## Resources

#####
Resource Type (85)

Modeling Scenario(57) Technique Narrative(1) Potential Scenario(17) Article or Presentation(8) Free Online Textbook(2)

#####
Differential Equation Type (85)

ODE(80) PDE(3) Difference(2) First(35) Second(36) Linear(40) Nonlinear(21) System(17) Constant Coeff(19) Homogeneous(28) Nonhomogeneous(14) Other(1)

#####
Technique (85)

Boundary Value Problems(6) Eigen Methods(2) Initial Value Problems(65) Integrating Factor(2) Laplace Transform(1) Matrices(1) Numerical Methods(7) Parameter Estimation(33) Qualitative Behavior(2) Separable(11) Separation of Variables(13) Substitution Methods(1) Other(3)

#####
Qualitative Analysis (85)

Equilibrium(5) Stability(2) Phase Plane(4) Graphical analysis(28) Eigenvalue analysis(2) Parameters(51) Other(18)

#####
Application Area (85)

Chemistry(5) Economics(1) Engineering(14) Life Sciences(25) Mathematics(25) Modeling (general)(69) Physics(48) Social Sciences(2)

#####
Course (85)

Calculus 1(1) Calculus 2(32) Calculus 3 (multivariable)(1) Differential Equations(84) Modeling(78) Other(1)

#####
Course Level (85)

Introductory(80) Upper Level(80) Graduate(1) High School(58) Other(2)

#####
Lesson Length (85)

Portion of one class period(37) One class period(19) Multiple class periods(10) One term (semester or quarter)(2) Other(24)

#####
Technology (85)

Derive(1) Excel(6) Mathematica(39) MatLab(1) Calculator(1) None(13) Other(32)

#####
Approach (85)

Directed(3) Guided(57) Develop model(2) Other(25)

#####
Skills (85)

Data collection(15) Data analysis(37) Statistics(2) Other(46)

#####
Key Scientific Process Skills (58)

Reading research papers(1) Reviewing prior research(3) Asking a question(56) Formulating hypotheses(46) Designing/conducting experiments(10) Predicting outcomes(22) Gathering data/making observations(14) Analyzing data(22) Interpreting results/data(28) Displaying/modeling results/data(25) Communicating results(25) Translating into mathematics(2)

#####
Assessment Type (58)

Homework(53) Solve problem(s)(1) Written assignment: Report(55) Written assignment: Literature review(1)

#####
Pedagogical Approaches (54)

Case Study(3) Computer Model(2) Physical Model(1) Guided inquiry/investigation(51)

#####
Vision and Change Core Competencies - Ability (59)

Create and develop models(55) Use quantitative reasoning(53) Design simulations(7) Tap into interdisciplinary study(5) Communicate and collaborate with mathematics community(1) Communicate and collaborate with other disciplines(4)

#####
Principles of How People Learn (57)

Motivates student to learn material(57) Focuses student on the material to be learned(51) Develops supportive community of learners(1) Reveals prior knowledge(4) Requires student to do the bulk of the work(1)

#####
Bloom's Cognitive Level (53)

Foundational: factual knowledge & comprehension(2) Application & Analysis(52)

#####
Includes clear efforts on Issues (1)

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

###### Applied Filters

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

##### 3-013-WhiffleBallFall-ModelingScenario

We are given data on the time and position of a whiffle ball as it falls to the ground. We attempt to model the falling ball and we confront the different resistance terms and models.Modeling Scenario

##### 3-016-FallingCoffeeFilters-ModelingScenario

We are given data on the time and position of a stack of coffee filters as it falls to the ground. We attempt to model the falling mass and we confront the different resistance terms and models.Potential Scenario

##### 2003-Bohren-Dimensional analysis-falling bodies--fine art of not solving differential equations

Dimensional analysis is a simple, physically transparent and intuitive method for obtaining approximate solutions to physics problems, especially in mechanics.Modeling Scenario

##### 3-017-StackedCoffeeFiltersFalling-ModelingScenario

Data on free falling 2, 4, 6, and 8 stacked coffee filters is offered. Students form a model using a resistance term proportional to velocity, velocity squared, or velocity to some general power. Parameters need to be estimated and models compared.Modeling Scenario

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

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

##### 3-019-ShuttleCockFalling-ModelingScenario

We are given data on the time and position of a shuttlecock as it falls to the ground from a set height. We attempt to model the falling object and we confront the different resistance terms and models.Modeling Scenario

##### 3-044-DeepWell-ModelingScenario

We drop a pebble in a deep well. Given the time elapsed from release of the pebble until we hear the splash determine the depth of the well.Potential Scenario

##### 1994-T_Gruszka-A Balloon Experiment in the Classroom

The following experiment involves a balloon, a stopwatch, and a measurement device such as a meter stick,Article or Presentation

##### 2011-Brian_Winkel-Cross_coursing_in_mathematics-physical_modeling_in_differential_equations_crossing_to_discrete_dynamical_systems

We give an example of cross coursing in which a subject or approach in one course in undergraduate mathematics is used in a completely different course.Modeling Scenario

##### 3-041-UpDown-ModelingScenario

Shoot a projectile straight up in the air. Determine maximum height the projectile will go. Consider time T(a) (0 < a < 1) it takes between when the projectile passes distance a.H going up and then coming down. Develop T(a) as a function of a.Modeling Scenario

##### 1-105-AnimalFall-ModelingScenario

This project uses Newton's Second Law of Motion to model a falling animal with a resistance term proportional to cross sectional area of the animal, presumed to be spherical in shape.Modeling Scenario

##### 1-055-WaterFallingInCone-ModelingScenario

We offer an opportunity to model the height of a falling body of water in a right circular cone (funnel) and to estimate an appropriate parameter based on data collected from a video of the experiment found on YouTube.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.Potential Scenario