Course Organization


Overview

This a one semester graduate course presenting some of the mathematics which will be used during the first and second year of graduate physics courses. First, we will study tensor analysis on manifolds, employing a notation which is common in general relativity, electrodynamics, and quantum field theory. Then we will study functions of a complex variable and present several applications. With these preliminaries we will give a concise introduction to some of the most common partial differential equations of physics. Through this study, we will analyze ordinary differential equations, focussing on linear differential operators and the analytic structure of their solutions. Finally, if time permits we will conclude the course with a short introduction to group theory.


The structure of the course is:

  1. Vectors and tensors and covariance:
  2. Coordinate Systems, covariant derivatives and differential operators
  3. Complex Analysis General Theory.
    • Power Series, the Cauchy Riemann equations, Cauchy theorem and the laurent expansion. Analytic continuation and singular points
  4. Application of Complex Analysis.
    • Analysis of oscillations. Fourier series and transform. Response functions.
    • Dispersion relations
    • The Gamma functions.
    • Other integral transforms, Fourier-Laplace, Hankel, and Mellon
  5. Differential Equations.
    • Types of Partial Differential Equations (e.g. boundary value vs. eigen-values vs. eigenvalue etc) and separation of variables
    • Greens functions and greens theorem
  6. Linear Differential Operators. Sturm Liouville Theory
    • Some "special" functions and their classification by singularities.
  7. Basic elements of group theory.
    • Finite groups and oscillations.
    • Representations of finite groups.
    • SU(2) and its representations.

Lecture Instructor:

Assoc. Professor, Derek Teaney: derek.teaney stonybrook.edu

Derek Teaney
Department of Physics & Astronomy
PO Box 3800
Stony Brook, NY 11764-3800

Office: Physics C-135

(631)632-4489, Fax 9718

Teaching Assistant, Yanliang Shi: yanliang.shi stonybrook.edu


Schedules

Class Meetings

The course consists of three lecture hours:

  • Lecture Hours: MWF 10:00-10:53 in Harriman Hall 112

Office Hours

Please feel free to contact me at anytime. My official office hours are,

  • C-135, TBD

Scheduled Final Exam

The final exam is on Tuesday, December 19th from 2:15--5:00 p.m in Harriman Hall 112. In all likelihood there will only be a takehome final exam, but you should keep this time period free in the (unlikely) event that I decide to give an exam.


Grade Determination

The grading will be based 80% on homework. A take home final exam will be given which is worth 20% of your grade. I reserve the right to change this as the course progresses within reasonable limits. For example, part of your grade may be based on class participation. Nevertheless, my intent of course is to follow these guidelines.

Homework is a major part of this course. Homeworks will be assigned weekly, and will be collected at the start of class . Homework handed in within a day after the due date/time will by given a 5% penalty. After this, late homeworks will be penalized at 10% per day.


The Book and Resources

A short typed summary of the formulas will be provided.

The recommended book for the course is

  • Mathematical Methods for Physicists by Arfken, Weber and Harris

You may not need the book. Lecture notes and a short typed summary (slightly more than a formula sheet) will be provided. Examples of the lecture notes and typed notes for the electrodynamics course are given here. I think that someone who attends class diligently and uses the notes will not need the book.


Some other books which I used when preparing the course are:

  • As an undergraduate, I benefited from A Brief on Tensor Analysis , by James G. Simmonds.
  • For complex analysis I have benefited from Serge Lang's book, and from Konrad Knopp's, Theory of Functions and most importantly the Problem Book in the Theory of Functions
  • Another good account, see Brown and Churchill , Complex Variables and Applications .
  • I have found: Methods of Theoretical Physics, Part I and II by Morse and Freshbach an invaluable, enjoyable, and surprisingly readable reference over the years.
  • For differential equations, and a deeper way to understand mathematical analysis in general, see the classic Bender and Orzag Advanced Mathematical Methods for Scientists and Engineers: Asymptotic Methods and Perturbation Theory .


