## SIMIODE Resource Guide

#### 1-001-Text-SepVariable

Technique narrative on solution method of separation of variables

1-002-Text-Integrating Factor

Technique narrative on solution method of integrating factor

1-003-Text-IntroNumericalMethods

Introduction to numerical methods for solving first order differential equations

1-005-Text-NavigatingNumericalMethods

Using a lost at sea situation to learn numerical methods

1-009-Text-Bifurcation

Early introduction to bifurcation with experimentation

1-015-Text-DimensionlessVariables

Scaling for differential equations and dimensionless variables is discussed

Activities

1-001-M&MDeathImmigration

Modeling Death and Immigration with M&M 's and Simulation

1-001A-M&MDeathImmigration-Variation

Variation on modeling death and immigration with M&M’s

1-001B-M&MDeathImmigrationMystery

Each student sets own immigration rate and others need to solve this mystery

1-001pgf- BirthDeathImmigration

Probability generating function approach to simulation.

1-002-Tossing

Modeling a simulation of a large number of dice tossings

1-003-CollegeSavings

Saving for Child's College Education

1-004-Microorganism Immigration

Modeling Immigration in a Petri Dish

1-005-OilSlick

Modeling the Spread of Oil Slick with Incomplete Data

1-005A-OilSlick

Same as 1-5-OilSlick but with client setting.

1-005a-ChemDataCollection

Analysis of incomplete reaction data

1-005b-ChemDataCollection

Analysis of incomplete reaction data

1-006-FinancingSavingsAndLoan

Bank Investment Analysis and Bank Loan Analysis

1-007-AntTunnelBuilding

How long does it take an ant to build a tunnel of length x in soil?

Modeling the spread of ICU’s in US Hospitals from 1958-1974

1-010-LSDAndProblemSolving

Modeling LSD in the body and correlating amounts with test performance.

1-011-Kinetics

Chemical Kinetics Models - Zeroth, First, and Second Order Reactions

1-011A-Kinetics

Same as 1-11-Kinetics but with more guidance and less narrative.

1-012-SublimationCarbonDioxide

Sublimation of Carbon Dioxide

1-013-Sleuthing

Situations associated with stopping cars, projectile steel ball, and time of death

1-014-DrainingContainers

For fixed volume column which radius of cylinder of water drains fastest

1-015-Torricelli

Modeling  falling column of water

1-016-DogDrugs

Modeling drugs for anesthesiology

Modeling spread of disease using logistic equation

1-018-LogisticPopModeling

Limited Growth Population Modeling

Sensitivity Analysis  - Data Collection Experiment Comparing of Rock Masses

1-020-IceMelt

Analyzing models on which melts first a sphere or cube of ice of the same volume

1-021-FeralCatControl

Model for three feral cat control policies

Model the spread of a number of technological advances

Rate of Spread of False and True articles on the Internet

1-024-MalariaControl

Modeling and numerical methods for first order malaria growth

1-025-MixingItUp

Modeling more and more complex salt mixing situations.

1-026-Evaporation

Modeling the evaporation of an alcohol and water mixture in various containers.

1-027-StochasticProcesses

Modeling randomness with stochastic processes.

1-028-SouthernSweetIcedTea

Data is offered to model making sweet iced team using luminescence

1-029-ConeToCubeFlow

Modeling water flowing from cone to cube and out

1-030-IntraocularGasBubbles

Modeling dissipation of intraocular gas bubbles used in eye surgery.

1-031-CoolIt

Changing temperature of container of water in a changing environment.

1-032-WordPropagation

Modeling the rate at which words propagate through English language text

1-033-SouthernBarbeque

Phases of barbequeing brisket are modeled using real data.

1-034-FishMixing

Student designed fishing strategies for mix of fish in lake

1-036-NeutralBuoyancy

Finding depth in water at which an object  settles to neutral buoyancy

Students conduct simulation of spread of common cold and model.

1-038-Ebola

Modeling Ebola epidemic with first order differential equation models

1-040-OutcomeSavings

Determining monthly deposit rate for long term savings goal

1-041-AirToTop

Variable ascent rate and air management in SCUBA diving

1-042-Kool-Aid

Modeling the amount of drink powder in a second tank of flow system.

