) Collaborative Work(2) Computer Model(2) Physical Model(2) Guided inquiry/investigation(87)

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Vision and Change Core Competencies - Ability (104)

Create and develop models(95) Use quantitative reasoning(94) Design simulations(26) Tap into interdisciplinary study(14) Communicate and collaborate with mathematics community(4) Communicate and collaborate with other disciplines(5)

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Principles of How People Learn (106)

Motivates student to learn material(103) Focuses student on the material to be learned(97) Develops supportive community of learners(2) Leverages differences among learners(2) Reveals prior knowledge(5) Requires student to do the bulk of the work(3)

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Bloom's Cognitive Level (98)

Foundational: factual knowledge & comprehension(11) Application & Analysis(92) Synthesis/Evaluation/Creation(1)

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Includes clear efforts on Issues (1)

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

###### Applied Filters

Modeling 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.Modeling Scenario

##### 1-165-FlushToilet-ModelingScenario

This activity analyzes the spread of a technological innovation using the Bass Model from Economics. The equation is a first-order, two-parameter separable equation and the solution has a characteristic S-shaped curve or sigmoid curve.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...Modeling Scenario

##### 6-040-StruggleForExistence-ModelingScenario

We use historical data from the 1930's in the Soviet Union and model competition between two species of yeast after modeling each species separately and estimate parametersTechnique Narrative

##### 1-005-NavigatingNumericalMethods-TechniqueNarrative

This technique narrative is a discovery-based approach to learning the basics of numerical methods for first order differential equations, by following the graphical and analytical perspectives of the forward Euler method and second order Taylor...Modeling Scenario

##### 1-155-CruiseControl-ModelingScenario

In this project we illustrate the design of a proportional-integral-derivative (PID) cruise control algorithm for an automobile. PID control is one of the most common techniques in control engineering.Potential Scenario

##### 1999-PS_Crooke-S_Hota_JJ_Martini-JR_Hochkiss-A Mathematical Model for Carbon Dioxide Exchange

A mathematical model is presented to study the effect of Tracheal Gas Insufflation (TGI) on the alveolar ventilation during passive, mechanical ventilation.Technique Narrative

##### 5-005-StiffDifferentialEquations-TechniqueNarrative

This material introduces the topic of ``stiffness'' for a system of ordinary differential equations (ODE's), through a series of examples. Stiffness is a property that a system of ODE's may posses that make it difficult to solve numerically.Modeling Scenario

##### 1-011-Kinetics-ModelingScenario

We make the connection between chemistry course and differential equations coursework. We do this through modeling kinetics, or rates of chemical reaction. We study zeroth, first, and second order reactions.Modeling Scenario

##### 1-095-RatingChessPlayers-ModelingScenarios

The goal of this activity is to have students build a mathematical model involving a system of first order difference equations from a verbal description of a scenario.Modeling Scenario

##### 5-076-LanchesterLaws-ModelingScenario

Lanchester's laws are used to calculate the relative strengths of military forces. The Lanchester equations are differential equations describing the time dependence of two armies' strengths A and B as a function of time,Modeling Scenario

##### 3-054-Relay-ModelingScenario

We use a differential equations of one dimensional projectile motion and an integration of velocity for total distance to model the relay between an outfielder and an infielder in throwing the ball to home plate.Modeling Scenario

##### 1-044-CollegeBound-ModelingScenario

Preparing for four years of college for a friend of the family's newborn is the task. Making assumptions about costs, timing, interest rates, and fiscal capabilities are the order of the day.Modeling Scenario

##### 1-144-HeatCool-ModelingScenario

We offer an opportunity to build a mathematical model using Newton's Law of Cooling for a closed plastic baggie of liquid inside a liquid container.Potential Scenario