## 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.

#### These materials are hyper-linked to Student Versions under Resources at https://www.simiode.org/ and they are available to all with no sign in or membership.

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#### Please use the Comments tab at each resource to make suggestions, point to corrections needed, relate experiences in your use of the resource, upload further resources we will add to the resource, discuss technical materials, and share your thoughts on the material. These comments will go to the author and the SIMIODE editorial leadership.

**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**

**1-007-Text-SeparationOfVariables**

** Using Ebola modeling to teach separation of variables technique**

** Early introduction to bifurcation with experimentation**

**1-010-Text-AtmosphericCO2Bifurcation**

** Study of bifurcation of atmospheric carbon dioxide**

**1-015-Text-DimensionlessVariables **

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

**1-015-Text-DimensionlessVariables **

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

** Tutorial on random perturbations for a linear first order equation**

**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**

** 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 how 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**

** Analyzing room temperature in a temperature changing environment**

** 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**

** Modeling an Op Amp Differentiator circuit using Multisim**

**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 **

** Investigate the Earth's climate using an energy balance model **

**1-115-ModelingWithFirstOrderODEs**

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

** Modeling the decay of tropical cyclone winds**

** Analysis of the Solow-Swan model of economic growth theory**

** Modeling population growth of a dairy farm**

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

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

** Modeling world population with varying growth rates,” **

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

** Modeling the process of entry into marriage by an individual**

** Modeling a fish harvesting operation over a 25 year time period**

** Modeling flight of rocket of changeing mass due to spent fuel**

** 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**

** Model of fraction of people who are first time married by a certain age.**

** Developing a model for sheep grazing**

** Developing a model for administering drugs to the inner ear**

** Developing a model for herbivores grazing **

** 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**

** Analytic solutions and linear approximation solutions compared to data**

**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.**

** Modeling a falling Styrofoam ball's motion.**

** 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**

** Estimating an unknown parameter in an oscillating spring mass system**

** Modeling wood block bobbing in water and falling ojbect**

** 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**

**Producing a spring meeting industrial specifications at lowest cost **

**Study of spring-mass-dashpot which is part of car suspension system **

** 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**

** Calculating concentration profile of cyclohexane**

** Modeling the fall of a piece of ice off a building**

**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**

** A study of LC circuits, beats, and wireless telegraphy**

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

** Building a circuit analytically in simulation, and physically.**

** Several different pendulum configurations are modeled and compared.**

**3-087-ThanosPopulationDynamicsInteractingSpecies**

** Thanos of "The Avengers" acts on world popultion modeled/strong>**

** 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**

** Understanding maximum frequency response to second order model**

**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**

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

**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**

** Modeling plasmid DNA degradation in rat plasma**

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

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

** Developing phase model to study oscillatory phenomena**

** 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**

** Using Lanchester's Laws to model strength of two armies' strengths**

** Using candies in simulations of attrition warfare**

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

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

**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**

** Model spread of fake news and ways to deter distributing misinformation**

** 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 COVID-19 Pandemic with SIR Model and Geogebra**

** 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**

** Using toy data to study competing populations of protozoa**

** 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 of the Haitian cholera epidemic.**

** 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 .**

** Modeling groundwater flow and developing effective PDE models with data collection .**

** 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**