SIMIODE Resource Guide
SIMIODE Resource Guide
Guide to Modeling Scenarios and Technique Narratives
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TABLE OF CONTENTS
Modeling One  First Order Differential Equations
Modeling Two  Numerically Solving Differential Equations
Modeling Three  Second Order Homogeneous Differential Equation Models
Modeling Four  Second Order NonHomogeneous Differential Equation Models
Modeling Five  Linear Systems of Differential Equation Models
Modeling Six  NonLinear Systems of Differential Equation Models
Modeling Seven  Changing the Venue for Solution Success  Laplace Transforms
Modeling Eight  Representing Natural Phenomena with Sines and Cosines
Modeling Nine  Modeling with Differential Equations in Higher Dimensions
APPENDIX
 This Guide is organized to follow the topics found in a traditional differential equations course.
 The numbering system reflects chapter sequencing in a standard differential equations text.
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 Strategies for Analytic Solutions and Qualitative Analysis
Technique NarrativesFirst Order Differential Equations
Second Order Differential Equations
Linear Systems of Differential Equations
Technique Narrative and Development
Technique narrative on solution method of separation of variables
Technique narrative on solution method of integrating factors
Early introduction to bifurcation with experimentation
1015TextDimensionlessVariables
Scaling for differential equations and dimensionless variables is discussed
Activities
Modeling Death and Immigration with M&M 's and Simulation
1001AM&MDeathImmigrationVariation
Variation on modeling death and immigration with M&M’s
1001BM&MDeathImmigrationMystery
Each student sets own immigration rate and others need to solve this mystery
1001pgf BirthDeathImmigration
Probability generating function approach to simulation.
Modeling a simulation of a large number of dice tossings
Saving for Child's College Education
1004Microorganism Immigration
Modeling Immigration in a Petri Dish
Modeling the Spread of Oil Slick with Incomplete Data
Same as 15OilSlick but with client setting.
Analysis of incomplete reaction data
Analysis of incomplete reaction data
Bank Investment Analysis and Bank Loan Analysis
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 19581974
Modeling LSD in the body and correlating amounts with test performance.
Chemical Kinetics Models  Zeroth, First, and Second Order Reactions
Same as 111Kinetics but with more guidance and less narrative.
1012SublimationCarbonDioxide
Sublimation of Carbon Dioxide
Situations associated with stopping cars, projectile steel ball, and time of death
For fixed volume column which radius of cylinder of water drains fastest
Modeling falling column of water
Modeling drugs for anesthesiology
Modeling spread of disease using logistic equation
Limited Growth Population Modeling
Sensitivity Analysis  Data Collection Experiment Comparing of Rock Masses
Analyzing models on which melts first a sphere or cube of ice of the same volume
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
Modeling and numerical methods for first order malaria growth
Modeling more and more complex salt mixing situations.
Modeling the evaporation of an alcohol and water mixture in various containers.
Modeling randomness with stochastic processes.
Data is offered to model making sweet iced team using luminescence
Modeling water flowing from cone to cube and out
Modeling dissipation of intraocular gas bubbles used in eye surgery.
Changing temperature of container of water in a changing environment.
Modeling the rate at which words propagate through English language text
Phases of barbequeing brisket are modeled using real data.
Student designed fishing strategies for mix of fish in lake
Finding depth in water at which an object settles to neutral buoyancy
Students conduct simulation of spread of common cold and model.
Modeling Ebola epidemic with first order differential equation models
Determining monthly deposit rate for long term savings goal
Variable ascent rate and air management in SCUBA diving
Modeling the amount of drink powder in a second tank of flow system.
Air conditioning cooling modeling.
Planning for full college education costs for the daughter of a friend.
Determining time of death given observations and environmental conditions.
Optimizing a barge trip upriver
Build one compartment salt mixing model
Studying tank in which water inflow containing salt increases.
Modeling the spread of a slime puddle from video collected data.
