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WTW238: Theme 5 (LU 5.1 - 5.3) Summary R133,00
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  3. University Of Pretoria (UP)
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  5. WTW 238 - Mathematics (WTW238)

Summary

WTW238: Theme 5 (LU 5.1 - 5.3) Summary
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This document contains the notes made while watching the lecture recordings with the textbook as a supporting reference. LU 5.1 - 5.3 have been summarised here: Eigenvalue problems, Heat equation, and Wave equation.

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  • December 24, 2022
  • 7
  • 2022/2023
  • Summary

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5.Eigenvalue problems Joure t) S.2
2 8ounddry value problem
Ppin 90q) yalues for a for whlch VP has

non triviql non"ero) Jolutions
parqmeter :a

M b1 b-4dcpicrimindnt Cinsiøe)
2d


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y(z):(emi2Czelme

root m
O (zero Repbated
ulx) Ce m z Ce ema,
ve :Complex/conjugdte rootsmpt1, qfo)_


egenvalue and eigehfundt ions
-yo) *0y0)0 (Pard meter Rigenvalue
ehdpoint vadlue_problem trdt ontains qparameter X "probleM

For what Valuer of he pdhd meter a doej thete PXISt_a_hon-tr'Val
Jolutjon ot endaoint value prehlem
non-rividl valuefor eigeh value
hon-trindl Solution = eigen funtHon

, LU5-2. Hedt equdtion
SoV SoV ov Trantf.
Scenglo 2
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u,0) f) ulz,o) q).
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To get ormy1a mahudlly
perdtion of ValY j0 bles.A
Transformdtion

FSeperdtich ot variable
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OHod e uahion
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Uzx'T T' X
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X T A
X
XtAX o T KT :0.|


Bou roary ordt+ions
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for X-prob le m

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