UNIVERSITY OF WATERLOO
FINAL EXAMINATION
FALL TERM 2008
Student Name (Print Legibly)
Signature
COURSE NUMBER
COURSE TITLE
COURSE SECTION(S)
DATE OF EXAM
'lll\lE PERIOD
DURATION OF EXAM
NUMBER, OF EXAM PAGES
INSTRUCTORS (please indicate your
6.
a.) E ( X ) np 10(0.5) 5
b.) Values X=0 and X=10 are the least likely, the extreme values
a) n = 50, p = 5/50 = 0.1, since E(X) = 5 = np.
50
50
50
50
49
48
2) 0.10 0.9 0.11 0.9 0.12 0.9 0.112
0
1
2
50 49
50 50
1
0
48
c) P( X 49)
49 0.1 0.9
NE 115 - HW 5 - Due Monday November 24, 2014
1. The mean water temperature downstream from a power plant cooling tower discharge
pipe should be more than 100F. Past experiences has indicated that the standard
deviation of temperature is 2F. The water temp
Assignment # 4 (Due Wednesday , November 12, 2014)
(Note: submit only problems marked with a *)
1)* PVC pipe is manufactured with a mean diameter of 1.01 inch and a standard
deviation of 0.003 inch. Find the probability that a random sample of n = 9 secti
1) Hypothesis testing
2) Tests on the mean and variance of a normal
population
3) Large sample tests on proportion
4) Testing for Goodness of fit
8-1 Hypothesis Testing
8-1.1 Statistical Hypotheses
Statistical hypothesis testing and confidence
interval e
UNIVERSITY OF WATERLOO
FINAL EXAMINATION
FALL TERM 3007
Student Name (Print LegibW)
I x. (:W I ,. (A I i? N E?
Signature ( w
X.
Student ID Number
COURSE NUMBER I\IATH 117 / SYDE 111
COURSE TITLE ' Calculus 2 for Engineering
COURSE SECTION(
UNIVERSITY OF WATERLOO
FINAL EXAMINATION
Name (Please Print Legibly)
Signature / x
Student ID Nu fiber
COURSE NUMBER M
COURSE TITLE
Calculus 1 for Engineering
COURSE SECTION(S) 001 002 003 004 005
DATE OF EXAM December 13th, 201
NE 112 Linear Algebra with Numerical Applications, Fall 2011
Final Examination
December 8, 2011
Instructions: Write your name on the front of the exam booklet and your student ID on the inside
of the first page.
Record all answers and show work in exam bo
NE 112 Linear Algebra with Numerical Applications, Fall 2012
Final Examination
December 10, 2012
Instructions: Write your name and your student ID on the front of the exam booklet. Pencil is
allowed on this exam. Box or highlight all final answers.
Record
NE 112 Linear Algebra with Numerical Applications, Fall 2013
Final Examination
Tuesday, December 10, 2013
Instructions: Write your name and your student ID on the front of the exam booklet. Record all
answers and show work in exam booklet, this sheet will
NE 112 Linear Algebra with Numerical Applications, Fall 2012
Midterm Examination
October 16, 2012
Instructions: Write your name on the front of the exam booklet and student ID on the inside
front cover.
Record all answers and show work in the exam booklet
NE 112 Linear Algebra with Numerical Applications, Fall 2013
Midterm Examination
October 17, 2013
Instructions: Write your name on the front of the exam booklet and student ID on the inside
front cover. Return the exam booklet only.
Record all answers and
NE 112 Linear Algebra with Numerical Applications, Fall 2011
Midterm Examination
October 20, 2011
Instructions: Write your name on the front of the exam booklet and your student ID on the inside
of the first page.
Record all answers and show work in exam
Math 117
Page 10 of 11
Final Examination - Fall 2014
Formulas
Trigonometric Identities
1
[1 + cos 2]
2
1
sin2 = [1 cos 2]
2
sin 2 = 2 sin cos
cos2 =
sin2 + cos2 = 1
1 + tan2 = sec2
1 + cot2 = csc2
sin(A + B) = sin A cos B + cos A sin B,
angle: 0
sine:
NE334: Lecture 30
July 22, 2014
Simulations of nano-scale
systems
What to do when you
dont know Z!
