M SS CHUSETTS INSTITUTE OF TECHNOLOGY
DEP RTMENT OF MECH NIC L ENGINEERING
2.161 Signal Processing - Continuous and Discrete
Fall Term 2008
Problem Set 1: Convolution and Fourier Transforms
Assigned: Sept. 9, 2008
Due: Sept. 18, 2008
Problem 1:
a) Plot th
18.305 Exam 1,
October 18, 04.
Closed Book.
Problem: Consider the differential equation
y + x 4 y : 0.
(a) Locate and classify the singular points, finite or infinite, of this differential equation. (10%)
(b) Find the WKB solutions of this equation. For w
6 856 Randomized Algorithms
David Karger
Handout #2, September 5, 2002 Homework 1, Due 9/11
M. R. refers to this text:
Motwani, Rajeez, and Prabhakar Raghavan. Randomized Algorithms. Cambridge: Cambridge University Press, 1995.
1. MR 1.1.
(a) Suppose you
M SS CHUSETTS INSTITUTE OF TECHNOLOGY
DEP RTMENT OF MECH NIC L ENGINEERING
2.161 Signal Processing - Continuous and Discrete
Fall Term 2008
Problem Set 2
Assigned: Sept. 18, 2008
Due: Sept. 25, 2008
Problem 1: A waveform f (t) with a real even spectrum F
j
j j
Y k j k j
kA j
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A61h%R Q @ C G B i G I q G S 9 I 9 Q q i S
E @i
uHw
w
B
VC
a @ C B i G I qj G E I 9
1Vs1A1PhHE A6ikpi G C %VDkh6tHlATS
Ik16Pu1lu1`Y%DB Ys6W%D1%1m%VgkvW5AV%tsA% 6W%1h6%1AAV1thcfw_DuV1kVtmg
9IIG G RQ Qi RQ B X9 R
Q i B
6 856 Randomized Algorithms
David Karger
Handout #4, September 17, 2002 Homework 1 Solutions
M.R. refers to this text:
Motwani, Rajeez, and Prabhakar Raghavan. Randomized Algorithms. Cambridge: Cambridge University Press, 1995.
Problem 1 MR 1.1.
(a) We re
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
DEPARTMENT OF MECHANICAL ENGINEERING
2.161 Signal Processing - Continuous and Discrete
Fall Term 2008
Solution of Problem Set 2
Assigned: Sept. 18, 2008
Due: Sept. 25, 2008
Problem 1:
Y (j) = H(j)F (j) and it is shown
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
DEPARTMENT OF MECHANICAL ENGINEERING
2.161 Signal Processing Continuous and Discrete
Fall Term 2008
Problem Set 1 Solution: Convolution and Fourier Transforms
Problem 1:
Use the convolution definition y (t ) = f $ h =
0 Wm {5mm Meier M Qvm
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as perfova m Llrh but can he smoo
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2.094
FINITE ELEMENT ANALYSIS OF SOLIDS AND FLUIDS
SPRING 2008
Homework 6 - Solution
Instructor:
Assigned:
Due:
Prof. K. J. Bathe
03/13/2008
03/20/2008
Problem 1 (20 points):
t
Lets define R =
t
t
R t
F
t
, F=
and U =
.
2kL
2kL
L
t
Since t F = t R at equ