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Downloads
Views
Date
Relevance
Potential Scenario
100
views
39
downloads
0
comments
2001-Edwards-Buckmire-A differential equation model of North American cinematic box-office dynamics
A new mathematical model is presented for the box-office dynamics of a motion picture released in North America.
cinema
movies
box-office
Article or Presentation
247
views
67
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
200
views
101
downloads
0
comments
2021-G_Nagy-Ordinary_Differential_Equations
This is an introduction to ordinary differential equations. We describe the main ideas to solve certain differential equations, like first order scalar equations, second order linear equations, and systems of linear equations.
differential equations
textbook
Modeling Scenario
271
views
426
downloads
0
comments
6-070-BeerBubbles-ModelingScenario
The goal of this project is to set up and numerically solve a first-order nonlinear ordinary differential equation (ODE) system of three equations in three unknowns that models beer bubbles that form at the bottom of a glass and rise to the top.
molecular forensics
BEER
sphere
bubble
Newton' Second Law
Ideal Gas Law
drag force
Hadamard
Stokes
mole
Technique Narrative
310
views
181
downloads
0
comments
1-030-RandomPerturbation-TechniqueNarrative
After a brief historical view of this problem, we will demonstrate the derivation of first order linear differential equations with random perturbations.
random perturbation
Brownian motion
Langevin equation
Riemann-Steiltjes integral
Wiener process
Ito's calculus
Modeling Scenario
301
views
282
downloads
0
comments
3-067-RLCSeriesCircuit-ModelingScenario
In this validation-oriented setup, the second order linear ordinary differential governing equation of a small signal RLC series AC circuit is solved analytically, and the results are compared with the data acquired from analyzing the numerical...
resistance
Multisim
circuit
RLC circuit
inductance
capacitance
cimulation
governing equation
Modeling Scenario
216
views
471
downloads
0
comments
3-076-CircuitBuilding-ModelingScenario
In this project students will establish a mathematical model for an electric circuit as a second-order ordinary differential equation with constant coefficients.
simulation
experiment
Multisim
circuit
inductance
capacitor
Kirchhoff's Voltage Law
resistor
Modeling Scenario
175
views
143
downloads
0
comments
3-150-ItsABlastFurnace-ModelingScenario
This project uses the steady-state heat equation to model the temperature distribution in an industrial furnace used for metal production, for example, a blast furnace.
steady state
heat equation
inverse problem
furnace
Modeling Scenario
273
views
388
downloads
0
comments
1-037-CommonColdSpread-ModelingScenario
This modeling scenario guides students to simulate and investigate the spread of the common cold in a residence hall. An example floor plan is given, but the reader is encouraged to use a more relevant example.
disease
common cold
residence hall
Potential Scenario
114
views
62
downloads
0
comments
2000-deOlivera-Delfino-Costa-Leite-Pinhole Water Flow From Cylindrical Bottles
The water flowing from the first bottle feeds the second one located below it. The same concepts of mass and energy conservation now lead to a non-trivial differential equation for the lowest bottle dynamics.
Torricelli's Law
Conservation of Energyt
Conservation of Mass
Bernoulli’s Theorem
Potential Scenario
246
views
47
downloads
0
comments
2006-Juska-Gedminiene-Ivanec-Growth of Microbial Populations-Mathematical Modeling-Laboratory Exercises-Model-Based Data Analysis
The aim is to teach the students to use a fresh approach to the problems they are familiar with, to come up with an articulate verbal model after a mental effort, to express it in rigorous mathematical terms, to solve (with the aid of computers).
population growth rate
logistic equation
Verhulst equation
generation time
lag time
Potential Scenario
133
views
35
downloads
0
comments
1984-W_Brunner-D__Focht-Deterministic Three-Half-Order Kinetic Model for Microbial Degradation
The kinetics of mineralization of carbonaceous substrates has been explained by a deterministic model which is applicable to either growth or nongrowth conditions in soil.
kinetics
nonlinear regression
sum of square errors
Monodlinearize
mineralization
substrates
carbonaceous
Modeling Scenario
437
views
276
downloads
0
comments
1-006-Financing-ModelingScenario
We describe two situations, one in which we are saving for a purpose and one in which we are borrowing for a purpose. In the first case we ask for discrete and continuous model of the situation and in the second case we ask that the results of...
finance
savings
loan
interest rate
payment
Potential Scenario
144
views
57
downloads
0
comments
2017-William_Bialek-Boxes and Arrows To Differential Equations
This material uses pictures to build kinetic models of reactions and then offers analytic solutions.
Michaelis-Menten
Enzyme
substrate
DNA\kinetis
Potential Scenario
221
views
69
downloads
0
comments
2017-Floyd_Ballard-Dice Activities for DE Models
This document includes descriptions of four activities that are appropriate for a calculus or differential equations class, all using dice to motivate a differential equation model for a real-world scenario.
simulation
curve fitting
c
dice
collect data
class activities
analyze data
class activity
Potential Scenario
142
views
84
downloads
0
comments
2015-Heiko_Enderling-Integrating experimental data to calibrate quantitative cancer models
For quantitative cancer models to be meaningful and interpretable the number of unknown parameters must be kept minimal. We focus on a tumor hierarchy of cancer stem and progenitor non-stem cancer cells.
cancer
tumor
fitting
agent-based
Potential Scenario
128
views
74
downloads
0
comments
2015-Beckmann-Sanchez-Cache Calculus-Modeling Caches through Differential Equations
We present cache calculus, a technique that models cache behavior as a system of ordinary differential equations, letting standard calculus techniques find simple and accurate solutions of cache performance for common access patterns.
discrete
cache
cache calculus
Potential Scenario
134
views
63
downloads
0
comments
2012-Lensyl-Urbano-The Draining of a Plastic Bottle-Integrating a Physics Experiment into Calculus
I punched a small hole (about 1mm radius) in a one gallon plastic bottle and had my students measure the rate at which water drained.
in-class activity
experiment
Torricelli's Law
cylinder of water
expderiment
Potential Scenario
140
views
46
downloads
0
comments
2011-Kurt_Kreith-The Mathematics of Global Change
The authors discuss broad issues and then focus on specifics like exponential growth, logistic growth, and the logistic equation with delay.
exponential growth
logistic growth
Potential Scenario
139
views
39
downloads
0
comments
2010-Singh-Mishra-athematical modeling approach to study growth rate of grassroots technological innovations
In this paper we have proposed a simple mathematical model by using ordinary differential equation to know the spread rate of technological innovations in rural India.
logistic
exponential
sigmoid
technological innovations
asymptotic
spread of innovation
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