Description of the course

Topics covered are:

• Partial differential equations. Basic classification (elliptic, hyperbolic, parabolic) with examples.
• Fourier methods including Fourier integrals and discrete Fourier series.
• Greens functions.
• Special solutions to particular elliptic PDEs on cylindrical and spherical geometries: Bessel and Legendre functions.
• Matrix algebra, eigenvalue decomposition.
• Systems of ordinary differential equations, linear as well as nonlinearDetermining steady states, finding stability properties, bifurcations and some chaos theory.

Examples for the various mathematical techniques will be taken from geophysics.

How is the course organized?

Lectures, four per week except weeks with public holidays when there will be two, for a total of 30 lectures and home assignments.

Examination

Examination will be in the form of submitted home assignments using examples and exercises taken from the course literature.

Schedule

Starts on 29 March and ends on 28 May, 2021.

Course Literature

Mathematical Methods in the Physical Sciences (Wiley). Author: Mary L. Boas. (The 2nd edition is available electronically from SUB). Geophysical examples will be taken from original scientific papers as well as from compendia from academic institutions.

Responsible teacher - contact

Erland Källén (erland.kallen@misu.su.se)