Mopdeling the growth of farmland with incomplete data
Modeling the falling of water in a right circular cone
Evaluating three models of fluid flow from a tank using data
A container is designed so water will fall out at constant rate of change in height.
1059ContainerShapeFallingWater
Modeling column of falling water in different shaped containers.
Building a model of sales of consumer products from a classic marketing study.
Several models offered for exponential growth in increased complexity
Modeling falling column of water with a box at the base of the column
Cooling of a baked potato and compare it to studentcollected data.
Modeling the US Census data with several different models.
1067ModelingWithSigmoidCurve
Modeling using logistic and Gompertz Sshape curves is offered.
Modeling harvesting of Atlantic cod fishery
Sherlock Holmes determines time of death
Estimating a parameter in Torricelli’s model of water exiting a container
Comparing two models of water flowing out of a container through exit hole
Modeling hos to heat your home while you are away
Building a simple model for drug administration
Two different models for growth of cancer tumor.
Modeling intravenous bolus of drug in the body
Modeling administration of medicinal pills
Spread of disease and applications to Sleeping Beuaty fairy tale
Comparing two ways to empty spherical tank of water
Building population models for various situations and using slope fields
Determining model for sucrose hydrolysis using lab data
Modeling temperature change and dissolution of sugar in brewing fruit tea
Using Elo’s Method for rating chess players and difference equations
1101ClassM&MDeathImmigration
Generating data and using individual model to estimate parameters
Several models are offered along with data for cancer growth models.
Comparing terminal velocity for variety of animal’s falling
Probability functions for Poisson process waiting time are built
1115ModelingWithFirstOrderODEs
Several short illustrations and two exercises for modeling
Analysis of the SolowSwan model of economic growth theory
Modeling a circular roller coaster to determine velocity to stay on track
Using recent sales data model the spread of plugin electric vehicles
Pharmacokinetic modeling of absorption of aspirin in body
Pharmacokinetic modeling of elmination of caffeine from the body
Pharmacokinetic modeling of elmination of digoxin from the body
Developing a model for administering drugs to the inner ear
Modeling the height of water in a tank with a leak and water pouring in
We use a simulation and observe long term behavior to estimate a parameter
Modeling Two  Numerically Solving Differential Equations
Narrative and Development
2001Numerical Methods Comparisons
Developing and caring for several numerical methods for first order equations
Modeling Three  Second Order Homogeneous Differential Equation Models
Narrative and Development
Under development.
Activities
Data on a spring mass system with resistance is given for modeling for analysis
3002ModelsMotivatingSecondOrder
From real data several ways to model spring mass system emerge.
Study of van der Pol’s equation with applications and spreadsheet simulation
Data on a bobbing container motivates model and parameter estimation
Hang Time Modeling
Exploring damping and forcing terms to discover energy in system
Using data on whiffle ball fall model resistance and predict the fall position.
Using data on stack of coffee filters to build model and estimate parameters.
Using data on stacked coffee filter falling from the literature build models.
Modeling a falling shuttlecock
We model the throw of an object to a person on a moving Ferris wheel.
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.
We model and determine the first passage time for underdamped oscillator
Relate times when projectile passes the same point – up and then down
Given total time of pebble fall to sound coming back tell how deep a well
Bounce a ball on a tilted ramp for optimal horizontal distance traversed
Place infielder in optimal position for minimum time relay through form outfield
Modeling vertical projectile motion with resistance to address some issues.
Drop a canister in column of water, collect data from video, model motion
An introduction to RLC circuits is offered including definitions and modeling.
Several different pendulum configurations are modeled and compared.
Modeling pendulum motion and verification of period with data
Data on a single mass spring system permits modeling of oscillator
3090TextChebyshevPolynomialSolution
Small study of Chebyshev Equation for which there are polynomial solutions
Modeling a simple spring mass with no damping conjecturing solutions
Modeling a simple spring mass with damping conjecturing solutions
3110MilitarySpringMassApplication
Modeling the shock absorber system for an Army vehicle.
