6 856 Randomized Algorithms
David Karger
Handout #4, September 21, 2002 Homework 1 Solutions
M. R. refers to this text:
Motwani, Rajeez, and Prabhakar Raghavan. Randomized Algorithms. Cambridge:
Cambridge University Press, 1995.
Problem
MR 1.8.
(a) The mi
18.305 Exam 2,
December 6, 04.
Closed Book.
1. Find, for R ; 1, the leading term for each of the following integrals:
2
4 2
a. X e ?Rx +x dx. 15 points.
1
K
4 2
b. X e iRx +x dx. 15 points.
?K
c. X
K
?K
e iR sinh x dx.
bonus 20 points.
2. Consider the di
2.094
FINITE ELEMENT ANALYSIS OF SOLIDS AND FLUIDS
SPRING 2008
Homework 7 - Solution
Instructor:
Assigned:
Due:
Prof. K. J. Bathe
04/03/2008
04/10/2008
Problem 1 (20 points):
(a)
1
cos 45 sin 45 2
0
0
0
t X = t R tU =
sin 45 cos 45 0
t
0
X=
( X)
0
t
1
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 3: Analog Filter design
Assigned: Sept. 25, 2008
Due: Oct. 2, 2008
Problem 1: Consider the following tw
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
DEPARTMENT OF MECHANICAL ENGINEERING
2.161 Signal Processing - Continuous and Discrete
Fall Term 2008
Problem Set 3 Solution: Analog Filter design
Problem 1: Use the nomenclature in the class handout. For both lters:
Pan
V nit/as
Lu. limes . 47.: T- * 12,; .: .w
1" or 1 "' -. , L arm L 4.>u1; cu
is. " 031mg: 3» 1v « {7. in! era
Voluw. mew;
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0: Huh"? r I» MA? , (4* (WW/r ,
L £IJf0
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
DEPARTMENT OF MECHANICAL ENGINEERING
2.161 Signal Processing - Continuous and Discrete
Fall Term 2008
Solution of Problem Set 4
Assigned: Oct. 2, 2008
Due: Oct. 9, 2008
Problem 1:
We have shown in class (see the Fouri
6.856 - Randomized Algorithms
David Karger
Handout #3, September 11, 2000 - Homework 2, Due 9/18
M.R. refers to this text:
Motwani, Rajeez, and Prabhakar Raghavan. Randomized Algorithms. Cambridge: Cambridge University
Press, 1995.
1. MR 1.8.
2. MR 2.3. C
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 4
Assigned: Oct. 2, 2008
Problem 1:
Due: Oct. 9, 2008
An AM (amplitude-modulated) radio signal f
f
M (t