**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