1-043-CoolingUpAndDown

Air conditioning cooling modeling.

1-044-CollegeBound

Planning for full college education costs for the daughter of a friend.

1-045-TimeOfDeath

Determining time of death given observations and environmental conditions.

Optimizing a barge trip upriver

1-051-OneTankSaltModel

Build one compartment salt mixing model

1-052-SaltWaterTanks

Studying tank in which water inflow containing salt increases.

Modeling the spread of a slime puddle from video collected data.

1-054-S-GrowthInFarmland

Modeling the growth of farmland with incomplete data

1-055-WaterFallingInCone

Modeling the falling of water in a right circular cone

1-057-FiguringFluidFlow

Evaluating three models of fluid flow from a tank using data

1-058-WaterClocks

A container is designed so water will fall out at constant rate of change in height.

1-059-ContainerShapeFallingWater

Modeling column of falling water in different shaped containers.

1-060-SalesMarketing

Building a model of sales of consumer products from a classic marketing study.

1-062-BacterialGrowth

Several models offered for exponential growth in increased complexity

Falling single column of water with three spigot holes

1-064-TorricelliBox

Modeling falling column of water with a box at the base of the column

1-061-PotatoCooling

Cooling of a baked potato and compare it to student-collected data.

1-066-USCensusModeling

Modeling the US Census data with several different models.

1-067-ModelingWithSigmoidCurve

Modeling using logistic and Gompertz S-shape curves is offered.

1-070-FisheryHarvest

Modeling harvesting of Atlantic cod fishery

1-071-NewtonWatsonTimeOfDeath

Sherlock Holmes determines time of death

1-073-WaterExitBottle

Estimating a parameter in Torricelli’s model of water exiting a container

1-074-BottleWaterFlow

Comparing two models of water flowing out of a container through exit hole

Modeling an RL series circuit with differential equations and Multisim software

1-079-HomeHeating

Modeling hos to heat your home while you are away

Building a simple model for drug administration

1-081-TumorGrowth

Two different models for growth of cancer tumor.

1-085-DrugBolus

Modeling intravenous bolus of drug in the body

1-086-MedicinalPill

Modeling administration of medicinal pills

Spread of disease and applications to Sleeping Beuaty fairy tale

1-090-EmptySphericalTank

Comparing two ways to empty spherical tank of water

1-091-Slopefields

Building population models for various situations and using slope fields

1-093-SucroseReaction

Determining model for sucrose hydrolysis using lab data

1-094-SteepingTea

Modeling temperature change and dissolution of sugar in brewing fruit tea

1-095-RatingChessPlayers

Using Elo’s Method for rating chess players and difference equations

1-101-ClassM&MDeathImmigration

Generating data and using individual model to estimate parameters

1-102-CancerGrowth

Several models are offered along with data for cancer growth models.

1-105-AnimalFalling

Comparing terminal velocity for variety of animal’s falling

1-108-PoissonProcess

Probability functions for Poisson process waiting time are built

1-109-EmployeeAttrition

Maintaining workforce of employees after attrition

1-115-ModelingWithFirstOrderODEs

Several short illustrations and two exercises for modeling

1-118-SolowEconomicGrowth

Analysis of the Solow-Swan model of economic growth theory

1-120-CircularRollerCoaster

Modeling a circular roller coaster to determine velocity to stay on track

Using recent sales data model the spread of plug-in electric vehicles

Using dodecahedral dice population to model death and immigration

1-130-AspirinAbsorption

Pharmacokinetic modeling of absorption of aspirin in body

1-131-CaffeineElimination

Pharmacokinetic modeling of elmination of caffeine from the body

1-132-DigoxinElimination

Pharmacokinetic modeling of elmination of digoxin from the body

1-138-InnerEarDrugDelivery

Developing a model for administering drugs to the inner ear

1-140-LeakyBucket

Modeling the height of water in a tank with a leak and water pouring in

1-141-M&MGameRevisit

We use a simulation and observe long term behavior to estimate a parameter

Using populations and modeling while enhancing MATLAB skills

Activities

Developing and caring for several numerical methods for first order equations

Activities

3-001-SpringMassDataAnalysis

Data on a spring mass system with resistance is given for modeling for analysis

3-002-ModelsMotivatingSecondOrder

From real data several ways to model spring mass system emerge.

