PHY1540S - MATHEMATICAL METHODS IN PHYSICS

First meeting: January 9

The table below provides useful information about the instructor.

*Fixed office hours may not be convenient for some of you. So do feel welcome to drop by at any time, any weekday, until 18h. If I am in my office and not otherwise busy with other people, you will have my undivided attention. You can also schedule an appointment by email.

**Should be used to communicate with the instructor about all course-related matters.
Note: email links are not activated in a (perhaps futile) attempt to defeat address-collection software.

Self-contained Lecture Notes will be posted further down on this web page; they should be viewed as the primary source for this course.

Please be aware that these notes are subject to modification at any time! You can always peek ahead by looking at last year's notes (also posted below). Also, at the beginning of each week the notes for that week will be posted. Every week or so the single-lecture files will be concatenated and added to a cumulative file with fully hyperlinked references to equations, sections, etc. This cumulative file will contain the definitive version of the notes for this year; only mistakes will be corrected.

The “official” textbook covering much, but not all, of the material is:

Mathematics of Classical and Quantum Physics by F. W. Byron and R. W. Fuller (Dover, 1992).

Other more or less general treatments:

Methods of Theoretical Physics, P. M. Morse and H. Feshbach (McGraw-Hill, 1955; 2 vol)
Mathematical Methods for Physicists, G. B. Arfken and H. Weber (Academic Press, 2001)
Mathematical Physics, S. Hassani (Springer, 2006)
Mathematical Analysis of Physical Problems, P. R. Wallace (Dover, 1984)
Methods of Mathematical Physics, H. Jeffreys and B. S. Jeffreys (Cambridge University Press, 1946)
Methods of Mathematical Physics, R. Courant and D. Hilbert (Wiley, 1989; 2 vol.)

Group Theory:

Lie Groups, Lie Algebras, and Some of Their Applications (Paperback), R. Gilmore (Dover, 2006)

Lie Groups, Physics, and Geometry: An Introduction for Physicists, Engineers and Chemists (Hardcover), R. Gilmore (Cambridge University Press, 2008)

Symmetry in Physics, J. P. Elliott and P. G. Dawber (Macmillan, 1979)

Matrices:

Matrix Theory, J. N. Franklin (Dover, 2000)
Basic Theorems in Matrix Theory, M. Marcus (NBS, 1960)

Tensors and Manifolds:

The Geometry of Physics - An Introduction (Paperback), T. Frankel, (Cambridge University Press, 2nd ed., 2004)

Gravitation (Paperback), C. Misner, K. Thorne, and J. Wheeler (Freeman, 1973) (although applied to Relativity, contains a very readable introduction to the modern approach to tensors)

Analysis, Manifolds and Physics Parts I and II, Y. Choquet-Bruhat, C. DeWitt-Morette (North-Holland) (a gold standard, but with a steep learning curve)

Differential Equations:

Ordinary Differential Equations, G. Birkhoff and G.-C. Rota, (4^th ed.,Wiley, 1991)

Green's Functions and Boundary Value Problems, I. Stakgold and M. Holst, (3^rd ed.,Wiley, 2011)

Other useful references:

Table of Integrals, Series, and Products, I. S. Gradshteyn and I. M. Ryzhik (Academic Press, 2000)
Mathematical Handbook for Scientists and Engineers, G. A. Korn and T. M. Korn (Dover, 2000)
Handbook of Mathematical Functions, M. Abramowitz and I. A. Stegun (Dover, 1969)

Evaluation of students will be based on the following:

1. Three assignments, each worth 10% of the course mark.

   Unless otherwise specified, assignments should be submitted by email to the above address by 17h on the due date. Some tolerance will be shown toward first-time late submissions when delays do not exceed one hour.

   Lateness penalty: unless exceptional circumstances arise and an extension is granted to the whole class, a penalty of 5% of the mark earned will be levied as soon as a submission is deemed late, and will be increased by 5% for one extra 24-hour period that it is late until the following Friday at 17h, after which no paper will be accepted.

   You are welcome to use Maple, Mathematica, WolframAlpha, or open-source symbolic manipulation software such as SageMath, as you see fit. If you do, your worksheet for the problem must be submitted with your paper.

   A friendly word of caution about the assignments. By all means discuss them with colleagues and with me if you feel stuck. At U of T, however, plagiarising from the web or anywhere/anybody else is an academic offence that you definitely do not want on your record. You may wish to (re)acquaint yourself with the Code of Academic Behaviour, or visit the Academic Integrity website. Random checks will be conducted to detect plagiarism.

2. A two-hour test around Reading Week, worth 30% of the course mark.

3. A final three-hour examination with an oral component, worth 40% of the course mark. This exam will be held at the end of April.

   The exam will consist of an initial two-hour period during which the candidate will work on a set of questions, after which we (the candidate and I) shall discuss their attempts for a maximum of ~ 55 minutes.

   All questions should be attempted during the writing period. This is more important than completely finishing each and every question, as there will be some time during the oral part to do this.

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The complete, hyperlinked, 2019-20 notes for the earlier modular version of the course can be downloaded in PDF format.

The complete, hyperlinked notes for 2023 are available.