Post on 01-Mar-2021
Recall Wave equation
UH C Uxx wax cueUlxio fixutixio gix
D Alembert's Salin to wave
eqnulx.tlII fixth t fix Ct
Xtlt1 Ee f g's ds
X Ct
h f
fix Io
u i x E l Effi x t e t t fix ch
t o
tea
t to
a
travelling in oppositedirections
Domain of dependence
UH t solves 4th 9UxWith UK is flX Uf x e glx
Find the largest interval on which
modifying fix and 91 1 Can changethe value of U 12.63
Uh b t flu 1 film
1 tf f glsias
SO Ulrio depends only on values of
fix GH in 1 16 Lo
i i
Higher dimensional wave eqn
Vibrating membrane
I't's
wave egni UH C ou
UH.y.tl gp 0 Bo
solve this using separation of variablesUK yet fix.y Git
oft aT GHI
04 if4 4 0
Boundary value
problem
solve this faka
New topic Sturm Liouville problem
Y t Xp o
461 414 0
di TET 4 _sis
Orthogonality h4mdx 0 Mtn
Ex Heat eqn
Cf Ut Koll x x 1 LUseparation of variables
41kt YING Ifs
p 41 1641 1 140 1 Gits1 241 3 Gif
lift th't'tw pdependson t depends on x
ko 4 t dyed 4 0
of lol 414 0
Boundary value problem
Y
Ex Radial heat flow
UK.y.tl UH O t
not depending on 0Ucr t
Ut OU Fmr r
Ucr tl o
unit o
uii a
separation of variablesUlriti ftp.G It
4 G'HF 444 Git
crop
Ty x
toll t dry o
Ofer Yury o
The general form of a Hurm Liouville
eqn is
P of't t 910 tar 4 0 a Eb
PHI 91 1 Text are fats of x
Pk 70 THI 70
Bcs holla 11,944 0
224lb Tfa 044 0
Goal Find eigenvalues daFind eigenfets 4h
othegonality of eigenfots
7hm all X are realI eigenvalues
X Cdr C 7g C
Each eigenspan is simplei e t din c eigenspace
g
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fix 7 E an fulxhit
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if m th
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