MPH6162 Mathematical Methods for Physics

Aims:

The course will cover some mathematical techniques commonly used in theoretical physics. This is not a course in pure mathematics, but rather on the application of mathematics to problems of interest in the physical sciences.

Content:

Depending on your initial preparation, to be assessed by a preliminary test that will not count for your final grade, we will cover some or all of the following topics: • Vector calculus in curvilinear coordinates; • The theory of analytic functions; • Linear algebra, vectors and tensors in physics; • Special functions and their physical applications; • Partial and ordinary differential equations; analytical and numerical methods for their solution. This is a course in mathematical physics, so the emphasis will always be on physical applications.

The course is divided into five broad topics, each taking 2-4 weeks or so. 

2. LINEAR VECTOR SPACES

1. THEORY OF ANALYTICAL FUNCTION

3. FUNCTION SPACE, ORTHOGONAL POLYNOMIALS, AND FOURIER ANALYSIS

4. DIFFERENTIAL EQUATIONS

5. SPECIAL FUNCTIONS

Details are in the attached course outline (and in the online MSc syllabus here https://eaifr.org/degree-programmes/masters-programme/ or here: https://eaifr.org/media/2825/syllabusmsc.pdf