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General Resource
73
views
18
downloads
0
comments
Instructor Solutions Second Edition SIMIODE Textbook HTML Version
This is material we make available for instructors teaching a modeling-first approach to differential equations when using the Second Edition of SIMIODE Textbook, Differential Equations: A Toolbox for Modeling the Real World in HTML Version.
textbook
html
SIMIODE textbook
Second Edition
Modeling Scenario
1018
views
146
downloads
0
comments
3-051-ProjectileMotions-ModelingScenario
We consider several instances of projectile flight without resistance, one on level ground and one from edge of cliff to determine maximum distance and placement.
trajectory
launching radiant
projectile motion
projectile
no resistance
angle of launch
Modeling Scenario
137
views
39
downloads
0
comments
3-052-OptimalProjectileFiring-ModelingScenario
We offer the opportunity to model a projectile's trajectory in several cases, all without resistance.
projectile motion
projectile
launch angle
maximum range
Modeling Scenario
127
views
45
downloads
0
comments
1-144-HeatCool-ModelingScenario
We offer an opportunity to build a mathematical model using Newton's Law of Cooling for a closed plastic baggie of liquid inside a liquid container.
temperature
Newton's Law of Cooling
cooling
Article or Presentation
893
views
58
downloads
0
comments
SIMIODE Spring 2024 Webinars - Insightmaker
We discuss the use of the FREE system dynamics software Insightmaker (https://insightmaker.com/) in a first course in Ordinary Differential Equations (with a modeling emphasis).
modeling
simulation
Software
python
systems
InsightMaker
flow
Category Theory
stock
stock-flow
Modeling Scenario
473
views
145
downloads
0
comments
3-033-S-TimeUpTimeDown-ModelingScenario
We seek to compare for the time a projectile takes to go vertically up with the time it takes to return to its starting position.
projectile motion
apex
vertical motion
Modeling Scenario
246
views
162
downloads
0
comments
1-027-StochasticProcesses-ModelingScenario
We build the infinite set of first order differential equations for modeling a stochastic process, the so-called birth and death equations. We will only need to use integrating factor solution strategy or DSolve in Mathematica for success.
Variance
Mean
stochastic
random
operations research
industrial engineering
Poisson process
traffic
Modeling Scenario
269
views
273
downloads
0
comments
5-024-PhGreatLakes
In this teaching modeling scenario, we demonstrate how lessons on salt-tank compartmental modeling can be used to predict phosphorus levels in the Great Lakes.
Great Lakes
limnology
comparment
pollution
compartmental models
phosphorous
Modeling Scenario
669
views
581
downloads
0
comments
3-034-CarSuspension-ModelingScenario
We examine the spring-mass-dashpot that is part of a car suspension, how the ride is related to parameter values, and the effect of changing the angle of installation. We model a ``quarter car'', meaning a single wheel.
design
spring-mass-dashpot
spring constant
underdamping
car suspension
suspension tolerance
static equilibrium
Modeling Scenario
239
views
147
downloads
0
comments
3-130-MatterOfSomeGravity-ModelingScenario
This project introduces the concept of an inverse problem (or parameter estimation), in the context of the simple linearized pendulum ordinary differential equation.
gravity
inverse problem
acceleration
Potential Scenario
175
views
54
downloads
0
comments
2017-GR_Gustafson-Differential Equations Course Materials
There are many applications from compartment and cascade analysis, recycling brine tank, home heating with multiple rooms, chemostat, microbes, heartbeats, lidocaine, nutrient flow in an aquarium, biomass transfer, pesticides, forecasting prices,...
chemostat
microbes
biomass
forecasting
transfer
compartment
pesticides
earthquake
tank
heating
lidocaine
brine
heartbeats
nutrient flow
aquarium
electric networks
circuits
logging
building
cascade
Potential Scenario
131
views
29
downloads
0
comments
2011-W_Wood-Squigonometry
The differential equations used to define a unit circle, namely x’(t) = - y(t), y’(t) = x(t), x(0) = 1, y(0) = 0 are generalized to produce interesting functions which satisfy trig like identities.
Trigonometry
Trigonometric Functions
parametric equations
circle
sine
cosine
squigonometry
inverse function
Article or Presentation
146
views
35
downloads
0
comments
2008-Keith_Landry-Brian_Winkel-Peak_Frequency_Responses_and_Tuned_Mass_Dampers
We present two applications of systems of ordinary differential equations concerning excitation of a structure through resonance and (1) peak frequency responses with stabilization of the structure by means of a (2) Tuned Mass Damper (TMD).
vibration
resonance
tuned mass damper
peak frequency response
excitation
Article or Presentation
145
views
62
downloads
0
comments
2004-Mark_McCartney-Using_second-order_ordinary_differential_equations_to_model_traffic_flow
A simple mathematical model for how vehicles follow each other along a stretch of road is presented. The resulting linear second-order differential equation with constant coefficients is solved and interpreted.
differential equations
traffic flow
vehicle follow
second order
Modeling Scenario
245
views
154
downloads
0
comments
1-035-DotseroVolcanoEruption-ModelingScenario
In this scenario, we use Carbon-14 dating of the Dotsero volcano in Colorado as a way of emphasizing this multistage process of modeling.
exponential decay
half-life
decay
Euler's method
carbon dating
decay rate
Carbon-14
Dotsero volcano
volcano
Article or Presentation
230
views
60
downloads
0
comments
2009-Brian_Winkel-Modelling_Growth_Of_an_OilSlick
An oil-slick spreads at sea. From time to time, but irregularly, a helicopter is dispatched. On each trip, it arrives over the slick, the pilot takes a picture, waits 10 minutes, takes another, and heads home. Model this.
differential equations
simulation
parameter estimation
difference equation
Free Online Textbook
171
views
65
downloads
0
comments
2018-Eduardo-Sontag-Lecture_Notes_on_Mathematical_Systems_Biology
I am often asked if it is OK to use these notes in courses at other universities. The answer is “of course!” though I strongly suggest that a link to my website be provided, so that students can always access the current version.
biology
textbook
systems
dyanmical system
Modeling Scenario
898
views
2033
downloads
0
comments
3-030-SecondOrderIntro-ModelingScenario
We outline the solution strategies involved in solving second-order, linear, constant coefficient ordinary differential equations, both homogeneous and nonhomogeneous and offer many application and modeling activities.
parameter estimation
non-homogeneous
Spanish
frequency
buoyancy
inverse problem
thrust
underdamped
first passage
spring mash dashpot
real
complex
homogeneous
superposition
parachute
overdamped
critically damped
buoy
quadratic equation
roots
rocket flight
Modeling Scenario
1118
views
5309
downloads
0
comments
5-001-LSD-ModelingScenario
We describe the use of a two compartment model of a linear system of first order linear differential equations to model lysergic acid diethylamide (LSD) in the body. We provide the data from the literature.
LSD
Spanish
compartment
pharmacokinetics
lysergic acid diethylamide
Modeling Scenario
357
views
217
downloads
0
comments
7-011-CoupledSystemLaplace-ModelingScenario
Differential equations and Laplace transforms are an integral part of control problems in engineering systems. We consider a baby warming device.
transfer function
polycarbonate
baby heater
coupled system
heating
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