Summary
WTW256 Summary of Theme 4 (LU 4.1 -4.3)
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This document contains a summary of LU 4.1 - 4.3.
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p 332-338p340 -341
Eigenvalues
4.1 intro 4.2
µ
. .
and -
vectors
<
y
:( ten;) exit
' ' '
first order > x
,y /
t
✗i i -12
↳ bitt
once
Homo :O Non horn -1-0
eigenvalue
-
form
diagonal C- × ) ( A- X2 )
'
✗ =A✗→
Homo •
t -
variables separated _
→
'
✗ =AXeF → Non
-
homo form •
Determinant 1A -
✗ 21
↳ A coeff before Kandy
eigenvector
=\ !:-#
"
solution vector → ✗ entries are \
" " t)
n differentiable 1
Use eigenvalues
•
separately
↓ , replace in diagonal
.
④ verification I
2) Ñ=o
]
•
CA ✗
-
1. Take Xi ( given ) and "" I
'
!É:/ variable inside
(8)
diffwrt
( )( %)
•
\
-
-
,
2. Identify Acgiven) _
3.
multiply × , with A
i -
AX , → row
operation
]* " ( IN @ df SYSTEMS ◦
•
perform
get value
row operations
Ford and b
Of Df
[
4- If RHS : LHS → solution !
can come in
7h 8. 1. 1. Existence of unique solution
•
conjugate pairs
↳
imaginary aeip
A and F continuous fn 's →
on interval I p34/ -342
that contains to
7h8 1. 2. superposition principle
-
4- } Eigenvalue
Eigenvector
'
×, ,XyX} → solutions othomoonintendlt
method Imaginary
✗
=
cixitczxzicsx }
solutions
pjgtinct , Red / Enon repeating
•
identify a
drop
-
are
linearly inoeps-iririnsiein.in
'
reata
+I
:
→ ⊖
"¥!%ˢ¥¥¥
-
11 1 11 I \
-5.1=1 >|≠◦
wcx-i.ir
in
. .
c. E. exit . . .
>
eminent [Bicostst -
)
Basin /Bt eat
form fund . Real 1m
④ show
set
that combination of complex
.
" ⊕
General solution ( constants NOVALUE !)
→
-
solution can be written as
[ Blcosptt Bisinpt] eat
G(t)e-2ᵗeCz(f) eat
→ combo of real-valued solutions
Mmm 2m Re
Higher order DEZ
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