Syllabus (updated 10/15/2003)
    
Physics 104A, Introductory Methods of Mathmatical Physics, Fall 2003           
Time:   Session I (CRN 85765): MWF 9:00-9:50; Place: 130 Phys/Geo
    Session II (CRN 91998): MWF 10:00-10:50; Place: 130 Phys/Geo

Teacher: Professor Ling-Lie Chau
Office: 431 Phys/Geo; phone: 752-2715; e-mail: chau@physics.ucdavis.edu
Office hours:  431 Phys/Geo; MWF 11:00-11:30am-extendable; or by appointment.

[For info about the teacher, go to either of the following two web sites and click the link “About the teacher Ling-Lie Chau.” These are the two websites of Davis Honors Challenge taught by Professor Chau. You might find other interesting info in these two websites, for example, “Dr. Chau’s Three Principles for Enhancing Performances and Living.”
http://honors.ucdavis.edu/faculty/chau/chau01/index.html
http://honors.ucdavis.edu/faculty/chau/chau02/index.html]

TA: Mr. Deng Zhang
Office: 434 Phys/Geo; e-mail: dzhang@physics.ucdavis.edu
Office hour:  434 Phys/Geo; Mondays, 3:00-3:30pm-extendable; or by appointment.
Readers:  
Mr. Konstantin Chudnovskiy; e-mail: chudnovskiy@ucdavis.edu
Office hour: 158 Roessler; Tuesdays, 1:00-1:30pm-extendable; or by appointment.
Mr. Micah Lundberg; e-mail: mjlundberg@ucdavis.edu
Office hour:  158 Roessler; Wednesdays, 12:00-12:30pm-extendable; or by appointment.

Grades:
Participation                                                         10%
Homework                                                           34%
Midterm 1 (1hr, Friday, 10/24/03 class time)        14%
Midterm 2 (1hr, Friday, 11/14/03 class time)        14%
Final (2hrs, to be announced)                28%

Prerequisites are Math 21A,B,C,D (Calculus), Math 22A (Linear Algebra) and Math 22B (Differential Equations); Physics 9B,C,D.

Course outline:
    * Matrices & Matrix Equations
    * First Order differential Matrix Equations
    * Homogeneous First and Second Order ODE
    * Fourier Transforms, Generalizations and δ-Function
    * Homogeneous First and Second Order PDE
    * Vector Spaces: Freedom of Basis to Matrices & Functions
    * Inhomogeneous Differential Equations, ODE & PDE

Reference books: 2-hr reserved at Shields Library
* L.-L. Chau: Mathematics for the Physical Sciences, draft version, to be published by University Science Books;
* M.L. Boas, Mathematical Methods in the Physical Sciences, 2nd edition, John Wiley & Sons.

Prerequisite Reference Books: 2-hr reserved at Shields Library
* S.K. Stein and A. Barcellos: Calculus and Analytic Geometry, 5th edition, McGraw-Hill (Math 21A,B,C level).
* 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).


Useful tables:
* 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 with Formulas, Graphs and Mathematical Tables, Editors M. Abramowitz and I.A. Stegun, National Bureau of Standards;
* Encyclopedic Dictionary of Mathematics, Mathematical Society of Japan.

* The goals of the course are to
** Teach up-to-date mathematical methods for the physical science;
** Cultivate logical and creative thinking ability and habit;
** Promote self-disciplining and participating skills and spirit.
The knowledge, ability and working habit emphasized and gained in this course will be valued not only in the academic world but also in industry, the financial world and government, where many of the students will go to work 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 closely related to lectures. So every lecture can be viewed as a homework and exam solving session. Full concentration in listening to lectures and taking lecture notes will save students’ 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 will not follow 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 Phy104A Fall2003, 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 exclusively used her lecture material. 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. Those students who must have a textbook may make a copy.]
 
* 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 form 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. Please always start the Subject of your e-mail by “104A,I (or II); ----” and then put a few words to capture the content of your e-mail. These will help filing and making reference to them.

* Bonus points are offered for outstanding homework, exams, active participations (in class, in office hours and by e-mails) and 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 had happened for my 104C and 223B. 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 104A 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 (3x50mins class plus 3x10mins 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 by 5pm for both Sessions I & II, every Wednesday in two boxes, one for each session, in front of the office of the TA, 434 Physics/Geology. Please make sure to drop in the one marked your session, I or II. Please always attach the HW assignment sheets, marked clearly with your names in print, in the front of your HW hand-in.  

* 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 Tuesday evening and they become available for students to read sometime Wednesday 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 Wednesday 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 that can be used. Therefore, for exams, all that 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, a student’s own dire health-related emergency can allow 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 Monday 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 104A,C or 204A,B.


[Those who do well in 104A will be encouraged to take Professor Chau’s 104C, Spring2004. It will cover Complex Analysis (from which students will learn the beautiful and powerful methods for understanding functions and doing integrals), Gaussian integrals (from which students will learn methods for solving problems in statistical mechanic and quantum mechanics), ordinary and partial differential equations (to which students will learn to find solutions in a systematic way using Green functions).

Further, those who do well in 104C will be welcome to take her Phy223B, Group Theory, in the Fall Quarter of 2005. It is a must-course for all physicists as well as for 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 whatever students plan to do after graduation.]