AE 221 – Aerospace Structures II – Spring 2004
Chapter 1 – Review – Practice Problems
Using the package(s) of your choice (Mathematica, Maple, Matlab, Gnuplot, …),
solve the following problems, which are typical of those you will face in AE 221.
1.
Plot
(
)
4
x
6
2
/
1
x-
x
3
x
2
3
+
+
+
stp
on
1
x
0
≤
≤
, where
(
)
⎩
⎨
⎧
≥
<
=
−
0
0
0
x
x
1
x
x
0
x
x
for
for
stp
is the so-called Heavyside (step) function.
2.
Plot (on the same graph and with the appropriate legends for the three curves),
(
)
( )
( )
x
a
x
x
3
a
x
f
cos
sin
,
+
=
on
1
x
0
≤
≤
, for
2
1
0
a
,
,
=
.
You may also make up a
title and axis-labels.
3.
Compute
[
]
(
)
(
)
dx
a
x
f
x
a
x
f
2
1
L
a
g
L
0
2
2
∫
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
+
⎟
⎠
⎞
⎜
⎝
⎛
∂
∂
=
,
,
,
, where
(
)
a
x
f
,
has been
defined in problem 2.
Plot
[
]
1
L
3
a
0
g
=
≤
≤
,
.
4.
Solve the following linear system
⎪
⎭
⎪
⎬
⎫
⎪
⎩
⎪
⎨
⎧
=
⎪
⎭
⎪
⎬
⎫
⎪
⎩
⎪
⎨
⎧
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎣
⎡
2
3
2
1
4
2
2
2
L
4
L
2
0
C
C
C
L
3
0
L
2
0
L
2
L
3
L
2
L
3
1
5.
Solve the following boundary value problem and plot the solution
Differential equation:
(
)
( )
3
x
x
w
4
+
=
on
1
x
0
≤
≤
Boundary conditions:
( )
( )
( )
( )
0
1
w
0
1
w
1
0
w
0
0
w
=
=
=
=
'
'
,
,
'
,
6.
Plot (from an appropriate angle and with appropriate resolution)
(
)
( )
(
)
z
5
e
2
z
yz
2
z
y
q
y
cos
sin
,
+
=
on
π
≤
≤
≤
≤
−
z
0
3
y
1
,
7.
Let
ij
δ
be the identity tensor.
Show that

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