000 03943nam a22005897a 4500
001 sulb-eb0023141
003 BD-SySUS
005 20160413122336.0
007 cr nn 008mamaa
008 130217s2013 sz | s |||| 0|eng d
020 _a9783034805636
_9978-3-0348-0563-6
024 7 _a10.1007/978-3-0348-0563-6
_2doi
050 4 _aQA351
072 7 _aPBKF
_2bicssc
072 7 _aMAT034000
_2bisacsh
072 7 _aMAT037000
_2bisacsh
082 0 4 _a515.5
_223
100 1 _aFreeden, Willi.
_eauthor.
245 1 0 _aSpecial Functions of Mathematical (Geo-)Physics
_h[electronic resource] /
_cby Willi Freeden, Martin Gutting.
264 1 _aBasel :
_bSpringer Basel :
_bImprint: Birkhäuser,
_c2013.
300 _aXV, 501 p. 37 illus., 18 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aApplied and Numerical Harmonic Analysis
505 0 _a1 Introduction: Geomathematical Motivation -- Part I: Auxiliary Functions -- 2 The Gamma Function -- 3 Orthogonal Polynomials -- Part II: Spherically Oriented Functions.- 4 Scalar Spherical Harmonics in R^3 -- 5 Vectorial Spherical Harmonics in R^3 -- 6 Spherical Harmonics in R^q -- 7 Classical Bessel Functions -- 8 Bessel Functions in R^q -- Part III: Periodically Oriented Functions -- 9 Lattice Functions in R -- 10 Lattice Functions in R^q -- 11 Concluding Remarks -- References -- Index.
520 _aSpecial 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.
650 0 _aMathematics.
650 0 _aGeophysics.
650 0 _aAtmospheric sciences.
650 0 _aHarmonic analysis.
650 0 _aPartial differential equations.
650 0 _aSpecial functions.
650 0 _aMathematical physics.
650 1 4 _aMathematics.
650 2 4 _aSpecial Functions.
650 2 4 _aMathematical Physics.
650 2 4 _aGeophysics/Geodesy.
650 2 4 _aPartial Differential Equations.
650 2 4 _aAbstract Harmonic Analysis.
650 2 4 _aAtmospheric Sciences.
700 1 _aGutting, Martin.
_eauthor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783034805629
830 0 _aApplied and Numerical Harmonic Analysis
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-0348-0563-6
912 _aZDB-2-SMA
942 _2Dewey Decimal Classification
_ceBooks
999 _c45233
_d45233