18.03 Problem Set 8
This is the complete version of PS8. Part II
29 (b)
(iv) has been slightly changed
(correcting a mistake) and renumbered
29 (c)
. Due by 12:45 P.M., Friday, May 2, 2008,
in the boxes at 2-106, next to the Undergraduate Mathematics Oﬃce.
I encourage collaboration on homework in this course. However, if you do your homework
in a group, be sure it works to your advantage rather than against you. Good grades for
homework you have not thought through will translate to poor grades on exams.
You
must turn in your own writeups of all problems, and, if you do collaborate,
you must write on the front of your solution sheet the names of the students
you worked with.
Because the solutions will be available immediately after the problem sets are due,
no
extensions will be possible
.
III. Fourier series, Dirac delta function, and Laplace transform
L29
F 18 Apr
Pole diagram; Weight and transfer function: SN 22, 23, EP 4.4.
L30
W 23 Apr
Review.
R19
Th 24 Apr
Exam preparation.
L31
F 25 Apr
Hour Exam III
IV. First order systems
L32
M 28 Apr
Linear systems and matrices: EP 5.1–5.3, SN 25, Notes LS.1.
R20
T 29 Apr
Linear systems and matrices; Trajectories vs solutions.
L33
W 30 Apr
Eigenvalues, eigenvectors: EP 5.4, Notes LS.2.
R21
Th 1 May
Normal modes.
L34
F 2 May
Complex or repeated eigenvalues: EP 5.4, Notes LS.3.
Part I. 29. (F 18 Apr)
Nothing.
30. (W 23 Apr)
Nothing.
31. (F 25 Apr)
Nothing: Hour Exam.
32. (M 28 Apr) (a)
Compute the matrix products
±
1 2
²
³
x
y
´
,
³
1
2
´
±
x y
²
,
³
a b
c d
´ ³
x
y
´
,
±
1 2
²
³
a b
c d
´
,
³
a b
c d
´ ³
x u
y v
´
.
(b)
Notes 4A-2, 4B-1, 4B-6.
33. (W 28 Apr)
Notes 4C-1. (See EP p. 344 for a description of how to ﬁnd the
determinant of a 3
×
3 matrix.)