Syllabus (updated 03/28/2003)
Physics 104C, Mathematical Physics (CRN 46057), Spring 2003
Time: Tu Th 10:30-11:50; Place: 130 Phys/Geo
Teacher: Professor Ling-Lie Chau
(For info about the teacher, go to http://honors.ucdavis.edu/chau/chau01/
and click the link “About the teacher Ling-Lie Chau”. If interested, also
look up “Dr. Chau’s Three Principles for Enhancing Performances and Living,”
at http://honors.ucdavis.edu/chau/chau02/, in the category of Directives.
These are the two websites of Davis Honors Challenge taught by Professor Chau.
You might find other interesting info in these two websites.)
Office: 431 Phys/Geo; phone: 752-2715; e-mail:chau@physics.ucdavis.edu
Office hours: 431 Phys/Geo; Tu Th 11:50pm-12:20pm-extendable; (By-request-only
Wed 1:10pm-extendable); or by appointment.
Reader: Mr. Matt Sudano
Phone: 530-297-7105; e-mail: mcsudano@ucdavis.edu
Office hours: Roessler 158, Mon 5:00-5:30-extendable; or by appointment.
Grades:
Participation
10%
Homework
34%
Midterm 1 (1hr, Thu, 5/5, 10:30-11:30) 14%
Midterm 2 (1hr, Thu, 5/22, 10:30-11:30) 14%
Final (2hrs, Tue, 6/10, 8:00-10:00)
28%
Prerequisite for the course is Professor Chau’s 104A, Fall 2002, to which
Math 22A (Linear Algebra) and Math 22B (Differential Equations) were prerequisites.
Course outline:
* Functions of One Complex Variable:
Cauchy-Riemann conditions; Cauchy’s integral theorem; Cauchy’s integral
formula; Laurent series (of which Taylor series is a special case); Residue
theorem; Dispersion relation; etc.
* Evaluation of Integrals:
Gaussian integral; Doing integrations by making use of techniques learned
in functions of one complex variable; Steepest-descent and stationary-phase
approximations; Central limit theorem and its applications in statistical
studies; etc.
* Topics in Vector Spaces:
Advanced topics (extending what was taught in Professor Chau’s 104A, Fall
2002): Ordinary and partial differential equations (and their unified understanding
with matrix equations), and a thorough understanding of the hydrogen atom,
etc.
* Calculus of Variation
* The importance and goals of the course: The importance of the course lies
in the training of analytic thinking as well as the more advanced applications
to basic physics. The goal of the course is to learn these listed topics and
their applications and to sharpen the analytic thinking ability of students.
After learning the material of this course together with that learned in 104A
taught by Professor Chau in Fall 2002, students will not need to take any
math-method courses like 204A,B wherever they go for graduate studies. More
importantly, these materials and the experience of learning them will provide
students with the rigorous thinking and methodology that will be valued by
industry, the financial world and government, where many of the students
will go to work after graduation.
[Those who do well in my 104C) will be welcome to take Professor Chau’s
Phy223B, Group Theory, in the Fall Quarter of 2004. It is a must-course
for all physicists as well as to EOSE engineers. As the way she has structured
it (using the textbook material she is writing "Group Theory for Quantum Mechanics
and Field Theories"), it provides a framework to describe all important interactions
in physics and gives a unifying view of all the fundamental courses in physics:
electromagnetism, gravity and quantum mechanics. The main topics covered
will be: the translation, rotation, Lorentz, and the inhomogeneous Lorentz
(i.e. translation plus the Lorentz, which is also called the homogeneous
Lorentz) groups. Students will learn precisely what photons, electrons,
protons, as well as gravitons are, and, if time allows, how they interact.
After taking her 104C and 223B, students will be at the current second-year
graduate level in math-phys, which will give students an advantage edge whatever
students plan to do after graduation.]
