Mathematical Physics

Overview

Advanced linear algebra: Definition and basic properties of a generic vectorial space, isomorphisms and homomorphisms. Generalised definition of scalar product and norm, base of a vectorial space, orthonormality.

Fourier series and Fourier transform. The Dirac delta function, Parseval’s theorem and the convolution theorem.

Partial differential equations: method of characteristics, PDE classification, d’Alembert’s solution, separation of variables.

Hamiltonian Mechanics. Definition of generalized and conjugated variables, principle of minimum action, Lagrangian and Hamiltonian formalism, Poisson’s brackets.

Learning Objectives

Students will be able to:

Display knowledge of, and apply practically, a range of mathematical techniques and properties in advanced mathematical techniques and concepts including linear algenbra, Fourier series and transforms, partial differential equations,and Lagrangian and Hamiltonian mechanics.

Formulate mathematical problems of physical systems and obtain analytical or approximate solutions.

Skills

Problem solving. Communicating mathematical concepts in a clear and concise manner both orally and in written form. Working independently and with a group of peers. Time management and the ability to meet deadlines.

Assessment

NONE