16.20 Handed Out: Lecture 5
Due: Lecture 9
HOME ASSIGNMENT #1
Warm-Up Exercises
Write out the following tensor equations in full:
(Note: these equations do not necessarily have any real meaning)
1.
G
i
= l
αβ
M
αβ
n
i
2.
A
ij
= Q
ijkl
τ
k
x
l
(for i = 2, j = 3)
3.
a
mn
∂u
n
+ f
m
= 0
∂t
4.
1
E = 2 σ
αβ
ε
αβ
5.
σ
23
= l
2m
l
3n
˜
σ
˜ ˜˜ mn
Practice Problems
6. Write out the succinct tensor equation that describes the following notation:
H
1
C
111
C
122
2C
112
M
11
H
2
= C
211
C
222
2C
212
M
22
H
3
C
311
C
322
2C
312
M
12
Note any assumptions that you had to make (if any).
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