Download Differential Equations for Mathematical Methods for Physics I | PHYS 6124 and more Study notes Physics in PDF only on Docsity! 4
DifPecentoo 4 wotton g ‘8
Exams of PDEs ta physics:
*) Poisson's equation:
as Y= E(B),
2 a 92 a
XQ ~ oxt 1 ay ost
— deotroskatios s - yretcocted . potential > P- chacae deudly
- aganichekto 9 3 ‘e- gcant, Dotamtia£ , P- mass densify
Z) \Nowa equatron: op t OP LC
ee ene A oe XQ Y a 2 te °
— EM worles in fry seaee © ~ speed of. Loght
— Geourtle weed tp Wofropde medium ,o- gpeed of Sound
3 . ‘ ;
> Diffusion equations ory 28 4 oer)
leak gourees
\g- Lonperakut @, k= thormal conalectivaty —_
Gpecitic heat) x Cden atty)
4) Schcadinger 2g uations ¥ 02 Ay -
DERCOAMAKT ROUAALON 3 AVY 4 NEY = ch ae
of UL WEE) = Huy eo
~Ey avy = EY
2m
AVL Linrec poxtrak deflecentiah aquakcons | which have
ko ba Sepp Lemart ack by approp tate. boun dary / trtheah.
cordtions,
TE ound /enet, concletrons- have curtetn aymrukty | PDEs
Can often be convertedck Ucbo ODEs.
AQ0,
Sapocorkton Of Nok tabses
AQL oquokions abe vole Laphaesan ,¥. Hits separable
tm 42087) deference orkrogonah coocalirate systema,
Look. at 3 yrogr Lamilrar cases
Holonok 2qr.okwan % Vv ky =O
4, Cockosian Coordinates, —
SY SW 4 BY 1 e2Y =o
SK BY? oR
Try VOW RD = KEV ze:
creda . “rn y Ly" L 2" kK° =O
deveding by Y: i Q*YN DAZ E@t
Qanckton of x Quncktanofy Lumchion of 2
yl _ h _ Y
a = Oy ) i= on 5 S = CQ. Ce, — Some constants )
For conuigeantys Cr+ Cat Ca = > Ke
Comesion S2pacorLon rok Sense if boumdactet hone
ognrestey Surmmetey 52g, Box of SRO Lx Ly be.
For inshenen, if YOyye~O eX K = 0, bx
Y= oy Ly
WO) ba
=> Opes (for YVR) ofthe hype
leak 5 Kl) = * (Lx) =0
Lal a A
Ly
ee
Centcal Colakion y le = 2 Meegeg KV Ze |
QyCayCs ve