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
isui ainqnt. 0-6. Jolutlons
'Ve 2 distinc real rookjS
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
SCendrio Scenari03
Rod'S endS qro Rod' erds dre Hodt eudtjon
insuldte o @erd not n Stdrddr d
uto,t) (xt0U Uz(0 t)*ua (a,t)*0 form
t ku UE kUa 1 hu.
u,0) f) ulz,o) q).
formula sheet hqs 0qud onJ
To get ormy1a mahudlly
perdtion of ValY j0 bles.A
Transformdtion
FSeperdtich ot variable
Forrod's ends 0'C f
OHod e uahion
ut kUxn.
UIz,)X2)Tit)
UtXT XT' XT
Uzx'T T' X
7 XT. t X
proble m. 7-prob ern
X T A
X
XtAX o T KT :0.|
Bou roary ordt+ions
YCL,t)X()T(6).-o
V ) X(«) TH) *0 TP o XC 0
Xo)-o Newlook or eroen volue prob/em
for X-prob le m
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
isui ainqnt. 0-6. Jolutlons
'Ve 2 distinc real rookjS
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
SCendrio Scenari03
Rod'S endS qro Rod' erds dre Hodt eudtjon
insuldte o @erd not n Stdrddr d
uto,t) (xt0U Uz(0 t)*ua (a,t)*0 form
t ku UE kUa 1 hu.
u,0) f) ulz,o) q).
formula sheet hqs 0qud onJ
To get ormy1a mahudlly
perdtion of ValY j0 bles.A
Transformdtion
FSeperdtich ot variable
Forrod's ends 0'C f
OHod e uahion
ut kUxn.
UIz,)X2)Tit)
UtXT XT' XT
Uzx'T T' X
7 XT. t X
proble m. 7-prob ern
X T A
X
XtAX o T KT :0.|
Bou roary ordt+ions
YCL,t)X()T(6).-o
V ) X(«) TH) *0 TP o XC 0
Xo)-o Newlook or eroen volue prob/em
for X-prob le m
