APLIKASI TRANSFORMASI FOURIER PADA PERSAMAAN DIFERENSIAL PARSIAL DENGAN FUNGSI NON PERIODIC

Muannisak, Lailatul (2009) APLIKASI TRANSFORMASI FOURIER PADA PERSAMAAN DIFERENSIAL PARSIAL DENGAN FUNGSI NON PERIODIC. Other thesis, University of Muhammadiyah Malang.

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Abstract

Differential equation is detectable in a physics problem and geometric if the function depends on two or more independent variables. It is not excessive if we say that only a simple physics system can modelling by ordinary differential equation. Fluid mechanic and mechanic dense, heat transfer, electromagnetic theory, and all kinds of physics is full with a problem that has to modelled by partial differential equation. Actually, the comparison of application of the partial differential equation larger than ordinary differential equation. One of kind of partial differential equation that important in technical and science is heat equation one-dimension and heat equation two-dimension. There are two method that we know to solve partial differential equation with periodic function there are using Fourier series and lap lace transformation. The use of Fourier series in only on a function that has a finite interval, and lap lace transformation can use to solve partial differential equation with a function that has a finite and semi-infinite interval. The other problem is come when the function is a no periodic function that has an infinite interval. The solving of the problem can’t use Fourier series or lap lace transformation. The solution is we have to use Fourier transformation to solve it. Based on the problem, the writer so interest to examine that problem in this thesis. The purpose of this writing is describing the application Fourier transformation to solve partial differential equation with no periodic function. And this writing delimitates on a heat equation one-dimension of an infinite homogeny stalk and heat equation two-dimension with steady of a square thin metal sheet. The application of Fourier transformation will change a partial differential equation and initial value to a new ordinary differential equation and initial value in w variable. The ordinary differential equation that provide is solved and we can use a new initial value is profitable a solution. Next, the solution for last partial differential equation can solve with Fourier transformation inverse from that ordinary differential equation. So as to easy to find the result of this inverse from Fourier transformation solution, we can use Fourier transformation table information. Based on the working through, providable that a solution of heat equation one-dimension with Initial requisite , and mix limit requisite is . And the solution of heat equation two-dimension with Initial requisite , and mix limit requisite Is.

Item Type: Thesis (Other)
Subjects: L Education > L Education (General)
Divisions: Faculty of Teacher Training and Education > Department of Mathematics and Computing
Depositing User: Anggit Aldila
Date Deposited: 20 Jun 2012 03:31
Last Modified: 20 Jun 2012 03:31
URI: http://eprints.umm.ac.id/id/eprint/8669

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