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.

The lecture is planned to be held in the presence mode at the TU. The lecture material (Power Point slides) will be provided in TUWEL.

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

Lecture notes for this course are sold via INTU (Wiedner Hauptstr. 8-10, 1040 Wien). The lecture material will be provided via TUWEL course.

Alle Pflichtvorlesungen der Mathematik (für Geodäsie), Differential- und Integralrechnung, lineare Algebra