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Title: Kakutani's solution of the dirichlet problem
Type of Resource: Animação/simulação
Objective: Observe the Kakutani's solution for thr dirichelet's problem
Abstract: Choose one of the three functions using the setter bar. Move the locator to a point in the unit circle. You will see the value of the selected function at this point displayed below the circle. Now increase the duration of motion. A Brownian path will emerge from the chosen point. Keep increasing the duration until the Brownian path hits the boundary of the circle. The value of the chosen function at the point where the path hits the boundary will appear below the value of the function at the point from which the path emerged. Now increase the number of paths, increasing the time duration, if necessary, to make sure they all hit the boundary. If the selected function is harmonic (the first and second choices), the average of the values of the function at the points where the Brownian paths hit the boundary will converge to the value of the function at the starting point of the path. If the selected function is not harmonic (the third choice), the average will converge to the value of a different (harmonic) function that coincides with the given function on the boundary
Observation: This demonstration needs MathematicaPlayer.EXE to run found in http://objetoseducacionais2.mec.gov.br/handle/mec/4737
Curriculum Component: Educação Superior::Ciências Exatas e da Terra::Física
Theme: Educação Superior::Ciências Exatas e da Terra::Física::Métodos Matemáticos da Física
Educação Superior::Ciências Exatas e da Terra::Física::Teorias Específicas e Modelos de Interação; Sistemática de Partículas; Raios Cósmicos
Author: Kozlowski, Andrzej
Language: English (en)
Country: United States (us)
Description: Knowledge in basic mathematical methods for physics,and the dirichelet's problem
Web Address: http://demonstrations.wolfram.com/KakutanisSolutionOfTheDirichletProblem/
Date: 2008
Rightsholder: The Wolfram Demonstrations Project & Contributors
License: Demonstration freeware using Mathematica Player
Submitter: Universidade Federal de São Carlos (UFSCAR)
URI: http://objetoseducacionais2.mec.gov.br/handle/mec/6452
This Educational Object appears in the following Types of resources: Educação Superior: Ciências Exatas e da Terra: Física: Animações/Simulações