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Special functions enable us to formulate a scientific problem by reduction such that a new, more concrete problem can be attacked within a well-structured framework, usually in the context of differential equations. A good understanding of special functions provides the capacity to recognize the causality between the abstractness of the mathematical concept and both the impact on and cross-sectional importance to the scientific reality. The special functions to be discussed in this monograph vary greatly, depending on the measurement parameters examined (gravitation, electric and magnetic fields, deformation, climate observables, fluid flow, etc.) and on the respective field characteristic (potential field, diffusion field, wave field). The differential equation under consideration determines the type of special functions that are needed in the desired reduction process. Each chapter closes with exercises that reflect significant topics, mostly in computational applications. As a result, readers are not only directly confronted with the specific contents of each chapter, but also with additional knowledge on mathematical fields of research, where special functions are essential to application. All in all, the book is an equally valuable resource for education in geomathematics and the study of applied and harmonic analysis. Students who wish to continue with further studies should consult the literature given as supplements for each topic covered in the exercises.

Geodynamics --- Functions, Special. --- Mathematics. --- Dynamic geology --- Tectonophysics --- Geophysics --- Special functions --- Mathematical analysis --- Functions, special. --- Physical geography. --- Differential equations, partial. --- Harmonic analysis. --- Special Functions. --- Mathematical Physics. --- Geophysics/Geodesy. --- Partial Differential Equations. --- Abstract Harmonic Analysis. --- Atmospheric Sciences. --- Geography --- Analysis (Mathematics) --- Functions, Potential --- Potential functions --- Banach algebras --- Calculus --- Mathematics --- Bessel functions --- Fourier series --- Harmonic functions --- Time-series analysis --- Partial differential equations --- Special functions. --- Mathematical physics. --- Geophysics. --- Partial differential equations. --- Atmospheric sciences. --- Atmospheric sciences --- Earth sciences --- Atmosphere --- Geological physics --- Terrestrial physics --- Physics --- Physical mathematics

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Spherical functions.

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The book provides the geoscientific context, that arises in gravimetric/magnetometric exploration. It essentially uses mathematics as a key technology for modeling issues on the basis of analysis and interpretation according to dense and precise gravitational/magnetic measurements. It is dedicated to surface and deep geology with potential data primarily of terrestrial origin. The book spans the interdisciplinary arc from geoengineering, especially geodesy, via geophysics to geomathematics and geology, and back again. It presents the recently published pioneering and groundbreaking multiscale mollifier methodologies realizing the bridging transfer from gravitational/magnetic measurements to approximative/numerical mollifier wavelet decorrelations with novel geologic prospects and layer-structure determination as outcome. Using the specific example of the German Saarland region, new important fields of application, especially for areas with mining-related cavities, will be opened up and subjected to an in-depth geologic detection.

Mathematical models. --- Geophysics. --- Numerical analysis. --- Mathematical Modeling and Industrial Mathematics. --- Numerical Analysis. --- Geology --- Geothermal engineering. --- Geothermal resources. --- Gravity --- Mathematics. --- Measurement.

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Auf dem Kriegspfad in Massai-Land; Musterung der Expedition; Lagerbild bei Mandara's Dorf; Blick auf den Kilima-Ndjaro uber den Djalla-See hin; Auf der Rhinoceros-Jagd; Der Kilima-Ndjaro und die Ndjiri-Ebene; Massai-Krieger von Kapte ...