In[17]:=
D
@
y, x
D
Out[17]=
Sin
B
1
+
x
3 2
F
2
x
c) Find the first 3 terms in the Taylor's series expansion of
about x=0.
In[18]:=
Series
@
Sqrt
@
a
+
Log
@
x
+
1
DD
,
8
x, 0, 3
<D
Out[18]=
a
+
x
2
a
+
H

1

2a
L
x
2
8a
3 2
+
I
3
+
6a
+
8a
2
M
x
3
48a
5 2
+
O
@
x
D
4
d) Let A=
1 2 5

2 4 1
0

1 3
and B=
1 1 1

2 6 0
4 2 7
. Compute the comutator ABBA and verify that
H
AB
L
T
=
B
T
A
T
and that
H
A B
L

1
=
B

1
A

1
Type the matrices in the old fashioed way :
In[19]:=
A
=
88
1, 2, 5
<
,
8

2, 4, 1
<
,
8
0,

1, 3
<<
Out[19]=
88
1, 2, 5
<
,
8

2, 4, 1
<
,
8
0,

1, 3
<<
In[20]:=
B
=
88
1, 1, 1
<
,
8

2, 6, 0
<
,
8
4, 2, 7
<<
Out[20]=
88
1, 1, 1
<
,
8

2, 6, 0
<
,
8
4, 2, 7
<<
Use MatrixForm to make sure we got it right :
In[23]:=
MatrixForm
@
A
D
Out[23]//MatrixForm=
1 2 5

2 4 1
0

1 3
In[24]:=
MatrixForm
@
B
D
Out[24]//MatrixForm=
1 1 1

2 6 0
4 2 7
Commutator =
In[25]:=
A.B

B.A
Out[25]=
88
18, 18, 27
<
,
8
8, 4, 9
<
,
8
14,

9,

22
<<
2
212HomeWork1sol.nb