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Book Cover
E-book
Author Freeden, W. (Willi)

Title Special functions of mathematical (Geo- )physics / Willi Freeden, Martin Gutting
Published Basel ; New York : Birkhäuser, ©2013

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Description 1 online resource
Series Applied and numerical harmonic analysis
Applied and numerical harmonic analysis.
Contents Auxiliary Functions -- The Gamma Function -- Orthogonal Polynomials -- Spherically Oriented Functions -- Scalar Spherical Harmonics in R3 -- Vectorial Spherical Harmonics in R3 -- Spherical Harmonics in Rq -- Classical Bessel Functions -- Bessel Functions in Rq -- Periodically Oriented Functions -- Lattice Functions in R -- Lattice Functions in Rq -- Concluding Remarks
Summary 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
Analysis Mathematics
Physical geography
Meteorology
Harmonic analysis
Differential equations, partial
Functions, special
Special Functions
Mathematical Physics
Geophysics/Geodesy
Partial Differential Equations
Abstract Harmonic Analysis
Meteorology/Climatology
Bibliography Includes bibliographical references and index
Subject Geology -- Mathematics.
Geophysics -- Mathematics
SCIENCE -- Earth Sciences -- Geography.
SCIENCE -- Earth Sciences -- Geology.
Geology -- Mathematics.
Geophysics -- Mathematics.
Genre/Form Electronic books
Form Electronic book
Author Gutting, Martin
ISBN 9783034805636
3034805632
3034805624
9783034805629