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 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, 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;
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:
Office hours: Roessler 158, Mon 5:00-5:30-extendable; or by appointment.

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.”

* 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.