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Mathematical methods
Last Updated: 2026-02-05 15:24:10
Abstract
The course will guide students in learning about solutions of partial differential equations arising in connection with various physical problems. Special attention will be paid to the solutions of Laplace’s equation in spherical and cylindrical polars. In addittion the basics of vector calculus will be discussed in order to support Geophysical Fluid Dynamics and Potential Field Theory courses.
Objective
The course will guide students in learning about solutions of partial differential equations arising in connection with various physical problems. Special attention will be paid to the solutions of Laplace’s equation in spherical and cylindrical polars. In addittion the basics of vector calculus will be discussed in order to support Geophysical Fluid Dynamics and Potential Field Theory courses.
Content
Introduction to partial differential equations, Sturm-Liouville problem, eigenvalues and eigenfunctions, orthogonality, orthogonal expansion, solution of 1-D wave equation, method of separation of variables, solution of 1-D heat equation, basics of vector algebra, vector calculus (differentiation and integration), curvilinear coordinates, differential operations in curvilinear coordinates, solution of Laplace’s equation in spherical polar coordinates, Legendre and associated Legendre polynomials, spherical functions, solution of Laplace’s equation in cylindrical polar coordinates, Bessel functions.
General Information
- Language
- English
- Levels
- MSC
- Frequency
- Yearly recurring
Examination
- Type
- session examination
- Mode
- written 120 minutes
- Aids
- None
Course Components
| Type | Title | Time & Place | Hours |
|---|---|---|---|
| lecture with exercise | Mathematical methods |
|
2 h weekly |