AM 351
Assignment No. 6
Fall 2005
Systems of First Order Linear DEs
Due: Tuesday, November 21, 2005, 1:30 p.m. (under my door)
1. Construct the first three iterates
u
0
,
u
1
and
u
2
of Picard’s method of successive substitution applied
to the following linear system IVP:
"
x
0
1
x
0
2
#
=
"
0
1

1
0
# "
x
1
x
2
#
,
"
x
1
(0)
x
2
(0)
#
=
"
1
0
#
.
(1)
(Work on each component
x
i
separately.) Compare your results with the solution of the IVP.
2. In Assignment No. 5, you determined the fundamental matrix Φ(
t,
0) for the linear system defined
by
x
0
=
Ax
where
A
=
"

3
2
2

3
#
.
(2)
Of course, we now know that Φ(
t,
0) =
e
t
A
. Find
e
t
A
via an appropriate similarity transformation
B
=
C

1
AC
.
3. Find the constant matrix
A
corresponding to the linear system
x
0
=
Ax
that has the following
general solution:
x
(
t
) =
C
1
e

2
t
1
1
!
+
C
2
e

t
1

1
!
.
(3)
Explain briefly the basis of your solution.
4. Course Notes, Problem Set 3, No. 2. (You can solve for
x
1
(
t
) and then use this result to solve for
x
2
(
t
).)
5. The force on a charge
q
due to the presence of an electrostatic field
E
and a magnetic field
B
is
given by
F
=
q
E
+
q
c
v
×
B
,
where
v
denotes the velocity of the charged particle and
c
is the speed of light. (In other words,
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 Spring '08
 SivabalSivaloganathan
 Mass, IVP., order linear des

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