L. Vandenberghe EE103
10/27/09
Midterm Solutions
Problem 1 (10 points). The cross-product a x of two 3-vectors a = (a1 , a2 , a3 ) and x = (x1 , x2 , x3 ) is defined as the vector a2 x 3 - a3 x 2 a x = a3 x 1 - a1 x 3 . a1 x 2 - a2 x 1 1. Assume a is fixe
Mechanical and Aerospace Engineering Department
MAE 101: Statics and Strength of Materials
Summer, 2010
Lecture: MW 11:30 am - 1:50 pm, KNSY PV 1200B
Discussion: T 11:30 am - 1:50 pm KNSY PV 1200B
Office Hours: M 2:30-3:30 pm, W 2:30-3:30 pm
Tel: 714-955-
EE113D DIGITAL SIGNAL PROCESSING DESIGN
L A B 4 : E X T E R NA L I N P U T S A N D
VO I C E T R A N S F O R M AT I O N
DURATION: 2 PERIOD
STEP 1:MANIPULATING A SINE WAVE
Figure out how to read the value of the dip switc
Homework 2
(Due on January 19, 2010)
Note:
All numbered problems are from Munson et al., 6th edition.
Read the sample homework on the course website.
Copying other peoples work (including previously posted solutions and solutions
from a solution manual
Homework 2
(Due on January 19, 2010)
Note:
All numbered problems are from Munson et al., 6th edition.
Read the sample homework on the course website.
Copying other people's work (including previously posted solutions and
solutions from a solution manua
Homework 6
(Due on February 23, 2010)
Note:
All numbered problems are from Munson et al., 6th edition.
Copying other peoples work (including, but not limited to, previously posted
solutions and solutions from a solution manual) is considered plagiarizin
Homework 7
(Due on March 2, 2010)
Note:
All numbered problems are from Munson et al., 6th edition.
Copying other peoples work (including, but not limited to, previously posted
solutions and solutions from a solution manual) is considered plagiarizing, a
Homework 8
(Due on March 9, 2010)
Note:
All numbered problems are from Munson et al., 6th edition.
Copying other peoples work (including, but not limited to, previously posted
solutions and solutions from a solution manual) is considered plagiarizing, a
Homework 9
(Dont need to turn in; solutions will be posted on March 12)
Note:
All numbered problems are from Munson et al., 6th edition.
Copying other peoples work (including, but not limited to, previously posted
solutions and solutions from a solution
L. Vandenberghe EE103
11/05/09
Homework 5 solutions
1. Exercise 8.1. We can note diagonal: 0 0 A= 0 1 (a) We have A = max
x=0
that A = P D where P is a permutation matrix, and D is 0 0 1 0 1 0 0 0 0 1 0 0
10-2 0 0 0 -3 0 10 0 0 4 0 0 -10 0 0 0 0 -10
.
L. Vandenberghe EE103
10/28/08
Midterm Exam
You have time until 9:20. Only this booklet should be on your desk. You do not need a calculator. Please turn off and put away your cellphones. Write your answers neatly and concisely in the space provided afte
L. Vandenberghe EE103
10/28/08
Midterm Solutions
Problem 1 (10 points). Express the following problem as a set of linear equations. Find a cubic polynomial f (t) = c1 + c2 (t - t1 ) + c3 (t - t1 )2 + c4 (t - t1 )2 (t - t2 ) that satisfies f (t1 ) = y1 , f
L. Vandenberghe EE103
12/10/08
Final Exam
You have time until 11:00AM. Only this booklet should be on your desk. Calculators are not allowed. Please turn off and put away your cellphones. Write your answers neatly and concisely in the space provided afte
L. Vandenberghe EE103
12/10/08
Final Exam Solutions
Problem 1 (10 points). a c b The length of one side of a triangle (c) can be calculated from the lengths of the two other sides (a and b) and the opposing angle () by the formula c= Two equivalent expres
EE103 Formulas
Vectors and matrices Relation between inner product and angle: xT y = x y cos (x, y)
Flop counts for basic operations ( is a scalar, x and y are n-vectors, A is an m n-matrix, B is an n p-matrix) Inner product xT y: 2n - 1 flops ( 2n flops
L. Vandenberghe EE103
12/3/09
Homework 8 solutions
1. We are interested in minimizing
m
g(x) =
i=1
ri (x)2
x = (uc , vc , R) and where ri (x) = (ui - x1 )2 + (vi - x2 )2 - x2 . 3 At iteration k of the Gauss-Newton method we solve the least-squares problem
L. Vandenberghe
EE103 Fall 2009
Homework 8
Due Thursday 12/3/09. 1. Exercise 14.6. We solve a specific instance of the problem in exercise 14.6. Download the file ch14ex6.m from the course website, and execute the Matlab command [u, v] = ch14ex6; to gener
L. Vandenberghe EE103
11/19/09
Homework 7 solutions
1. Exercise 12.1(b). The figure shows g(x) and (E - x)/R for E = 15, R = 3.
8 7 6 5 4 3 2 1 0 0 1 2 3 4
There are three solutions that we can find by iterating x := x - f (x) x3 - 6x2 + 10x - (E - x)/R =
L. Vandenberghe EE103
11/12/09
Homework 6 solutions
1. Exercise 9.9. The first plot is for = 1, the second plot is for = 100, the last plot is for = 10000. For = 1, there is not enough smoothing, for = 10000 we have too much smoothing, and = 100 seems abo
L. Vandenberghe EE103
10/15/09
Homework 3 solutions
1. Exercise 4.5. We can write f (u1 , u2 ) as f (u1 , u2 ) = u2 p11 + 2u1 u2 p12 + u2 p22 + u1 q1 + u2 q2 + r. 1 2 For given u1 and u2 , this is a linear function of the unknowns p11 , p12 , p22 , q1 , q