00709 - Mathematical Methods Of Physics

Learning outcomes

AT the end of the course the student acquires notions and methodologies necessary for study and understanding of the modern physics. In the first part of the course, the student becomes familiar with the theory of the holomorphic functions and able to calculate contour integrals on the complex plane. In the second part of the course, the student studies the formalism of the linear spaces of infinite dimensionality, in particular, the Hilbert spaces and is able to use this mathematical formalism to the study of quantum mechanics.

Course contents

Holomorphic funcrtions. Calcuation of integrals in the complex plane by the residue method. Laurent series. Multivalued functions.  Topological spaces. Compactness. Metric spaces. Hausdorff spaces. Separability. Linear spaces. Normed spaces. Banach spaces. Hilbert spaces. Operators in the Hilbert spaces. Bounded and continuous operators. Unbounded operators. Complete ortonormal systems. Fourier series. Ortogonal polynomials. Legendre polynomials. Hermite polynomials. Chebyshev polynomials. Laguerre polynomials.Convolution of functions. Fourier transformation.

Readings/Bibliography

Lecture notes.

Teaching methods

Lectures and exercises.

Assessment methods

Oral exams, including exercises.

Office hours

See the website of Alexandr Kamenchtchik