Good luck with all your final exams and a Merry
Christmas!
Extra
office hours (beyond my normal office hours): Friday, December
13th: 4 pm to 7 pm and Monday, December 16th: 4 pm to
7 pm You should pick up any unclaimedassignments
and tests. Diego's office hours: Tues, Dec 10. 4:30 -
5:30 pm Thurs Dec. 12 4:30 - 5:30 pmMon, Dec 16:
4:00 - 6:30 pm
Click here for your term
marks (except for the last assignment). They are displayed in
ascending order of the last four digits of your student ID number. Please check your marks and report any discrepancy to me before
the semester ends. ------------------------------------------------------------------------------------------------------------------------------
Here are some links where you can find a discussion
about the SO(4) symmetry of the hydrogen atom that V. Fock
discovered:
einstein.drexel.edu/~bob/LieGroups/LG_14.pdf
hep.uchicago.edu/~rosner/p342/projs/weinberg.pdf
math.umn.edu/~karl0163/docs/fock.pdf
math.ucr.edu/home/baez/classical/runge_pro.pdf
Very recently, a "quantum
microscope" was able to produce a true image
(not simulated) of some orbitals of the hydrogen atom: http://physics.aps.org/articles/v6/58
Read Chapter 19, 22 and 20.
Click
here
for some short
answers (not
complete
solutions)
to
Assignment #5
Assignment #5
was due on
Thursday,
November 21st,
2013 at the
beginning of
the lecture
period in
class. Please
click here
for the cover
sheet which
you attach
(with your
name and
student id #
on it) to your
assignment. Click
here
for short
answers to
Test #2
(these are
just answers,
you are
supposed to
show the
appropriate
steps in the
Test) Test
#2 was held on Tuesday,
November 12th from 19:00 to
20:00 in T29, Room 101 (A to
P) and 105 (Q to Z) The
test covered the material
from Chapters 17, 18, 20 and
21. Click
here
for short
answers (not
complete
solutions)
to
Assignment #4 Assignment #4 was
due on
Thursday,
November 7th,
2013 at the
beginning of
the lecture
period in
class.
Read Chapter 21
Read Chapter 18 (until things sink in!) and Chapter 21.
Click here
for my notes on some properties of Bessel that we are using
(notes from last year). Click
here
for a table of
basic facts
about
orthogonal
polynomials
that Diego
compiled.
Click
here
for my notes
on
Legendre,
here
for Hermite
and here for
Laguerre
polynomials
(notes from
last year).
Click
here
for short
answers (not
complete
solutions)
to
Assignment #3 Assignment
#3
was due on
Thursday,
October 24th,
2013 at the
beginning of
the lecture
period in
class.
Please finish reading Chapter 18 and start reading Chapter
20 (you can omit 20.6 and 20.7) and the first three sections of
Chapter 21 Please
finish reading Chapter 18 this week.
Click
here
for short
answers to
Test #1
(these are
just answers,
you are
supposed to
show all the
appropriate
steps in the
Test) Test #1 was
held on Tuesday, October 15th
(the day after Thanksgiving!) from 19:00
to 20:00 in T29, Room 101 (A to P)
and 105 (Q to Z). The
test covered the material from Chapters 8, 9, 12, 13, 14, 15 and
16 and what I did in my lectures up to and including
the lecture on Tuesday, October 8th.
Click here
for my notes on Chapter 16 and here
for my notes on Chapter 17 (both from last year).
Please finish reading Chapter 16 and read Chapter 17 and 18 for this
week.
Click here
to listen to some "experimental music" made with an interesting
circular drum.
Click here
for my answers (not complete solutions!) to
Assignment #2 Assignment #2 was
due on
Thursday,
October 3rd,
2013 at the
beginning of
the lecture
period in
class.
(Note: I simplified question #2)
Please finish reading Chapter 14 and 15 and read Chapter 16 for this
week. Click
here
for a full-blown course on Fourier transforms at Stanford (if
you watch the videos you will notice that they have better
blackboards!)
