## 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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**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**

**Strategies for Analytic Solutions and Qualitative Analysis - Technique Narratives**

**First Order Differential Equations**

**Second Order Differential Equations**

**Linear Systems of Differential Equations**

**NonLinear Systems of Differential Equations**

**Partial Differential Equation Solution Strategies**

**Technique Narrative and Development**

**1-001-Text-SepVariable**

Technique narrative on solution method of separation of variables

** **Technique narrative on solution method of integrating factor

Early introduction to bifurcation with experimentation

**1-015-Text-DimensionlessVariables **

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

**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

**1-001pgf- 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 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

**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

Probability functions for Poisson process waiting time are built

**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

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**

**Activities**

**2-001-N****umerical Methods Comparisons**

Developing and caring for several numerical methods for first order equations

**Modeling Three - Second Order Homogeneous Differential Equation Models**

**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 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 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

**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.

__3-140-TwoSpringOneMassFixedEnds__

Modeling two spring, single mass with fixed ends

**Modeling Four - Second Order NonHomogeneous Differential Equation Models**

**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**

**Activities**

Modeling Dialysis Machine

Optimization for a Chemical Reaction

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

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

**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.

**Modeling Six - NonLinear Systems of Differential Equation Models**

**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

**Modeling Seven - Changing the Venue for Solution Success - Laplace Transforms**

**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

**Modeling Eight - Representing Natural Phenomena with Sines and Cosines**

**Activities**

**8-002-Text-TrigSumRepresentation **

Representing functions as sums of trigonometric functions

**Modeling Nine - Modeling with Differential Equations in Higher Dimensions**

**Activities**

**9-001-Text-SkinBurnModelNumericalMethods**

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

Tuning a Stringed Instrument with the Wave Equation

Modeling a suspended beam and collecting data to justify the model

**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**