Lectures

Geomathematics

Prof. Willi Freeden

Die Übungsblätter und aktuelle Informationen zur Vorlesungen finden sich hier.

Termine der Vorlesung:

Di, 10:00 - 11:30, 48-582
Do, 15:30 - 17:00, 48-582

Termine der Übung:

Mi, 10:00 - 11:30, 48-538

Inhalt

Geoscientific research influences new industrial developments as well as our everyday life. The possible reversion of the Earth's magnetic polarity in the next centuries and the indications of climatic changes are examples for open problems motivating further investigations. Nowadays, every aspect of the Earth's properties requires a sophisticated mathematical model. Moreover, present and future satellite missions represent in particular new mathematical challenges to scientists. As a consequence, modern mathematical methods are needed for the improvement of the Earth models and allow the development of advanced methods for solving the ocurring problems. This is the aim of geomathematics. he lecture gives an introduction into selected topics of geomathematics. It discusses the mathematical modeling and development of solution methods for problems like mass distribution, magnetic field and gravity field in the system Earth.

Literatur

W. Freeden, T. Gervens, M. Schreiner: Constructive Approximation on the Sphere - With Applications to Geomathematics, Oxford Science Publication;

W. Freeden: Multiscale Modelling of Spaceborne Geodata, Teubner;

W. Freeden, V. Michel: Multiscale Potential Theory - With Applications to Geoscience, Birkhäuser;

W. Freeden, M. Schreiner: Spherical Functions in Mathematical Geosciences (A Scalar, Vectorial, and Tensorial Setup), Springer;

V. Michel: A Multiscale Method for the Gravimetry Problem - Theor. and Num. Aspects of Harmonic and Anharmonic Modelling, Shaker;

Voraussetzungen

Analysis and Linear Algebra

Special Functions of Mathematical (Geo) Physics

Prof. Willi Freeden

Die Übungsblätter und aktuelle Informationen zur Vorlesungen finden sich hier.

Termine der Vorlesung:

Di, 15:30 - 17:00, 49-506
Do, 10:00 - 11:30, 49-506

Termine der Übung:

Mi, 15:30 - 17:00, 49-506

Inhalt

The lecture gives an elementary approach to the theory of special functions in mathematical physics with special emphasis on geophysically relevant aspects. The essential topics of the lecture are in chronological order: the Gamma function, orthogonal polynomials, spherical polynomials (scalar, vectorial, and tensorial case), and Bessel functions. All fields will be assisted by geophysically relevant applications.

Literatur

W. Freeden, T. Gervens, M. Schreiner, Constructive Approximation on the Sphere (With Applications to Geomathematics), Oxford Science Publications, Clarendon, 1998.

W. Freeden, V. Michel, Multiscale Potential Theory (with Applications to Geoscience), Birkhäuser Verlag, Boston, 2004.

W. Freeden, M. Schreiner: Spherical Functions in Mathematical Geosciences (A Scalar, Vectorial, and Tensorial Setup), Springer, 2009.

C. Müller, Spherical Harmonics, Lecture Notes in Mathematics, 17, Springer, 1966.

C. Müller, Analysis of Spherical Symmetrics in Euclidean Spaces, Springer, 1998.

N.N. Lebedew: Spezielle Funktionen und ihre Anwendungen, BI, 1973.

Voraussetzungen

Analysis and Linear Algebra

Einführung in die Vektoranalysis

Prof. Gabriele Steidl

Die Übungsblätter und aktuelle Informationen zur Vorlesungen finden sich hier.

Termine der Vorlesung:

Mo, 11:45 - 13:15, 24-102

Termine der Übung:

Mo, 08:15 - 09:45, 44-465
Di, 08:15 - 09:45, 11-241
Di, 13:45 - 15:15, 48-582
Mi, 08:15 - 09:45, 13-222

Oberseminar Geomathematik

Prof. Willi Freeden, Dr. Martin Gutting

Inhalt

Diskussion forschungsrelevanter Themen in der Geomathematik, in der Regel Vorträge aus der AG Geomathematik.