Click here
for my lecture about ODE's (from last year).
Click here
for my short answers (not complete solutions!)
to Assignment #1.
Click here for my
lecture about Laplace transforms (from last year).
Please finish reading Chapter 13 and read Chapter 14 and 15
for this week.
I will finish Chapter 13 on Monday and your TA, Diego Ayala, will be
lecturing for me on Tuesday, this week.
I will be back on Thursday and will give a very quick review of
ODE's (Chapters 14 and 15) that you need to know for this course Click here
for my synopsis of Fourier Series and here
for Fourier Transforms. Please read it carefully, in conjunction
with Chapter 12 and 13.1 in the textbook, to prepare yourself
for the lectures this week. Assignment #1
was due on Thursday, September 19th, 2013 at the beginning
of the lecture period in class. Please hand it to me
(Min-Oo)
Finish reading Chapter 9 and do the assignment!
Click
here for my synopsis of
basic linear algebra, that you need to know. Please read it
carefully, in conjunction with Chapter 8 in the textbook, to
prepare yourself for the next two lectures!
The first tutorial
will be on Wednesday, September 11th at 9:30 in HH/320. Diego
Ayala will be your TA.
The first lecture was at 09:30 on Thursday, September
5th, 2013 in Hamilton Hall Room 109
Click
here for a detailed syllabus of the course (a
week by week description, which will be regularly
updated) and for homework problems. Students are responsible for
reading the relevant material from the textbook
and/or the reference books and/or any other resources
(freely available on the internet) and
also for working out most of the
exercises in the bookon their own
(known as experiential learning) in
preparation for the lectures.
Topics to be covered : Linear algebra and eigenvalue problems, normal
modes, Fourier series, Fourier transforms, Laplace transforms,
ordinary differential equations, Sturm-Liouville problems,
special functions of Mathematics Physics (Legendre, Hermite,
Laguerre, Chebyshev, Gamma, Bessel, etc.), spherical harmonics,
partial differential equations of Mathematical Physics (Laplace,
Poisson, Heat, Wave, Schrödinger etc.), separation of variables,
Green's function,
quantum harmonic oscillator, hydrogen atom.
Required Textbook:
"Mathematical Methods for Physics and Engineering",
3rd edition, by K.F. Riley, M.P. Hobson & S.J. Bence,
published by Cambridge University Press (same as last year!)
Other introductory textbooks:
"Mathematical Methods for Scientists and Engineers" by Donald A.
McQuarrie (this was the textbook a couple of years ago)
"Mathematical Methods in the Physical Sciences" by Mary L.
Boas (actually I've never seen this book, but some people
say it's good!)
"Mathematical Methods for Physicists" by George B. Arfken and Hans
J. Weber (a classic, although I've never read it either!)
"Advanced Engineering Mathematics" by Erwin Kreyszig (another
commonly used textbook)
Course Objective:
We will cover the material from Chapters 8(review of linear
algebra), 9, 12, 13, 14(review of basic ODE), 15, 16. 17, 18, 20,
21, 19 and selected sections from Chapters 22 and 23 of the
prescribed text book.
Students are responsible for reading
the relevant material from the textbook and/or the
reference books and/or any other resources (freely
available on the internet) and
also for working out most of the exercises in the
bookon their own (that's
known as experiential learning) in preparation for the
lectures
For a
weekly update on what is covered in the course see the course syllabus
Course Work:
1. Tutorials: There will be a
weekly tutorial.
2. Assignments: There will be five
written assignments to be handed in on the due dates that will
be announced in class. Late assignments will not be graded.
Assignment #1due: Thursday, September 19th at the beginning of
the lecture period in class.Click here for short answers
Assignment #2 due: Thursday, October
3rd at the beginning of the lecture period in
class. Click
here for short answers
Assignment #3 due: Thursday,
October 24th at the beginning of the
lecture period in class.
