Home > Studying Physics > Geophysics Second Cycle > Mathematical Methods in Geophyscs

Study programme: Geophysics
Study cycle: Master (second)
Module: for all modules
Core of the programme:
Year: 1
Semester: 1

Lectures: 45 hours
Exercises: 30 hours
Seminar: 0 hours

No. of ECTS credits: 5

Language: Slovenian
Specifics: homework problems

# Mathematical Methods in Geophyscs

## Objectives of the course and intended learning outcomes (competences)

Deepening and strengthening of the knowledge of basic mathematical methods for the application in geophysical problems.

## Contents (Syllabus outline)

Calculus with physical quantities: dimensions, application of differencials, polynomial approximations.
Vector analysis recollection: scalar product, cross product, gradient, divergence, curl, succesive application of ∇, Laplace operator ∇^2.
Laplace equations for gravity, potential current, stationary diffusion of heat and mass, hydrostatic equilibrium, Darcy law.
Vector fields and coordinate systems: cylindrical and spherical (geographic) coordinates, inertial systems and accelerated reference frame, system forces.
Gauss theorem, Stokes theorem, equations of mathematical physics in differential and integral form.
Tensor analysis: gradient of a vector, tensor in physics: electrical and heat conductivity in anisotropic media, deformation tensor. Eigevalues of symmetric tensor.
Ordinary differential equations: Direct integration: 1D stationary fileds of pressure and temperature. Linear differential equations of 2nd rank: harmonic and forced oscillations, resonant response of seismograph, hydrostatic stability.
Partial differential equations: diffusion equation of heat and mass, Navier-Stokes equation of hydrodynamics, wave equation for sound and elastic media, waves on liquid surface and in air masses. Boundary conditions. Methods and solutions: separable solutions, travelling waves: sound waves, seismic P and S waves, Rossby waves.

## Basic literature

• I. Kuščer in A. Kodre: Matematika v fiziki in tehniki. Ljubljana, DMFA, 1994, 394 str, ISBN 961-212-033-1.
• Middleton, G. V., Wilcock, P. R.: Mechanics in the earth and environmental sciences, Cambridge University Press, 1999, XVI+459 str., ISBN 0-521-44124-2.

## Expected achievements

Knowledge and understanding
Knowledge of geophysical problems and understading of mathematical methods in connection with geophysical.

Apllicability
Application of methods of mathematical physics.

Reflection
Mathematical methods in geophysics.

Transferable skills
Application of mathematical methods, formulation of concrete applied problems and their solutions.

## Teaching methods

Lectures, exercises, homework problems.

## Prerequisites

Finished bachelor study.

## Assesment methods

The assessment consists of two parts, an oral theoretical exam and a practical exercises exam. The practical exercises exam (50 % of final grade) can be completed with 2 half-term exams. The oral theoretical exam is 50 % of the final grade. The candidate successfully completes the assessment by obtaining a grade 6 (pass) to 10 (excellent) in both parts of the exam.

## Methods of quality assessment

Self-evaluation, anonymous student questionnaire.

## Course coodinator and his references

• prof. dr. Peter Prelovšek