## Resources

#####
Resource Type (88)

Modeling Scenario(29) Technique Narrative(5) Potential Scenario(46) Article or Presentation(7) Free Online Textbook(1)

#####
Differential Equation Type (88)

ODE(80) PDE(2) Difference(3) Delay(3) Integral(1) First(36) Second(18) Linear(21) Nonlinear(20) System(28) Constant Coeff(8) Homogeneous(7) Nonhomogeneous(13) Other(2)

#####
Technique (88)

Boundary Value Problems(7) Fourier Series(1) Initial Value Problems(65) Integrating Factor(3) Laplace Transform(7) Numerical Methods(12) Parameter Estimation(33) Qualitative Behavior(7) Separable(2) Separation of Variables(8) Other(6)

#####
Qualitative Analysis (88)

Equilibrium(6) Stability(7) Phase Plane(3) Graphical analysis(22) Eigenvalue analysis(1) Parameters(61) Other(18)

#####
Application Area (88)

Chemistry(5) Economics(5) Engineering(11) Humanities(1) Life Sciences(32) Mathematics(52) Modeling (general)(72) Physics(33) Social Sciences(6)

#####
Course (88)

Calculus 2(30) Calculus 3 (multivariable)(1) Differential Equations(87) Modeling(80)

#####
Course Level (88)

Introductory(86) Upper Level(83) High School(41)

#####
Lesson Length (88)

Portion of one class period(20) One class period(15) Multiple class periods(2) One term (semester or quarter)(1) Other(51)

#####
Technology (88)

Excel(9) Maple(3) Mathematica(16) MatLab(4) R(1) None(6) Other(55)

#####
Approach (88)

Directed(6) Guided(29) Open-ended(2) Develop model(2) Other(51)

#####
Skills (88)

Data collection(11) Data analysis(48) Programming(1) Statistics(2) Other(39)

#####
Key Scientific Process Skills (34)

Reviewing prior research(3) Asking a question(34) Formulating hypotheses(33) Designing/conducting experiments(3) Predicting outcomes(6) Gathering data/making observations(6) Analyzing data(11) Interpreting results/data(13) Displaying/modeling results/data(14) Communicating results(11)

#####
Assessment Type (34)

Homework(32) Written assignment: Report(26)

#####
Pedagogical Approaches (31)

Case Study(2) Computer Model(1) Guided inquiry/investigation(28)

#####
Vision and Change Core Competencies - Ability (34)

Create and develop models(31) Use quantitative reasoning(32) Design simulations(3) Tap into interdisciplinary study(9) Communicate and collaborate with mathematics community(1) Communicate and collaborate with other disciplines(4)

#####
Principles of How People Learn (34)

Motivates student to learn material(34) Focuses student on the material to be learned(33) Leverages differences among learners(1) Reveals prior knowledge(1)

#####
Bloom's Cognitive Level (28)

Foundational: factual knowledge & comprehension(5) Application & Analysis(23)

#####
Includes clear efforts on Issues (0)

###### Applied Filters

Modeling Scenario

##### 3-110-MilitarySpringMassApplication-ModelingScenario

The is a collection of different scenarios for the shock system of a trailer. In each scenario, students will transform the shock system of a trailer into a second-order differential equation, solve, and interpret the results.Modeling Scenario

##### 7-010-MultipleDoses-ModelingScenario

Two multiple dose drug administration regimens are offered. A drug is to maintain a certain level (above a set minimum and below a set maximum) in the blood stream and one regimen involves bolus injections and another involves steady drip flow...Free Online Textbook

##### 2016-I-Liang_Chern-Mathematical Modeling_and_Ordinary_Differential_Equations

We let the author's Table of Contents speak for itself.Potential Scenario

##### 2009-Martinez-Luaces-Modelling Applications Inverse Modelling

The discussion in this paper will deal with non-typical inverse problems and how they can be used in engineering courses.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 functionArticle or Presentation

##### 2008-Brian_Winkel-Fourier_Series-Optimization_Opportunity

We discuss the introduction of Fourier series as an immediate application of optimization of a function of more than one variable.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,Potential Scenario

##### 2009-Das-EtAl-Bioeconomic harvesting of a pre-predator fishery

This paper deals with the problem of non-selective harvesting of a preyâ€“predator system by using a reasonable catch-rate function instead of usual catch-per-unit-effort hypothesis.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.Potential Scenario

##### 2016-Mehmet_Pakdemirli-Mathematical design of a highway exit curve

Using fundamental principles of physics and calculus, the differential equation determining the curve function is derived.Modeling Scenario

##### 1-032-WordPropagation-ModelingScenario

This activity is a gentle introduction to modeling via differential equations. The students will learn about exponential growth by modeling the rate at which the word jumbo has propagated through English language texts over time.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

##### 7-008-MachineReplacement-ModelingScenario

Students build an integro-differential equation model using a convolution for machine replacement strategies for two different machine failure models.Article or Presentation

##### 2007-Joseph_Myers-Brian_Winkel-Modeling_a_Mystery_Circuit_in_Mathematics_Class_Using_Differential_Equations_Laplace_Transforms_and_Transfer_Functions

We discuss the introduction, student discovery, and teaching of a system of differential equations which model a circuit.Potential Scenario