Other Items

E-mail

Email to your University email account is an important way of communicating with you for this course. For most students the email address is firstname.lastname@stonybrook.edu. It is your responsibility to read your email received at this account.

For instructions about how to verify your University email address see this: http://it.stonybrook.edu/help/kb/checking-or-changing-your-mail-forwarding-address-in-the-epo. You can set up email forwarding using instructions here: http://it.stonybrook.edu/help/kb/setting-up-mail-forwarding-in-google-mail. If you choose to forward your University email to another account, we are not responsible for any undeliverable messages.


Disability Support Services (DSS):

If you have a physical, psychological, medical or learning disability that may impact your course work, please contact Disability Support Services, ECC (Educational Communications Center) Building, room 128, (631) 632-6748. They will determine with you what accommodations, if any, are necessary and appropriate. All information and documentation is confidential.


Academic Integrity:

Each student must pursue his or her academic goals honestly and be personally accountable for all submitted work. Representing another person's work as your own is always wrong. Faculty are required to report any suspected instances of academic dishonesty to the Academic Judiciary. Faculty in the Health Sciences Center (School of Health Technology & Management, Nursing, Social Welfare, Dental Medicine) and School of Medicine are required to follow their school-specific procedures. For more comprehensive information on academic integrity, including categories of academic dishonesty, please refer to the academic judiciary website at http://www.stonybrook.edu/commcms/academic_integrity/index.html


Critical Incident Management Statement:

Stony Brook University expects students to respect the rights, privileges, and property of other people. Faculty are required to report to the Office of Judicial Affairs any disruptive behavior that interrupts their ability to teach, compromises the safety of the learning environment, or inhibits students' ability to learn. Faculty in the HSC Schools and the School of Medicine are required to follow their school-specific procedures.


Assessment of Student Performance:

  • Homework assignments, examinations, and term papers should be evaluated and returned promptly. Written comments, explaining the instructor's criteria for evaluation and giving suggestions for improvement, should be provided.
  • Instructors are responsible for providing students with appropriate and timely notification about their academic performance in a course. An examination or other assessment measure should be administered, graded, and returned to students before the end of the ninth week of classes.
  • Examinations and term papers submitted at the end of the term should be graded and either returned to students or retained for one semester.
  • Any change to the course grading policy during the semester must be announced and made available to all students enrolled in the course. Assigning additional work to individual students who wish to improve their grades, during or after the semester, is prohibited.
  • Instructors must observe the Final Examination Schedule available at http://www.stonybrook.edu/registrar. Instructors of courses taught on the semester schedule may only give a unit exam in class during the last week of the semester if a final examination is also given during the Final Examination Period.
  • Instructors must observe state laws, federal laws, and University policies regarding accommodations as noted in the Bulletin (e.g., student participation in University-sponsored activities or equivalent opportunity/religious absences). Accommodations such as make-up exams, assignments, or other coursework that fall outside of the purview of these laws and policies are at the discretion of the instructor.

Professional Conduct and Interaction with Students:

  • Instructors must report all suspected occurrences of academic dishonesty to the Academic Judiciary Committee (for classes in the College of Arts and Sciences, College of Business, School of Marine and Atmospheric Sciences, and School of Journalism) or the Committee on Academic Standing and Appeals (for classes in the College of Engineering and Applied Sciences).
  • Instructors should always be aware that in teaching and advising they represent the University. They are bound by the University's sexual harassment policies. Instructors are also bound by University policies that prohibit any consensual relationships with students that might compromise the objectivity and integrity of the teacher-student relationship. Examples include romantic, sexual, or financial relationships.
  • Instructors should strive to maintain the privacy and confidentiality of students' examinations, homework, and final grades.
  • In dealing with students, instructors should be polite, helpful, and fair. They should take into account the wide range of cultural factors and physical challenges that can affect learning, and should attempt to help students overcome any disadvantages.