Teorema kekonvergenan pada generalized function

Harini , Dyah (2003) Teorema kekonvergenan pada generalized function. Undergraduate thesis, FMIPA UNDIP.

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Abstract

Untuk menjabarkan bagaimana massa suatu benda didistribusikan di sepanjang panjang benda, diperkenalkan fungsi densitas massa p(x). Jika massa terpusat hanya pada satu titik tunggal, menurut pandangan fisika fungsi densitas massa adalah nol di setiap titik kecuali pada titik tunggal tersebut, dan integral atas sebarang interval tidak akan berharga nol sebab massa terpusat pada titik tersebut. Dalam pandangan matematika, jika fungsi berharga nol hampir di setiap titik, integral atas sebarang interval akan berharga nol. Untuk menggeneralisasikan fungsi tersebut agar dapat diterima secara matematis adalah dengan menggunakan teori distribusi. Suatu fungsional E disebut `distribusi' jika is linear dan kontinu,. artinya untuk sebarang test function 4(x) konvergen dalam CD mengakibatkan barisan bilangan F(,) konvergen dalam R. Perkalian distribusi hanya dapat dilakukan dengan fungsi yang infinitely differentiable. Setiap distribusi adalah terdifferensial dan derivatifnya merupakan distribusi juga. Jika barisan distribusi konvergen distribusional ke distribusi E , maka barisan distribusi En' akan konvergen distribusional ke distribusi In order to describe how the mass of an object is distributed along its length, one introduces a mass-density function p(x). If the mass is concentrated at a single point, in the physical point of view, a mass-density function is zero everywhere except at the single point, and its integral over any interval is non zero, because the mass is concentrated at the point. From the mathematical point of view, if the function has value 0 almost everywhere, the integral over any interval must be zero. To generalize the function so that acceptable mathematically, we use distribution theory. A functional is called `distribution'if it is linear and continuous, it means that for arbitrary convergent sequence of test function 4,(x) in 0 causes the sequence of number 'F (On) converge in R. Distributions can be multiplied by an infinitely differentiable function only. Every distribution is differentiable and its derivative is also a distribution. If the sequence of distribution distributionally converge to the distribution T, so the sequence of distribution Tn t will be distributionally converge to the distribution V.

Item Type:Thesis (Undergraduate)
Subjects:Q Science > QA Mathematics
Divisions:Faculty of Science and Mathematics > Department of Mathematics
ID Code:31617
Deposited By:Mr UPT Perpus 1
Deposited On:23 Nov 2011 14:36
Last Modified:23 Nov 2011 14:36

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