1. Most people did well on the multiple answer section. I will only discuss common misconceptions, here.
(a) Which of the following operations are symmetric under a change of the spatial vectors
a and b (i.e. exchanging them does not aect the result)?
c (
NAME:
MAT 212 Fall 2013 Sections 1 and 2
Test on Chapter 15
Rules:
- no books, notes or calculator only your exam and blank sheets
that you can get from the front;
- your exam should be your own work only no exchanging information with others or peaking a
MAT 212 Fall 2013 Sections 1 and 2
Test on Chapter 13
1. Tangent planes:
Consider the two surfaces S1 and S2 defined by the equations
for S1 : 14 x2 + y 2 + 19 z 2 = 1 ,
for S2 : z = x2 y 2 .
Consider the point Q with coordinates (1, 0, 3 3/2), lying on S
MAT 212 Fall 2013 Sections 1 and 2
Test on Chapter 12 (and section 15.2)
1. Lines in 3-dimensional space
Two lines are defined as follows: line L1 goes through (2, 2, 0) and (0, 0, 2); line L2 goes through (0, 1, 0) and
(1, 0, 0).
a) Sketch these lines.
b
Probability Review
John Norstad
j-norstad@northwestern.edu
http:/www.norstad.org
September 11, 2002
Updated: November 3, 2011
Abstract
We define and review the basic notions of variance, standard deviation, covariance, and correlation coefficients for ran
Econ 432S
Christopher Timmins
Duke University
Fall 2015
Environmental Justice: The Economics of Race,
Place and Pollution
Time TBD
Location TBD
Instructor Christopher Timmins
209 Social Sciences Building
christopher.timmins@duke.edu
(919) 929-7285
Office
1. Flux through a surface
Consider the surface 5 given by the piece between the horizontal planes z = 3 and z = 3 of the circular
cylinder with radius 2 with the zaxis as symmetry axis. Compute the ux through 5, in the direction away
- " _ a:(1z) '-' y(1z
1. Tangent planes
Consider the two surfaces 51 and 52 dened by the equations
for51:%:132 + y2 + %z2 = 1,
for& : z =32 3?.
Consider the point Q with coordinates (1, U, 3x/g/2), lying on 51. The goal of this problem is to nd for which
points R on 52 the tan
soLuTioN Sct Chm (:e/at - Fa .2013.
1. Lines in 3dimensional Space
Two lines are dened as follows: line L1 goes through (2,2,0) and (0, 0, 2); line L2 goes through (0,1,0) and
(1,0,0).
a) Sketch these lines.
b) Do they intersect? If they do, give their in
1. Computing a volume?
Consider the solid body bounded by the planes 3: = 0, y = 1, y + z = 5, y 2/"; = 3 and 23: + z = 6. (The
leftmost gure below shows all these planes. To make the plot less busy, the next two gures show respectively
3, and then the ot
A Class of Methods for Solving Nonlinear
Simultaneous
Equations
By C. G. Broyden
1. Introduction. The solution of a set of nonlinear simultaneous equations is
often the final step in the solution of practical problems arising in physics and engineering. T
FALL 2015 COMPSCI290.2 COMPUTER SECURITY
Assignment 3 Solution
1. TOR
In the TOR anonymizing overlay routing network, any one can set up a relay
node.
(a) What kind of information can a snoopy operator of a relay learns when it is
the first relay
FALL 2015 COMPSCI290.2 COMPUTER SECURITY
Assignment 1 Solution
1. Bob is tired of typing a long and complex password every time he logs into his
remote server using the SSH protocol. Alice suggests using asymmetric cryptography
for password-less authe
Duke University Bursar s Office
- Direct Deposit Authorization for Student Account Refunds
Please provide the following information to sign up for direct deposit of refunds from your student account and other
related student reimbursements. The completed
Computer Science 290-02 Solutions to Assignment 4
Due: December 4, 2015, 11:59 pm
Bruce Maggs
Instruction: Please use Sakai to hand in this assignment.
For each question, write down all the steps that you perform, and provide appropriate
output (copy the
/. Inst. Maths Applies (1973) 12, 223-245
On the Local and Superlinear Convergence of
Quasi-Newtqn Methods
C. G. BROYDEN, J. E. DENNIS Jr. AND JORGE J. MORE
Department of Computer Science, Cornell University,
Ithaca, N. Y. 15850, U.S.A.
[Received 26 March
NAME:
MAT 212 Fall 2013 Sections 1 and 2
Test on Chapter 14
Rules:
- no books, notes or calculator only your exam and blank sheets
that you can get from the front;
- your exam should be your own work only no exchanging information with others or peaking a
Math 103.05
April 19, 2012
Carla Cederbaum
Midterm 3
Midterm 3
Do not open this test booklet until you are directed to do so.
You have 75 minutes to complete this exam.
This exam is closed book. You are not allowed to use a calculator.
Throughout the
Math 103.11
November 22, 2011
Carla Cederbaum
Test 2
1. Use linear approximation to estimate
(3.2)2 + (4.1)2 .
f (x, y ) =
x2 + y 2
x=3
x = 0.2
y=4
y = 0.1
f
= fx (x, y ) x + fy (x, y ) y
x
y
=
x+
x2 + y 2
x2 + y 2
3
4
=
0.2 + 0.1 = 0.2
5
5
f (3.2, 4.1)
Math 103.11
December 9, 2011
Carla Cederbaum
Test 3
Test 3 Solutions
1. Suppose there is a closed simple smooth curve C in the xy -plane which is contained entirely
in the rst quadrant.
(a) You are given the following information about the curve:
If you
EXAM 1
Math 103, Spring 2011, Ye Li.
You have 75 minutes.
No notes, no books, no calculators.
YOU MUST SHOW ALL WORK AND EXPLAIN ALL REASONING
TO RECEIVE CREDIT. CLARITY WILL BE CONSIDERED IN GRADING.
Good luck!
Name
ID number
1.
2.
3.
I have adhered to t
Name:
Honor Code: I pledge my honor that I have not violated the honor code during this examination
Copy below, and sign.
Multivariable Calculus
MAT 103 Test on Chapter 14
Questions 1, 2 and 3 are worth 4 points; question 4 is worth 8 points.
1
0.
2
1. T
1. True or False
Mark for each of the following questions whether the assertion is true or false (by putting
a mark in the corresponding circle), and explain your reasoning in 1 or 2 lines. (For each
of these, 1 or 2 lines suce amply as explanation.) In w
Name:
Honor Code: I pledge my honor that I have not violated the honor code during this examination
Copy below, and sign.
0.
Multivariable Calculus
MAT 103 Test on Chapter 15
All questions are worth 5 points.
1
1. True or False
Mark for each of the follo
THE LAPLACIAN SPECTRUM OF GRAPHS
Bojan Mohar
Department of Mathematics
University of Ljubljana
Jadranska 19, 61111 Ljubljana
Yugoslavia
Abstract. The paper is essentially a survey of known results about the spectrum
of the Laplacian matrix of graphs wit