Syllabus
Numerical Mathematics. Solution of systems of linear algebraic equations: Gaussian elimination and LU factorization, generalised matrix inversion, singular value decomposition, iterative methods. Approximation, interpolation, spline. Linear regression. Numerical derivative and integral. Discrete Fourier analysis: analysing periodic functions, analysing nonperiodic functions, sampling and digitizing signal functions, Fourier analysis of sampled time signals, the effect of time limitation, the fast Fourier transform. Digital signal processing: noise, mean and trend removal, digital filtering.
Problem solving exercises are based on MATLAB.
Annotation
The aim of this course is the numerical mathematics methods used in applied geophysics. Exercises are based on use of MATLAB program.
Numerical methods of solving systems of linear equations, including and Gauss generalized inversion.
The basic methods of approximation and interpolation of numerical data seiries.
The basics of numerical derivation and integration.
Fourier transform, its discrete implementation.
The nunerical methods taught are so general that they can be used in virtually all disciplines.
For students interested in the follow-up master's study of Applied Geology, focusing on applied geophysics, the completion of this course is practically necessary to understand a number of data processing methods in applied geophysics.
The course is strongly practically oriented, MATLAB is used to perform calculations. Prior knowledge of MATLAB is an advantage for students, but it is generally assumed that students without previous knowledge of MATLAB also apply.