After successful completion of the course, students are able to select appropriate methods of interpolation and approximation for different applications, perform simple frequency analyses, numerically solve initial value problems, term features and parameters for the characterization of curves and surfaces in the 3D-domain, classify mapping projections and explain spherical harmonics.
Interpolation methods, Fourier and wavelet analysis, spherical harmonics, numerical integration, other mathematical tools used in geodesy and cartography.
Illustration of the techniques with Power Point slides, calculation of practical examples, demonstrations with MATLAB.
The following topics are discussed in parts during the oral exam:
• Interpolation: methods, advantages, disadvantages, properties
• Approximation: quality criteria, application, orthogonal functions
• Fourier transform: DFT, application, problems, convolution
• Frequency analysis in general: sampling, techniques, problems
• Numerical integration
• Characterization of 3D curves, Frenet frame
• Characterization of surface geometry, fundamental forms
• Map projections: metric properties, classification of projections
• Spherical harmonics: applications, properties - calculation
• Tensor calculus: relevance, basic terms
Alle Pflichtvorlesungen der Mathematik (für Geodäsie), Differential- und Integralrechnung, lineare Algebra