3-004-VanderPol

Study of van der Pol’s equation with applications and spreadsheet simulation

3-006-Buoyancy

Data on a bobbing container motivates model and parameter estimation

3-008-HangTime

Hang Time Modeling

3-009-BallDropInWater

Analysis of a falling ball in liquid to reach terminal velocity

3-010-EnergyInSpringSystems

Exploring damping and forcing terms to discover energy in system

3-013-WhiffleBallFall

Using data on whiffle ball fall model resistance and predict the fall position.

3-016-FallingCoffeeFilters

Using data on stack of coffee filters to build model and estimate parameters.

3-017-StackedCoffeeFilters

Using data on stacked coffee filter falling from the literature build models.

3-019-ShuttleCock Fall

Modeling a falling shuttlecock

3-029-FerrisWheelCatch

We model the throw of an object to a person on a moving Ferris wheel.

3-030-SecondOrderIntro

Broad introduction to second order homogeneous and nonhomogeneous, linear, constant coefficient, differential equations with many applications

Design a stadium which is fair to home run hitters in all directions.

3-040-FirstPassageTime

We model and determine the first passage time for underdamped oscillator

3-041-UpDownPassPoint

Relate times when projectile passes the same point – up and then down

3-043-BallisticsModeling-SpongeDart

Building and comparing models for Sponge Dart ballistics.

3-044-DeepWell

Given total time of pebble fall to sound coming back tell how deep a well

3-045-RampBounce

Bounce a ball on a tilted ramp for optimal horizontal distance traversed

3-054-Relay

Place infielder in optimal position for minimum time relay through form outfield

3-065-UpDown

Modeling vertical projectile motion with resistance to address some issues.

3-070-FallingInWater

Drop a canister in column of water, collect data from video, model motion

3-075-RLCCircuits

An introduction to RLC circuits is offered including definitions and modeling.

3-080-PendulumModeling

Several different pendulum configurations are modeled and compared.

3-085-SimplePendulum

Modeling pendulum motion and verification of period with data

3-090-OneMassSpring

Data on a single mass spring system permits modeling of oscillator

3-090-Text-ChebyshevPolynomialSolution

Small study of Chebyshev Equation for which there are polynomial solutions

3-101-SpringMassFirstTry

Modeling a simple spring mass with no damping conjecturing solutions

3-102-SpringMassDamped

Modeling a simple spring mass with damping conjecturing solutions

3-110-MilitarySpringMassApplication

Modeling the shock absorber system for an Army vehicle.

3-140-TwoSpringOneMassFixedEnds

Modeling two spring, single mass with fixed ends

Activities

4-020-AnIEDBlast

Modeling the effects of an Improvised Explosive Device

4-023-MysteryCircuit

Students assigned various input voltages to a circuit  to see what the circuit is.

Input Output Analysis analyzing steady state to estimate parameters.

4-050-ResonanceBeats

We study the notions of resonance and beats for undamped system

4-055-ShatterWineGlass

Shattering wine glasses and other resonance phenomena are studied

4-060-CircuitTuner

Building the differential equation for a radio tuner

Technique Narrative and Development

5-005-StiffDifferentialEquations

An introduction to stiff differential equations and attendant numerical solutions

Activities

5-005-Dialysis

Modeling Dialysis Machine

5-007-ChemOpt

Optimization for a Chemical Reaction

5-090-SolidParticleErosion

Tutorial and modeling problems associated with pitting of ductile surface.

5-0012-LipoproteinMetabolism

Medical study data to build and affirm build a model for low-density-lipoprotein.

5-014-TwoSpringMass

Build Free Body Diagram and model for two spring configuration.

5-022- ColdPill

Modeling flow of drug from gastrointestinal tract to bloodstream for peak

5-025-Eviction

A model for eviction in the United States is built.