Click
here for short
answers
Assignment #4 due: Thursday,
November 7th at
the beginning of the lecture period in
class
Click
here for short
answers
Assignment #5 due: Thursday,
November 21st at the
beginning of the lecture period in
class Click here for short
answers
3. Homework:In addition to the assignments, there will be extra
homework problems, which are not graded, Students should discuss
these problems during the tutorial. Click here for Homework..
4. Tests:There will be two
one-hour tests. The exact dates and locations will be announced in
class and this course home page.
TEST #1Tuesday, October15th ,
19:00 - 20:00 in T29, Rooms 101 and 105 Click
here
for short
answers
TEST #2 Tuesday,
November 12th , 19:00 - 20:00 in T29, Rooms 101 and 105 Click
here
for short
answers
5.
Final Examination: This will be a 3-hour final examination,
scheduled by the Registrar’s office during the exam period in
December.
Grading Scheme
Assignments:
25% (= 5 x 5%)
Tests:
30% (= 2 x 15%)
Final
Exam: 45%
Academic Dishonesty:
You are expected to exhibit honesty
and use ethical behaviour in all aspects of the learning process.
Academic credentials you earn are rooted in principles of honesty
and academic integrity. Academic dishonesty is to knowingly act or
fail to act in a way that results or could result in unearned
academic credit or advantage. This behaviour can result in serious
consequences, e.g. the grade of zero on an assignment, loss of
credit with a notation on the transcript (notation reads: “Grade
of F assigned for academic dishonesty”), and/or suspension or
expulsion from the university. It is your responsibility to
understand what constitutes academic dishonesty. For information
on the various types of academic dishonesty please refer to the
Academic Integrity Policy, located at http://www.mcmaster.ca/academicintegrity
The following illustrates only three
forms of academic dishonesty:
1. Plagiarism,
e.g. the submission of work that is not one’s own or for which
other credit has been
obtained.
2. Improper
collaboration
in group work.
3. Copying
or
using unauthorized aids in tests and examinations.
When using the MSAF, also report your
absence to me (the course instructor M. Min-Oo) within
2 working days by email (minoo@mcmaster.ca) and
contact me in person to learn what relief may be
granted for the work you have missed, and relevant
details such as revised deadlines, or time and
location of a make-up exam. Please note that the MSAF
may not be used for term work worth 30% or more, nor
can it be used for the final examination. Please refer
to http://registrar.mcmaster.ca/CALENDAR/2013-14/pg2246.html
for the exact rules
Calculators:
Only the
standard McMaster calculator Casio fx 991MS+ can be used for
the tests and the final examination.
Important
Notice:
The
instructor
and the university reserve the right to modify or revise
information contained in this course during the term. The
university may change the dates and deadlines for any or all
courses in extreme circumstances. If either type of
modification or revision becomes necessary, reasonable notice
and communication with the students will be given with
explanation and the opportunity to comment on changes. It is
the responsibility of the student to check their McMaster
email and course websites weekly during the term and to note
any changes.
Tentative schedule of Topics
(the numbers are
chapters and sections from the text book)
Week 1 (05/09 to
06/09): Chapter 8 (review of linear algebra)
Week 2 (09/09 to 13/09):Chapter 8 (review of linear
algebra), Chapter 9 (normal modes)
Week 3 (16/09 to
20/09): Chapter 12 (review of Fourier
series), Chapter
13.1 (Fourier Transforms)
Week 4 (23/09 to 27/09): Chapter 13.2 (Laplace
Transforms), Chapters 14 and 15 (Review of Ordinary
Differential Equations)
Week 5 (30/09 to
04/10): Chapter
16 (Power Series solutions of O.D.E.'s)
Week 6 (07/10 to 11/10):Chapter 17 (Sturm-Liouville Theory
and eigenfunction methods), 18.1,
18.2, 18.3 (Legendre polynomials, Legendre functions,
spherical harmonics)