## Resources

###### Applied Filters

##### Resource Type

Modeling Scenario Technique Narrative Potential Scenario Article or Presentation Free Online Textbook General Resource Sample Syllabus Assessment Rubric or Guide SCUDEM EXPO

##### Differential Equation Type

ODE PDE Difference Delay Integral First Second Higher Linear Nonlinear System Constant Coeff Homogeneous Nonhomogeneous Other

##### Technique

Boundary Value Problems Eigen Methods Exact Equations Fourier Series Initial Value Problems Integrating Factor Laplace Transform Linear Algebra Matrices Numerical Methods Parameter Estimation Qualitative Behavior Separable Separation of Variables Series Substitution Methods Theory (general) Undetermined Coefficients Variation of Parameters Other

##### Qualitative Analysis

Equilibrium Stability Attractor Phase Plane Graphical analysis Eigenvalue analysis Parameters Other

##### Application Area

Chemistry Economics Engineering Humanities Life Sciences Mathematics Modeling (general) Physics Social Sciences Other

##### Course

Precalculus Calculus 1 Calculus 2 Calculus 3 (multivariable) Differential Equations Modeling Other

##### Course Level

Introductory Upper Level Graduate High School Other

##### Lesson Length

Portion of one class period One class period Multiple class periods One term (semester or quarter) One year Other

##### Technology

Derive Excel GeoGebra Maple Mathematica MathCad MatLab Octave Python R SAGE Calculator None Other Desmos

##### Approach

Directed Flipped Guided Open-ended Discussion Develop model Other

##### Skills

Data collection Data analysis Programming Statistics Other

##### Key Scientific Process Skills

Reading research papers Reviewing prior research Asking a question Formulating hypotheses Designing/conducting experiments Predicting outcomes Gathering data/making observations Analyzing data Interpreting results/data Displaying/modeling results/data Communicating results Translating into mathematics

##### Assessment Type

Assessment of individual student performance Assessment of student groups/teams Assignment Exam/quiz, in class Exam/quiz, take home Homework Answer clicker-type question(s) Answer essay question(s) Answer fill in the blank question(s) Answer multiple choice question(s) Answer short answer question(s) Answer true/false question(s) Create a concept map Create a diagram, drawing, figure, etc. Create a website Create graph, table etc. to present data Design an experiment or research study Design/present a poster Give an oral presentation Informal in-class report Interpret data Order items (e.g. strip sequence) Participate in discussion Peer evaluation Post-test Pre-test Produce a video or video response Respond to metacognition/reflection prompt Self evaluation Solve problem(s) Written assignment: One minute paper Written assignment: Brochure Written assignment: Essay Written assignment: Figure and or figure legend Written assignment: Report Written assignment: Literature review

##### Pedagogical Approaches

Think-Pair-Share Brainstorming Case Study Clicker Question Collaborative Work One Minute Paper Reflective Writing Concept Maps Strip Sequence Computer Model Physical Model Interactive Lecture Pre/Post Question Guided inquiry/investigation

##### Vision and Change Core Competencies - Ability

Create and develop models Use quantitative reasoning Design simulations Tap into interdisciplinary study Communicate and collaborate with mathematics community Communicate and collaborate with other disciplines Understand the relationship between material and society

##### Principles of How People Learn

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

##### Bloom's Cognitive Level

Foundational: factual knowledge & comprehension Application & Analysis Synthesis/Evaluation/Creation

##### Includes clear efforts on Issues

Diversity Equity Inclusion Enhancement of all

Modeling Scenario

##### 1-078-MonodGrowthModel-ModelingScenario

Students model growth of bacteria E. coli in a limiting nutrient environment using data from a historical study.
bacteria
nutrient cycles
growth
Monod
consumption

