## 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

##### 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.
parameter estimation
non-homogeneous
Spanish
frequency
buoyancy
inverse problem
thrust
underdamped
first passage
spring mash dashpot
real
complex
homogeneous
superposition
parachute
overdamped
critically damped
buoy
quadratic equation
roots
rocket flight

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

##### 3-065-UpDown-ModelingScenario

We model the height of a launched object which is subject to resistance proportional to velocity during its flight. We ask questions about the motion as well, e.g., highest point or apex and terminal velocity.
terminal velocity
Newton's Second Law of Motion
velocity
motion
apex

Modeling Scenario

##### 3-104-BungeeJumping-ModelingScenario

In this project, students design a bungee jumping cord (cross-sectional area and length) that will keep jumpers safe. Students communicate their recommendations as a letter to a client interested in starting a bungee jumping business.
design
falling
mass
spring\
bungee
elesticity
recommendation
consult

Technique Narrative

##### 1-015-DimensionlessVariables-TechniqueNarrative

This material introduces the idea of ``rescaling'' for ordinary differential equations (ODE's) by the use of dimensionless variables. In practice this is an extremely common and useful prelude to the analysis and solution of ODE's.
linearization
dimensional analysis
time scale
scaling
dimensionless variables
spatial scale

Technique Narrative

##### 9-001-SkinBurnModelNumericalMethods-TechniqueNarrative

The heat equation is an important partial differential equation (PDE) which describes the distribution of heat in a given region over time. Numerical methods play an important role in solving these.
Maternal-Fetal interface
heat equation
Conservation of Energyt
heat flux
Euler's forward method
central difference
skin burn
hyperthermia
thermal conductivity
layers

Technique Narrative

##### 3-090-ChebyshevPolynomialSolution-TechniqueNarrative

The Chebyshev equation is presented as a vehicle to view series solutions techniques for linear, second order homogeneous differential equations with non-constant coefficients.
series soluotion
polynomial solutions
Chebyshev polynomials
Chebyshev differential equations

Modeling Scenario

##### 3-043-BallisticModeling-SpongeDart-ModelingScenario

The goal of this project is for students to develop, analyze, and compare three different models for the flight of a sponge dart moving under the influences of gravity and air resistance.
projectile motion
air resistance
ballistics
dimensional analysis
Newtonian mechanics
sponge dart
Nerf gun
Nerf dart
Buckingham's Theorem

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

##### 1-013-SleuthingWithDifferentialEquations-ModelingScenario

We present several situations in which differential equation models serve to aid in sleuthing and general investigations.
projectile motion
acceleration
Newton's Law of Cooling
speeding

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.
animal
Netwon's Second Law of Motion
falling body
terminal velocity
air resistance
Newton
air friction
fall

Modeling Scenario

##### 1-120-CircularRollerCoaster-ModelingScenario

Students study the dynamics of a circular roller coaster and work out the equations of motion in the ideal case as well as considering the interesting complication of including kinetic friction. This problem is an excellent introduction for students
population dynamics
energy
Fluid Mechanics
m
friction
roller coaster
integration by8 parts

Modeling Scenario

##### 3-001-SpringMassDataAnalysis-ModelingScenario

We offer data on position of a mass at end of spring over time where the spring mass configuration has damping due to taped flat index cards at the bottom of the mass. Modeling of a spring mass configuration and estimation of parameters are the core.
data
damping
spring-mass system
Newton's Second Law of Motion
spring constant
Hooke's Law

Modeling Scenario

##### 3-002-ModelsMotivatingSecondOrder-ModelingScenario

Ordinary differential equations involve second derivatives and second derivatives appear in many contexts, chief among them are the study of forces and resulting motion. This is principally because of Newton's Second Law of Motion.
resistance
spring mass
oscillation
Hooke's Law
dampening

Modeling Scenario

##### 3-006-Buoyancy-ModelingScenario

We offer data from a physical experiment in which the depth of a container in water is measured and ask students to build a model of buoyancy based on Newton's Second Law of Motion and a Free Body Diagram. We ask students to estimate the parameters.
data collection
experiment
buoyancy
Newton's Second Law of Motion