PC4230 Mathematical Methods in Physics

Semester I, 1998/99

Level: Honours

Prerequisite: PC3214 Further Mathematical Methods in Physics

Timetable:

• Lectures: Monday and Tuesday, 10-11a.m. (Physics Resource Room)
• Tutorials: Monday 1-2p.m.; Friday 12-1p.m. (Physics Resource Room)

Synopsis

Textbooks:

Two good general references are:

• B. Schutz, Geometrical Methods of Mathematical Physics Cambridge U.P. (1980)
• B. Felsager, Geometry, Particles and Fields Springer-Verlag (1998)

Other books that you may want to check out:

• R.H. Wasserman, Tensors and Manifolds Oxford U.P. (1992) [QC 20.7 Cal.W]
• W.L. Burke, Applied Differential Geometry Cambridge U.P. (1985)
• H. Flanders, Differential Forms Academic Press (1963)
• S.H. Weintraub, Differential Forms: A Complement to Vector Calculus Academic Press (1997) [QA 381 Wei]

Tutorials:

• Exercise 1 [dvi,ps,pdf]
• Exercise 2 [dvi,ps,pdf]
• Exercise 3 [dvi,ps,pdf]
• Exercise 4 [dvi,ps,pdf]
  

Some advice on downloading the files

Miscellaneous:

• A lesson on tensors (in special relativity) by Peter Dunsby.
• The advantages of using differential forms in electromagnetic theory (including an IEEE paper titled Teaching electromagnetic field theory using differential forms).
• Lectures on integration of several variables (using differential forms) by Michael Adler. [Before you send all 193 pages to the printer, preview it to see if it would be useful to you. In the author's own words, these notes were written for mechanical, civil and environmental engineers with a "Just Gimme the Facts" attitude.]
• Are there pictorial examples that distinguish covariant and contravariant vectors? by Bernard Jancewicz.
• VRML Gallery of Electromagnetism by Rob Salgado. Visualise p-form fields in electromagnetism using virtual reality!

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