3140TwoSpringOneMassFixedEnds
Modeling two spring, single mass with fixed ends
Modeling Four  Second Order NonHomogeneous Differential Equation ModelsNarrative and Development
Under development.
Activities
Modeling the effects of an Improvised Explosive Device
Students assigned various input voltages to a circuit to see what the circuit is.
Input Output Analysis analyzing steady state to estimate parameters.
We study the notions of resonance and beats for undamped system
Shattering wine glasses and other resonance phenomena are studied
Building the differential equation for a radio tuner.
Modeling Five  Linear Systems of Differential Equation Models
Narrative and Development
Under Development
Activities
Modeling Dialysis Machine
Optimization for a Chemical Reaction
Medical study data to build and affirm build a model for lowdensitylipoprotein.
Build Free Body Diagram and model for two spring configuration.
Modeling flow of drug from gastrointestinal tract to bloodstream for peak
A model for eviction in the United States is built.
Amount of salt in two water tanks is modeled in several ways
Analyzing a model of the production of sulphur compounds in a Montana airshed.
Applying a second mass to keep structure from experiencing resonance
5040TunedMassDampersPart II
Applying second mass to keep structure from large displacement
Modeling the recolonization of the human race on a distant planet.
Modeling Six  NonLinear Systems of Differential Equation Models
Narrative and Development
Under Development
Activities
English Boarding School NonLethal Influenza
Using the study of nonlinear pendulum to implement numerical methods
Using SIR model peak flu and total recovery times are determined
Build a model of a mid seventeenth century English village epidemic
Insect Colony Optimal Control
Modeling ths campus Zombie Game HvZ
6007 FunctionsAndDerivativesInSIRModels
Relating functions and derivatives in SIR Models
Linearization and Support from Homogeneous System Analysis

Creating a model to capture the essence of social media campaigns
 6012RiverCrossing
Building a model to help cross a river with current to land at specific spot
Making policy recommendations from models of spread of Ebola
Modeling rumor and disease spread.
6019EnablingEpidemicExploration
Several strategies for estimating parameters in models of epidemics
6020AlgaePopulationSelfReplenishment
Investigate the massive algal blooms that struck Lake Chapala, Mexico
Building a three trophic level model of acorns, rodents, and snakes
Moving against a headwind create model of drone flight to fixed delivery point
Describe the flight path of a drone delivering a package using numerical methods
Use Excel to observe qualitative behavior a predatorprey model
Amount of salt in two water tanks is modeled when tank volumes are changing
Modeling complex salt levels in a falling column of water.
Modeling the amount of shampoo in a bottle during a shower
Using historical data to model multiple species growth
Modeling the rise and size of beer bubbles in a sitting glass of beer
Modeling Seven  Changing the Venue for Solution Success  Laplace Transforms
Narrative and Development
Under Development
Activities
7005LaplaceTransformOverview
Introduction and application of Laplace Transforms
Laplace Transforms  Convolution Applications  Replacement Theory
Modeling several multiple dose approaches for drugs is considered.
7020ThermometerInVaryingTempStream
Study thermometerwhile sitting in a stream whose temperature oscillates
Several approaches model flow of consecutive streams of salt into a container
Modeling Eight  Representing Natural Phenomena with Sines and Cosines
Narrative and Development
8002TextTrigSumRepresentation
Representing functions as sums of trigonometric functions.
Activities
Under Development
Modeling Nine  Modeling with Differential Equations in Higher Dimensions
Narrative and Development
9001TextSkinBurnModelNumericalMethods
Numerical methods for Heat Equation are introduced in context of skin burn issues.
Activities
Tuning a Stringed Instrument with the Wave Equation
Modeling a suspended beam and collecting data to justify the model
Modeling Ten – Technique Narrative  General Modeling
APPENDIX
Strategies for Analytic Solutions and Qualitative Analysis
First Order Differential Equations
Second Order Differential Equations
3090TextChebyshevPolynomialSolution
Linear Systems of Differential Equations
5030Text LinNonHomoSystemSol
NonLinear Systems of Differential Equations
Under Development