## OER Materials

###### 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

##### 1-007-AntTunnelBuilding-ModelingScenario

We pose the prospect of modeling just how long an ant takes to build a tunnel. With a bit of guidance students produce a model for the time it takes to build a tunnel of length x into the side of a damp sandy hill.
Spanish
hormiga
tÃºnel
ant
tunnel

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

Modeling Scenario

##### 7-011-CoupledSystemLaplace-ModelingScenario

Differential equations and Laplace transforms are an integral part of control problems in engineering systems. We consider a baby warming device.
transfer function
polycarbonate
baby heater
coupled system
heating

Technique Narrative

##### 7-006-LaplaceTransformBirth-TechniqueNarrative

We present a way of introducing the Laplace Transform as the continuous analogue of a power series expression of a function.
Transformations
power series

Technique Narrative

##### 5-012-LinearSystemConjecture-TechniqueNarrative

Students go from the solution for y'(t) = k*y(t) to a natural extension to the solution conjecture of a system of two constant coefficient, homogeneous, linear differential equations introducing eigenvalues and eigenvectors through student...
discovery learning
conjecture
solution
substitution

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

Technique Narrative

##### 1-002-IntegratingFactor-TechniqueNarrative

We develop a strategy to solve first order differential equations by transforming one side of the equation to the derivative of a product of two functions, thereby making it easy to antidifferentiate that side.
Integrating Factor

Technique Narrative

##### 1-001-SepartionOfVariables-TechniqueNarrative

We discuss strategies to solve first order, ordinary differential equations with mathematical models when the variables may be separated.
solutions
strategy
method
applications

Modeling Scenario

##### 1-021-FeralCatControl-ModelingScenario

Students act as professional mathematical consultants and write a report analyzing the client's problem. The client company is a fictional organization which advocates for the use of trap-neuter-return (TNR) as a control method for feral cat...
population growth
control
feral cats
population control
neuter
trap-kill
trap-neuter-return

Modeling Scenario

##### 1-039-StochasticPopModels-ModelingScenario

We develop strategies for creating a population model using some simple probabilistic assumptions. These assumptions lead to a system of differential equations for the probability that a system is in state (or population size) n at time t.
Probability
population dynamics
Variance
Mean
stochastic
deterministic

Modeling Scenario

##### 1-041-AirToTop-ModelingScenario

One common rule taught to SCUBA divers is to ascend no faster than thirty feet per minute. In this project we will examine safe variable ascent rates, time required for a safe ascent using variable ascent rates.
SCUBA
ascent
air management
breathing
diving
underwater

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

##### 1-067-ModelingWithSigmoidCurves-ModelingScenario

The assignment considers two well-known models of population growth, Verhulst-Pearl and Gompertz models, for which qualitative and quantitative analyses are provided. The graphs of the corresponding functions have a sigmoidal or S-shape.
logistic
Gompertz
sigmoid
Verhulst-Pearl

Modeling Scenario

##### 1-068-WaterBottleCooling-ModelingScenario

Students create of a differential equation describing how fluid in a water bottle will change its temperature to approach the ambient temperature in a room.
b
Newton's Law of Cooling
water bottle
autonomous
bottle

Modeling Scenario

##### 1-071-NewtonWatson-ModelingScenario

Sherlock Holmes determines the time of death for a body found on a street in London and we need to reproduce his astute analysis
temperature
death
Newton's Law of Cooling
time of death
Sherlock Holmes