Modeling Scenario

##### 3-061-ChemEngApps-ModelingScenario

Students go through a chemical engineering problem: calculate concentration profile of cyclohexane within a catalyst pellet by solving a second order linear differential equation; then analyze the concentration as the radius of the catalyst...
Spanish
porous medium
catalyisis
cyclohexene
hydrogel
dehydrogenation
hyperbolic trig functions

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.
design
spring-mass-dashpot
spring constant
underdamping
car suspension
suspension tolerance
static equilibrium

Modeling Scenario

##### 1-059-ContainerShapeFallingWater-ModelingScenario

We examine many different physical situations to determine the time it takes a fixed volume of water to flow out of different shape containers through the same size exit hole at the bottom of the container.
containers
Torricelli's Law
shape
discharge coefficient

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,
Lanchester's laws
sensitivity analysisanalysis

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...
applied mathematics
forces
Free Body Diagram
Improvised Explosive Devices
sum of forces

Modeling Scenario

##### 5-030-AirshedSulphur-ModelingScenario

Temperature inversions and low wind speeds trap air pollutants in a mountain valley for a period of time. Gaseous sulfur compounds are a significant air pollution problem. We offer a model for analysis to predict long-term levels of levels of...
sulphur
pollution
airshed
hydrogen sulfide
sulfur dioxide

Modeling Scenario

##### 5-040-TunedMassDampers-PartII-ModelingScenario

Studentsbuild mathematical models to mitigate dangerous swaying in structures using structural improvements called Tuned Mass Dampers (TMD). We model the motion of the original structure as a spring-mass-dashpot with stiffness replacing spring...
structure
resistance
spring-mass-dashpot
earthquake
vibration
control
damping
tuned mass damper
stiffness
reduction of vibration

Modeling Scenario

##### 5-090-SolidParticleErosion-ModelingScenario

By applying Newton's second law, and making a collection of reasonable assumptions, students will derive a system of differential equations that model the path of a rigid particle as it gouges material from a more ductile surface.
classical mechanics
solid mechanics
Newton's Laws of Motion
rigid body
plasticity
pitting
ductile surface

Modeling Scenario

##### 6-010-SocialCampaign-ModelingScenario

The epidemic modeling problem is formulated as a system of three nonlinear, first order differential equations in which three compartments (S, I, and R) of the population are linked.
disease
growth rate
Judgment and Decision Making
SIR model
infections disease
social campaign
recovery rate
delay time
joining process
quitting process
exponential distribution

Modeling Scenario

##### 6-015-CombatingEbolaEpidemic-ModelingScenario

This project offers students a chance to make a policy recommendation based on analysis of a nonlinear system of differential equations (disease model). The scenario is taken from the fall of 2014 when the Ebola outbreak in West Africa.
disease
Ebola
Analysis
Policy
decision

Modeling Scenario

##### 6-019-EnablingEpidemicExploration-ModelingScenario

We became aware of several interesting possibilities for a modeling opportunity with data and we invited you to explore the several routes to parameter estimation in a SIR model with respect to the data offered.
Akaike Information Criterion
Michaelis-Menten
epidemic
saturation
gradient
least sum of square errors

Modeling Scenario

##### 6-023-DroneHeadingHome-ModelingScenario

We describe a comprehensive project in modeling through a two dimensional system of equations and a first order system of differential equations a drone heading home.
drones
oursuit
flight path
change of variables

Modeling Scenario

##### 6-026-IsleRoyaleModeling-ModelingScenario

The primary aim of this project is to draw a connection between differential equations and vector calculus, using population ecology modeling as a vehicle.
ecology
optimization
predator-prey
population
vector calculus
Lagrange multipliers
least squares
Islel Royale

Modeling Scenario

##### 6-029-TumorGrowth-ModelingScenario

This modeling scenario guides a student familiar with single ordinary differential equation (ODE) models towards the development of a more complex system of two ODEs for describing the evolution of tumor growth over time.
Pop_Growth Pilot
logistic
comparment
tumor
synthetic data
sum of squares error