5-028-SaltCompartments

Amount of salt in two water tanks is modeled in several ways

5-030-AirshedSulphur

Analyzing a model of the production of sulphur compounds in a Montana airshed.

5-040-TunedMassDampers-Part I

Applying a second mass to keep structure from experiencing resonance

5-040-TunedMassDampers-Part II

Applying second mass to keep structure from large displacement

5-080-SpaceFlightRecolonize

Modeling the recolonization of the human race on a distant planet.

Activities

6-001-Epidemic

English Boarding School NonLethal Influenza

6-002-EulerCromerPendulum

Using the study of nonlinear pendulum to implement numerical methods

6-003-SchoolFluEpidemic

Using SIR model peak flu and total recovery times are determined

6-004-VillageEpidemic

Build a model of a mid seventeenth century English village epidemic

6-005-InsectColonyOpt

Insect Colony Optimal Control

6-006-ZombieGameHvZ

Modeling ths campus Zombie Game HvZ

6-007- FunctionsAndDerivativesInSIRModels

Relating functions and derivatives in SIR Models

6-008-PursuitModels

Linearization and Support from Homogeneous System Analysis

6-010-SocialCampaigns

Creating a model to capture the essence of social media campaigns

6-011-HumansVsZombies

Modeling variations of  Humans vs Zombies battles

6-012-RiverCrossing

Building a model to help cross a river with current to land at specific spot

6-015- CombatingEbolaEpidemic

Making policy recommendations from models of spread of Ebola

6-018-ExploringSIRModel

Modeling rumor and disease spread.

6-019-EnablingEpidemicExploration

Several strategies for estimating parameters in models of epidemics

6-020-AlgaePopulationSelf-Replenishment

Investigate the massive algal blooms that struck Lake Chapala, Mexico

6-021-AcornsRodentsSnakes

Building a three trophic level model of acorns, rodents, and snakes

Moving against a headwind create model of drone flight to fixed delivery point

6-024-DronePackageDelivery

Describe the flight path of a drone delivering a package using numerical methods

6-025-WhalesAndKrill

Use Excel to observe qualitative behavior a predator-prey model

6-028-SaltCompartments

Amount of salt in two water tanks is modeled when tank volumes are changing

6-030-SaltTorricelli

Modeling complex salt levels in a falling column of water.

6-035-Shampoo

Modeling the amount of shampoo in a bottle during a shower

6-040-StruggleForExistence

Using historical data to model multiple species growth

6-065-InternetPlatformUsers

Modeling the dynamics of Internet platform user's volume

6-070-BeerBubbles

Modeling the rise and size of beer bubbles in a sitting glass of beer

Technique Narrative and Development

7-011-Text-CoupledSystemLaplace

Using a baby warmer coupled system Laplace transforms are presented.

Activities

7-005-LaplaceTransformOverview

Introduction and application of Laplace Transforms

7-008-MachineReplacement

Laplace Transforms - Convolution Applications - Replacement Theory

7-010-MultipleDoses

Modeling several multiple dose approaches for drugs is considered.

7-020-ThermometerInVaryingTempStream

Study thermometer while sitting in a stream whose temperature oscillates

7-040-TankInterruptMixing

Several approaches model flow of consecutive streams of salt into a container

Activities

8-002-Text-TrigSumRepresentation

Representing functions as sums of trigonometric functions

Activities

9-001-Text-SkinBurnModelNumericalMethods

Numerical methods for Heat Equation are introduced in context of skin burn issues.

9-012-PDEGuitarTuning

Tuning a Stringed Instrument with the Wave Equation

9-020-HorizontalBeam

Modeling a suspended beam and collecting data to justify the model

APPENDIX

Strategies for Analytic Solutions and Qualitative Analysis

First Order Differential Equations

1-001-Text-SepVariables

1-002-Text-IntegratingFactor

1-009-Text-Bifurcation

Second Order Differential Equations

3-090-Text-ChebyshevPolynomialSolution

Linear Systems of Differential Equations

5-030-Text- LinNonHomoSystemSol

Fourier Series Development

8-002-Text-TrigSumRepresentation