Mathematical Methods in Physics
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Brock Calendar entry:
Techniques of mathematical physics in the context of physically relevant problems. Vector calculus in curvilinear coordinate systems, applied linear algebra, Fourier series and Fourier transforms, special functions of mathematical physics, and least-squares approximations.
Prerequisites: MATH 2P03, 2P08 and 3P06
The goal of this course is to provide students with the mathematical skills necessary to tackle problems in quantum mechanics, electromagnetic theory, statistical and solid state physics at the advanced undergraduate and introductory graduate levels.
There is no required textbook for the course. The main source of information
will be the lecture notes. The students are encouraged to consult numerous textbooks
available in the library.
One good suggested book is:
- Mathematical Methods for Physicists by George B. Arfken, Hans. J. Weber, Frank E. Harris
Any of the other previous editions of the book will also be fine.
Topics covered in the course:
Vector calculus, gradient, divergence and curl, integral theorems: Gauss', Stoke's, and Green's, their alternate forms, vector calculus identities and their applications
Dirac delta function and its derivatives.
Beta, Gamma, and Digamma functions
Fourier series, Fourier Transform, convolution theorem and applications.
Matrices and determinants with a view to their applications in quantum mechanics.
Special functions in mathematical physics and their applications:.
Legendre polynomials, spherical harmonics, Ordinary and spherical Bessel functions, Hermite and Lagurre polynomials, orthogonality, completeness and recurrence relations,
expansion of fucntions in series of special functions.
Functional derivatives and integrals
Selected problems from Calculus of Variation.
Note: The above list is tentative. We may not have the time to cover some topics, while others may be
added. The examination will be only on the material actually covered in the lectures.
1 midterm test(closed book): 30%;
final exam (closed book): 40%
A minimum of 50% in the final exam is needed to pass the course
Late assignments will not be accepted unless approved by the instructor