* This is a lecture-based (-with-textbook-material-available) course. Lectures
are self-contained and sufficient for doing homework and taking the exams
of the course. Exams are based upon lectures and homework materials. (Homework
and exams are closed related to lectures. So every lecture can be viewed as
a homework and exam solving session. Full concentration in listening to lecture
and taking lecture notes will save you time in doing homework and in preparing
for exams.) Therefore, it is essential that students attend the lectures
and take good notes, then review and restructure their own derivation, outline
and conclusion. Students are encouraged to form study groups for reviewing
lectures and discussing them. Professor Chau's lectures will be based upon,
but not following exactly, her textbook material “Mathematics for the Physical
Sciences”. It is on 2-hour reserve in Shields Library, along with other
reserve books listed below. (Students of Phy104C Spring2003, and only
they, are allowed to copy Chau’s book material for their personal use for
the course. Students need to observe the copyright of the material.) If students
have time, it will be beneficial to read these materials reserved in the
library. However, it is not necessary. Most (if not all) A+ and A students
of Professor Chau’s previous 104A and 104C classes totally based upon her
lectures. So have confidence in this method of teaching and learning. Be
conscientious and studious in lecture attending, notes taking and studying.
This method saves students time and money. [It takes away textbooks as “crutches
and excuses ” for the students to not pay full attention to the lectures or
even miss classes (and then not to read textbooks systematically) and for
the teacher to not be exact and precise in lecturing. However, the textbook
material is available. Make a copy if some students must have it.]
* If some students do find time to read Professor Chau’s book material,
she would welcome them to ask questions and to make comments, and to let
her know about typos. Those who make important original contributions will
be acknowledged when the book is published and those who help make important
improvements (including pointing out typos) will be rewarded with a free copy
of the chapter, after the end of the course.
* If a student has to miss a class, which should by all means be avoided,
it is the student’s responsibility to make arrangements with other students
to obtain the lecture notes. However, one should remember to return favors.
Collaboration works only when there is give and take. Students are encouraged
to help other fellow students. (One of the best ways to learn is to teach
and help others.)
* Participation will take into consideration attendance and various kinds
of participation (which are open for your creative implementation). Attendance
will be recorded for each class. (The attendance sheet will be passed around
to be signed in the beginning of each class. Any students who will need to
leave early should mark on it the time they will leave. Students who come
to class 5 minutes after the class starting time can sign the attendance sheet
after the class and indicate arrival time.) Besides during class and office
hours, students are most welcome to ask questions by e-mail. E-mail provides
a very efficient way of communication. We should all make the best use of
it. Professor Chau will respond as soon as possible. Those e-mail communications
that are relevant and helpful to the whole class will be sent to the whole
class. (Students should always specify if they want any of their communications
to be kept confidential.) Check e-mail frequently, at least twice a day.
* Bonus points are offered in homework, exams and for active participations
(in class, in office hours and by e-mails) and to homework chosen as class
solution. Bonus points will be counted toward the total score and also be
listed separately as an honor and distinction to be counted toward Participation.
All bonus points and other participation records will be used toward deciding
A+ and grade up-lifting.
* Grading will be decided both “absolutely” and “relatively”: There
is a certain absolute standard of the course, above which one passes and below
which one fails. Also there is certain absolute standard, above which one
gets an A+. Therefore, in principle all of you can get an A or A+. (This actually
happened to my 104C class in the Spring2002 Quarter. Hopefully it will happen
to this class.) The grading will also make sure that the better performing
students obtain better grades, so the grading is also “relative.”
Rules:
* Students need to put in the total 12 hours/week for 104C as required by
the "Carnegie unit" rule listed in the UCD Catalogue. Students are advised
to spend the 12 hours/week as follows:
** Attending lectures:
3 hours (2x80mins class plus 2x10mins overhead time)
** Studying and reorganizing
notes: 3 hours (2x1.5 hours)
** Doing homework: 6 hours.
If students do all of the above, it will be impossible for students to not
obtain a good grade. Not only is it the most effective way, it is the most
enjoyable way. The methodology will serve the students well no matter what
they endeavor to do.
