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Special Functions of Mathematical (Geo-)Physics (Hardcover, 2013 ed.)
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Special Functions of Mathematical (Geo-)Physics (Hardcover, 2013 ed.)
Series: Applied and Numerical Harmonic Analysis
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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.
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