1
Fundamentals
In order to perform molecular simulations, we need:
Statistical mechanics (because we cannot
specify everything!)
Quantum Mechanics (thats
NE 334 Lecture 34, July 30 2014
Reading: This and next lectures: Chapter IX
FermiDirac Statistics and Intrinsic Semiconductors.
Crystalline Solids:
Each atom/ion brings electrons to assembly of atoms making up solid: some are called atomic
core, some ato
NE 334 Lecture 33, July 29 2014
Reading: This and next lectures: Chapter IX
The StronglyDegenerate FermiDirac Gas.
Low temperatures and/or high density: consider, for example, the freeelectron model of
metals
for electrons, as we have only translational
NE 334 Lecture 31, July 23 2014
Reading: This and next lectures: Chapter IX
FermiDirac and BoseEinstein Statistics.
FermiDirac distribution
Two cases :
BoseEinstein distribution
(for fermions)
(for bosons)
These are the only exact distributions.
N molecu
NE 334 Lecture 32, July 24 2014
Reading: This and next lectures: Chapter IX
A dierent limiting case is of importance for BoseEinstein particles. We know that nk cannot
be negative; moreover, we may write nBE as
k
nBE
k
e k
=
1 e
k
1
=
1
e
k
1
.
We may al
NE 334 Lecture 28, July 18 2014
Reading for this lecture: Chapter VIII Next lectures: Bose-Einstein and Fermi-Dirac Statistics;
Secs. IX.1-IX.4
nal exam info
problem set 4 (simulations)
Examples:
(a) Dissociation of I2 .
Let us consider the gas phase diss
NE 334 Lecture 29, July 22 2014
Reading: This and next lectures: Bose-Einstein and Fermi-Dirac Statistics; Secs. IX.1-IX.4
Quantum statistics: setting the stage.
Until now, quantum restrictions upon wavefunctions have not had to be considered except
when
NE 334 Lecture 27, July 11 2014
Reading for this lecture: Chapter VIII Next lecture: Bose-Einstein and Fermi-Dirac Statistics;
Secs. IX.1-IX.4
KP =
(zC /N0 )C (zD /N0 )D U /RT
0
.
e
(zA /N0 )A (zB /N0 )B
(1)
Aside : Some practical matters:
We shall examin
NE 334 Lecture 21, June 25, 2015
Reading for this lecture: Section IV.5,Sections V.1-V.2 Reading for upcoming lecture: Chapter
V
Debye model (continued)
We are now set to calculate all thermodynamic properties of a Debye crystal. Let us, however,
simply f
NE 334 Lecture 24, July 2, 2014
Reading for this lecture and upcoming one: Chapter V
Symmetry Requirements for Homonuclear Diatomics.
In the same way that total (1, 2) for a He atom must be antisymmetric under the exchange of
the two He 1s electrons (beca
NE 334 Lecture 25, July 3 2014
Reading for this lecture and upcoming ones: Chapter V, Chapter VIII
Nuclear spin contribution to properties.
More generally, for a homonuclear diatomic molecule made up of atoms with nuclear spin Ia :
Ia MIa +Ia
pair of nucl
NE 334 Lecture 26, July 10 2014
Reading for this lecture and upcoming ones: Chapter VIII
Statistical Mechanical Expression for KP
General equilibrium reaction
A A + B B
C C + D D ,
Setting the Stage.
Gibbs energy for a pure gas: start from canonical parti
NE 334 Lecture 23, July 2 2014
Reading for this lecture and upcoming one: Chapter V
Reminder:
Molecules: = trans + int
translations and internal molecular motions are considered to be independent of one another
z(T, V ) = ztrans (V, T )zrot (T )
additive
NE 334 Lecture 22, June 26 2014
Reading for this lecture and upcoming lecture: Chapter V
Introduce two further approximations:
1) Replace V (R) by parabola tted to minimum
2) Separation of vibrational and rotational motions: assume that diatomic has xed i
NE 334 Lecture 18 and, June 11, 2014
Reading for this lecture: Section IV.5 Next lecture: bring the old midterms and pick questions.
Monatomic Solids
A. The Simple Harmonic Oscillator (SHO).
Energy levels:
1
= ( + 2 )hosc ,
= 0, 1, 2,
The canonical part