* Homework is due 6pm, every Wednesday in a box in front of Professor Chau’s
office, 431 Physics/Geology. No late homework will be accepted, except for,
only for, the student’s own dire health-related emergency. In that case, the
student must obtain an official letter from a verifiable M.D. who certifies
that the student’s health conditions (no specifics needed) are such that the
student absolutely cannot do the homework before the due time. Whether a
late homework is accepted will be determined on a case-by-case basis. A percentage
of the late homework score may be deducted. The precise percentage of the
deduction will also be decided on a case-by-case basis. Also understand that
once the solution is out, no late homework can be considered, period. (Generally,
the homework solutions are delivered, with comments and scores, to Shields
Reserve sometime Monday evening and they become available for students to
read sometime Tuesday morning, both in hard copy and on the web.) Students
should start homework as early as possible. The human brain has the amazing
capability of solving problems without the person’s conscious awareness (but
one needs first to put in the problem clearly). So, input the homework
problem early and take advantage of this capability of the brain.
* Graded homework will be given back to students at the end of the next
Tuesday class.
* Solutions to the homework will be chosen from students’ solutions. Bonus
points will be given to those whose solutions are chosen.
* Exams are “closed book." Paper will be provided and only those can be
used. Therefore, for exams, all students have to bring are their favorite
writing utensils and a well-prepared, clear mind (for which sufficient sleep
is absolutely essential). Only, and only, student’s own dire health-related
emergency can excuse the student to miss the exams. In that case, the student
must obtain an official letter from a verifiable M.D. who certifies that
the student’s health conditions (no specifics needed) are such that the student
absolutely cannot come to take the exam. Whether a make-up exam is granted
will be determined on a case-by-case basis. A percentage of the make-up exam
score may be deducted. The precise percentage of the deduction will also
be decided on a case-by-case basis.
* Any corrections or rebuttals to graded homework must be done in writing
and given with the full graded homework to Professor Chau before the next
Tuesday class. They will be answered in writing. The same procedure applies
to graded exams, except that the deadlines for rebuttal will be specified
at the exams.
* Students are not allowed to look at homework, exams or their solutions
from past Physics 104C or 204A,B.
Textbook, 2-hr-reserved at Shields Library:
* L.-L. Chau: Mathematics for the Physical Sciences, draft version,
to be published by University Science Books. (Students of 104C Spring2003,
and only they, are allowed to copy Chau’s book material for their personal
use for this course. Students need to observe the copyright of the material.)
Reference books, 2-hr-reserved at Shields Library:
* R.V. Churchill and J. Ward: Complex Variables and Applications
, McGraw-Hill, c1996;
* G.B. Arfken and H. Weber: Mathematical Methods for Physicists,
Academic Press;
* J. Mathews and R.L. Walker: Mathematical Methods of Physics; W.
A. Benjamin;
* B. Colman and D. R. Hill: Introductory Linear Algebra with Applications
, 7th edition, Prentice Hall, (Math 22A level);
* W.E. Boyce and R.C. DiPrima: Elementary Differential Equations and
Boundary Value Problems, 7th edition, John Wiley & Sons, (Math 22B
level).
* Handbook of Mathematical Functions with Formulas, Graphs and Mathematical
Tables, Editors M. Abramowitz and I.A. Stegun, National Bureau of Standards.
Useful tables and encyclopedic:
* Tables of Integrals and Other Mathematical Data, H.B. Dwight,Macmillan;
* Tables of Integrals, Series and Products, I.S. Gradshteyn and L.M.Ryzhik,
Academic Press;
* Handbook of Mathematical Functions, M. Abramowitz and I.A. Stegun,
Applied Mathematics Series, vol. 55, 1964 (Washington: National Bureau of
Standards; reprinted by Cover Publications, New York);
* Encyclopedic Dictionary of Mathematics, Mathematical Society of
Japan.