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Views
Date
Relevance
Technique Narrative
397
views
204
downloads
0
comments
9-001-SkinBurnModelNumericalMethods-TechniqueNarrative
The heat equation is an important partial differential equation (PDE) which describes the distribution of heat in a given region over time. Numerical methods play an important role in solving these.
Maternal-Fetal interface
heat equation
Conservation of Energyt
heat flux
Euler's forward method
central difference
skin burn
hyperthermia
thermal conductivity
layers
Potential Scenario
114
views
43
downloads
0
comments
1981-Geoffrey_Berresford-Differential Equations and Root Cellars
This is a classic module from UMAP in which the heat equation in one dimension is fully developed by using the standard technique of measuring the heat flow in and out of a small element of mass and equating them at equilibrium.
temperature
thermal conductivity
heat flow
thermal diffusivity
root cellar
Modeling Scenario
187
views
164
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
Potential Scenario
240
views
81
downloads
0
comments
2012-Bech-EtAl-Resources For Engineering Applications Of Math
Illustrations of applied mathematics including statics, truss, heat equation, column analysis, coupled oscillators, feedback control, AC circuit, chemical reactions, kinetics.
kinetics
heat equation
column analysis
coupled oscillators
feedback control
AC circuit
chemical reactions
Modeling Scenario
257
views
262
downloads
0
comments
1-079-HomeHeating-ModelingScenario
This project concerns using Newton's Law of Cooling to model the heating of a house. In particular, if one is going away for awhile, is it more economical to leave a house at a desired temperature or reheat it upon return?
Optimal Control Theory
temperature
heat
furnace
Newton's Law of Cooling
home heating
specific heat
Potential Scenario
137
views
65
downloads
0
comments
2013-Michael-Evans-Growth and Decay
Sometimes, we can describe processes of growth and decay—whether physical, chemical, biological or sociological—by mathematical models.
exponential growth
exponential decay
isotopes
populations
resource depletion
Potential Scenario
112
views
37
downloads
0
comments
2004-Hill-Lozowski-Sampson-Experiments on ice spikes and a simple growth model
We observed ice-spike growth using time-lapse digital photography, using two water types in two different containers.
ice
ice spike
bulk heat transfer
mass conservation
Potential Scenario
244
views
85
downloads
0
comments
2017-Justin_Krueger-Parameter Estimation Methods for Ordinary Differential Equation Models with Applications to Microbiology
We demonstrate the feasibility of principal differential analysis using simulation studies and then apply the method to intestinal and vaginal microbiota data.
microbiology
Lotka Volterrra
microbiota
Modeling Scenario
225
views
335
downloads
0
comments
9-015-UnearthingTruth-ModelingScenario
This project introduces \textit{electrical resistivity tomography}, a technique of interest for geophysical imaging, used to produce images of underground features or structures by using electrical current.
geophysical
Imaging
Statistical inverse problem
tunnel
conduction
Holocaust
Vilnius
Divergence Theorem
flux
Laplace's equation
impedance
electrical resistivity tomography
tomography
resistivity
Modeling Scenario
253
views
246
downloads
0
comments
7-020-ThermometerInVaryingTempStream-ModelingScenario
We present a first order differential equation model for the temperature of a mercury thermometer which is sitting in a stream of water whose temperature oscillates. We suggest a solving strategy which uses Laplace Transforms.
temperature
steady state
thermometer
heat exchange
transfer function
phase lag
Invers Laplace Transform
Free Online Textbook
237
views
118
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
236
views
99
downloads
0
comments
4-065-GasInjection-ModelingScenario
Students use programs (or create their own code) based on exponential box-scheme approximations for solving systems of nonlinear differential equations that contain small parameters for the highest derivative terms or singularities in boundary...
Prandtl-Blasius equations
boundary layer
gas injection
esponential box scheme
uniform convergence
FORTRAN
Free Online Textbook
156
views
60
downloads
0
comments
2016-Langtangen-Pedersen - Scaling of Differential Equations
Nowadays, the greatest practical benefit of scaling is related to running numerical simulations, since scaling greatly simplifies the choice of values for the input data and makes the simulations results more widely applicable.
scaling
dimensionless
continuum mechanics
Potential Scenario
161
views
68
downloads
0
comments
1972-R_C_Rothermel-A Mathematical Model for Predicting Fire Spread in Wildland Fuels
The development of a mathematical model for predicting rate of fire spread and intensity applicable to a wide range of wildland fuels is presented from the conceptual stage through evaluation and demonstration of results to hypothetical fuel models.
prediction
forest fire
fire management
fire spread
fuel
Free Online Textbook
202
views
126
downloads
0
comments
2014-Robert_Terrell-Notes_on_Differential_Equations
We point out that the title is not Solving Differential Equations; we derive them, discuss them, review calculus background for them, apply them, sketch and compute them, and also solve them and interpret the solutions.
octave
engineering
textsbook
Free Online Textbook
143
views
53
downloads
0
comments
2014-William_Trench-Elementary_Differential_Equations-Books_and_Monographs
This is the most widely cited and referenced free online text for differential equations and is very complete. These two books are exactly what they say they are.
differential equations
textbook
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