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WTW256: LU 4.1: INTRODUCTION TO SYSTEMS OF LINEAR DIFFERENTIAL EQUATIONS Lecture notes $4.59   Add to cart
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WTW256: LU 4.1: INTRODUCTION TO SYSTEMS OF LINEAR DIFFERENTIAL EQUATIONS Lecture notes
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  • Course
  • WTW 256 - Differential Equations
  • Institution
  • University Of Pretoria (UP)

Lecture notes were made while watching the recorded lectures assigned to watch. These notes include theory (theorems) and worked out examples from the lecturer. These specific notes cover Introduction to systems of differential equations.

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Document information

  • July 11, 2022
  • 6
  • 2021/2022
  • Class notes
  • Ms l mostert
  • All classes

Subjects

  • wtw
  • 256
  • wtw256
  • vector
  • wronskian

Written for

  • University of Pretoria (UP)
  • WTW 256 - Differential Equations
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4. I. Systems of linear DE 's
more than one dependent variable , each dependent


onasingleindepvaridble.ec
ample
* need " and y that satisfies
:* # atty , ett both of these equations .




¥ ,
=
2 # ee
#
yyi
}



write in MATRIX NOTATION

✗ (f)
' =
AF > F- ( t )

I (f)
( ylt ) ]
= nlt )

constants / doesn't have
"
lyin them
t%t↓ Ect )
;)
A

[ ] [
e
= =




2 et



Thatch ×
' =

AI -1
F- ( t)
,
I Cto )=Ño

7h 8. It .




If the entries in the matrix A- and F- are continuous on an
interval containing to Ivp will have solution
, then a
unique
on this interval

, consider

I ☒ [ %)
'




:[ et )
t 't
nice)=[ 's ]
+


z


all these this ale .
continuous @ c -8,0)

to =
0 C- C- 8,8 )


[IN THIS COURSE ]
First order homo, linear
systems of DF
with
Instant coeff .




*
'
=
AX
,
☒ Cto ) -
Fo
se
example y
2

[ ]I
3
* AI
'




2×+391
I
= =

=
i ,
Homo
-




ot
w

dy constants
"
Y
=

d-t
-


+
,



continuous




\"&"ÉY linear combination of solutions is
that is if I, , ,
Iz .
. . In are
999in a
solutions of ✗
solution
'
=
AI then




X-t-cii lix-zi.i.ycnxnwil bedsolutiohbi.at 8.1.2 .




let 51,512 ,
. .
.in be a set of solutions vectors of

✗ AF
'
=
on an interval 2 .




The set is linearly dep on L if there exists constants

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