## SIMIODE Resource Guide

## SIMIODE Resource Guide

**Guide to Modeling Scenarios and Technique Narratives**

**This is a growing list of resources and as developed, refereed, edited, and finalized, new materials will be published. To see how to contribute your own teaching materials go to Author Information.**

#### This Guide is organized to follow the topics found in a traditional differential equations course, hence, the numbering system reflects chapter sequencing in a standard differential equations text.

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**Technique Narrative and Development**

** Technique narrative on solution method of separation of variables**

** 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**

** Early introduction to bifurcation with experimentation**

**1-015-Text-DimensionlessVariables **

** Scaling for differential equations and dimensionless variables is discussed**

**1-060-Text-RegularPerturbation**

** Tutorial with activities on using Regular Perturbation to solve differential equations**

**Activities**

** 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**

**1-001C-PopulationDecayThenSome**

** Variation on modeling death and immigration with hotel modeling and MatLab**

** Modeling the comings and goings of hotel patrons using various models.**

**1-001pgf- BirthDeathImmigration**

** Probability generating function approach to simulation.**

** Modeling a simulation of a large number of dice tossings**

** Saving for Child's College Education**

**1-004-Microorganism Immigration**

** Modeling Immigration in a Petri Dish**

** Modeling the Spread of Oil Slick with Incomplete Data**

** Same as 1-5-OilSlick 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 1958-1974**

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

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

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

**1-012-SublimationCarbonDioxide **

** 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.**

** Modeling 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.**

**1-059-ContainerShapeFallingWater**

** 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

** Falling single column of water with three spigot holes**

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

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

** Modeling the US Census data with several different models.**

**1-067-ModelingWithSigmoidCurve**

** Modeling using logistic and Gompertz S-shape 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 the Earth's climate using known parameters**

** Modeling an RL series circuit with differential equations and Multisim software**

** 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.**

**Foucault Knife Edge Test, an optical test used in lens making is modeled.**

**A falling meteorite is modeled with a number of factors considered.**

**Randomized spread of viral disease and full model build and fit**

** Modeling intravenous bolus of drug in the body**

** Modeling administration of medicinal pills**

**1-087-ThanosPopulationDynamics**

** Villain Thanos attempts to retore balance to the world**

** Spread of disease and applications to Sleeping Beauty fairy tale**

** Comparing two ways to empty spherical tank of water**

** Building population models for various situations and using slope fields**

**World record sprinter's maximum effort race is modeled**

** 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**

**1-101-ClassM&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**

** Modeling the rate at which drying takes place in a cloth wet with water**

** Probability functions for Poisson process waiting time are built**

** Maintaining workforce of employees after attrition**

**A simulation with coins and data on the spresd of information **

**1-115-ModelingWithFirstOrderODEs**

** Several short illustrations and two exercises for modeling**

** Analysis of the Solow-Swan 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 plug-in electric vehicles**

** Using dodecahedral dice population to model death and immigration**

** 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**

**1-143-PopulationModelVariations-MATLAB**

** Using populations and modeling while enhancing MATLAB skills**

**Activities**

**2-001-Numerical Methods Comparisons**

** Developing and caring for several numerical methods for first order equations**

**Activities**

** 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.**

** 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**

** Analysis of a falling ball in liquid to reach terminal velocity**

** Exploring damping and forcing terms to discover energy in system**

**Using Euler's Method in maximizing distance for throwing a ball**

** 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**

**3-043-BallisticsModeling-SpongeDart**

** Building and comparing models for Sponge Dart ballistics.**

** 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 gear trains built with various gear combinations**

** Modeling vertical projectile motion with resistance to address some issues.**

** Comparing analytic solution and numerical simulation for RLC series AC circuit.**

** 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**

**3-090-Text-ChebyshevPolynomialSolution**

** 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**

**3-110-MilitarySpringMassApplication**

** Modeling the shock absorber system for an Army vehicle.**

**Estimating acceleration due to gravity from pendulum modeling.**

**3-140-TwoSpringOneMassFixedEnds**

** Modeling two spring, single mass with fixed ends**

**Steady-state heat equation to model temperature distribution in industrial furnace**

**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**

**Technique Narrative and Development**

**5-005-StiffDifferentialEquations**

** An introduction to stiff differential equations and attendant numerical solutions**

**Using the matrix exponential to solve linear systems of ODEs**

**Consequences of conjecturing solutions to linear systems of ODEs**

**Activities**

**5-002-**PhasePortraitForRelationshipDynamics

**Using phase plane portraits to analyze Romeo and Juliet's relationship**

**Using Variation of Parameters to solve linear nonhomogeneous systems.**

** Modeling Dialysis Machine**

** Optimization for a Chemical Reaction**

** Tutorial and modeling problems associated with pitting of ductile surface.**

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

** Build Free Body Diagram and model for two spring configuration.**

** Modeling flow of drug from gastrointestinal tract to bloodstream for peak**

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

** A model for eviction in the United States is built.**

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

** Applying a second mass to keep structure from experiencing resonance**

**5-040-TunedMassDampers-Part II**

** Applying second mass to keep structure from large displacement**

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

**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**

**6-007- 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**

** Modeling variations of Humans vs Zombies battles**

** 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.**

**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**

** 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 predator-prey 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 dynamics of Internet platform user's volume**

** 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**

** Laplace Transforms - Convolution Applications - Replacement Theory**

** Modeling several multiple dose approaches for drugs is considered.**

**7-020-ThermometerInVaryingTempStream**

** Study thermometer while sitting in a stream whose temperature oscillates**

** 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 .**

** Gentle progression from ODE to PDE modeling through invasive species model.**

**Modeling a traveling wave in porous medium.**

** Tuning a Stringed Instrument with the Wave Equation**

**Using electrical resistivity tomography to unearth tunnels**

**Build equipment, conduct experiment, model data - has it all**

** Modeling a suspended beam and collecting data to justify the model**

**Technique Narrative and Development**

**Activities**

**Using tiling of hallways to motivate difference equation modeling**

**APPENDIX**

**Strategies for Analytic Solutions and Qualitative Analysis**

**First Order Differential Equations**

**Second Order Differential Equations**

** 3-090-Text-ChebyshevPolynomialSolution**

**Linear Systems of Differential Equations**