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Special Functions of Mathematical (Geo-)Physics

Author: Willi Freeden

Publisher: Springer Science & Business Media

Published: 2013-02-15

Total Pages: 501

ISBN-13: 3034805632

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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.

Book Synopsis Special Functions of Mathematical (Geo-)Physics by : Willi Freeden

Download or read book Special Functions of Mathematical (Geo-)Physics written by Willi Freeden and published by Springer Science & Business Media. This book was released on 2013-02-15 with total page 501 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Spherical Functions of Mathematical Geosciences

Author: Willi Freeden

Publisher: Springer Science & Business Media

Published: 2008-12-14

Total Pages: 609

ISBN-13: 3540851127

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In recent years, the Geomathematics Group, TU Kaiserslautern, has worked to set up a theory of spherical functions of mathematical physics. This book is a collection of all the material that group generated during the process.

Book Synopsis Spherical Functions of Mathematical Geosciences by : Willi Freeden

Download or read book Spherical Functions of Mathematical Geosciences written by Willi Freeden and published by Springer Science & Business Media. This book was released on 2008-12-14 with total page 609 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years, the Geomathematics Group, TU Kaiserslautern, has worked to set up a theory of spherical functions of mathematical physics. This book is a collection of all the material that group generated during the process.

Mathematical Methods for Geophysics and Space Physics

Author: William I. Newman

Publisher:

Published: 2016

Total Pages: 250

ISBN-13: 9781523124589

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Graduate students in the natural sciences--including not only geophysics and space physics but also atmospheric and planetary physics, ocean sciences, and astronomy--need a broad-based mathematical toolbox to facilitate their research. In addition, they need to survey a wider array of mathematical methods that, while outside their particular areas of expertise, are important in related ones. While it is unrealistic to expect them to develop an encyclopedic knowledge of all the methods that are out there, they need to know how and where to obtain reliable and effective insights into these broader areas. Here at last is a graduate textbook that provides these students with the mathematical skills they need to succeed in today's highly interdisciplinary research environment. This authoritative and accessible book covers everything from the elements of vector and tensor analysis to ordinary differential equations, special functions, and chaos and fractals. Other topics include integral transforms, complex analysis, and inverse theory; partial differential equations of mathematical geophysics; probability, statistics, and computational methods; and much more. Proven in the classroom, Mathematical Methods for Geophysics and Space Physics features numerous exercises throughout as well as suggestions for further reading. Provides an authoritative and accessible introduction to the subject Covers vector and tensor analysis, ordinary differential equations, integrals and approximations, Fourier transforms, diffusion and dispersion, sound waves and perturbation theory, randomness in data, and a host of other topics Features numerous exercises throughout Ideal for students and researchers alike An online illustration package is available to professors.

Book Synopsis Mathematical Methods for Geophysics and Space Physics by : William I. Newman

Download or read book Mathematical Methods for Geophysics and Space Physics written by William I. Newman and published by . This book was released on 2016 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: Graduate students in the natural sciences--including not only geophysics and space physics but also atmospheric and planetary physics, ocean sciences, and astronomy--need a broad-based mathematical toolbox to facilitate their research. In addition, they need to survey a wider array of mathematical methods that, while outside their particular areas of expertise, are important in related ones. While it is unrealistic to expect them to develop an encyclopedic knowledge of all the methods that are out there, they need to know how and where to obtain reliable and effective insights into these broader areas. Here at last is a graduate textbook that provides these students with the mathematical skills they need to succeed in today's highly interdisciplinary research environment. This authoritative and accessible book covers everything from the elements of vector and tensor analysis to ordinary differential equations, special functions, and chaos and fractals. Other topics include integral transforms, complex analysis, and inverse theory; partial differential equations of mathematical geophysics; probability, statistics, and computational methods; and much more. Proven in the classroom, Mathematical Methods for Geophysics and Space Physics features numerous exercises throughout as well as suggestions for further reading. Provides an authoritative and accessible introduction to the subject Covers vector and tensor analysis, ordinary differential equations, integrals and approximations, Fourier transforms, diffusion and dispersion, sound waves and perturbation theory, randomness in data, and a host of other topics Features numerous exercises throughout Ideal for students and researchers alike An online illustration package is available to professors.

Mathematical Aspects of Seismology

Author: Markus Båth

Publisher: Elsevier

Published: 2013-09-24

Total Pages: 428

ISBN-13: 1483274977

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Developments in Solid Earth Geophysics, 4: Mathematical Aspects of Seismology introduces studies of the more advanced parts of theoretical seismology. The manuscript first ponders on contour integration and conformal transformation, methods of stationary phase and steepest descent, and series integration. Discussions focus on Love waves in heterogeneous isotropic media, Laguerre's differential equation, Hermite's differential equation, method of steepest descent, method of stationary phase, contour integration in the complex plane, and conformal transformation. The text then examines series integration, Bessel functions, Legendre functions, and wave equations. Topics include general considerations of the wave equation, expansion of a spherical wave into plane waves, common features of special functions and special differential equations, applications of Legendre functions, Legendre polynomials, Bessel's differential equation, and properties of Bessel coefficients. The book explores the influence of gravity on wave propagation, matrix calculus, wave propagation in liquid media, integral equations, calculus of variations, and integral transforms. The text is a valuable source of data for researchers wanting to study the mathematical aspects of seismology.

Book Synopsis Mathematical Aspects of Seismology by : Markus Båth

Download or read book Mathematical Aspects of Seismology written by Markus Båth and published by Elsevier. This book was released on 2013-09-24 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: Developments in Solid Earth Geophysics, 4: Mathematical Aspects of Seismology introduces studies of the more advanced parts of theoretical seismology. The manuscript first ponders on contour integration and conformal transformation, methods of stationary phase and steepest descent, and series integration. Discussions focus on Love waves in heterogeneous isotropic media, Laguerre's differential equation, Hermite's differential equation, method of steepest descent, method of stationary phase, contour integration in the complex plane, and conformal transformation. The text then examines series integration, Bessel functions, Legendre functions, and wave equations. Topics include general considerations of the wave equation, expansion of a spherical wave into plane waves, common features of special functions and special differential equations, applications of Legendre functions, Legendre polynomials, Bessel's differential equation, and properties of Bessel coefficients. The book explores the influence of gravity on wave propagation, matrix calculus, wave propagation in liquid media, integral equations, calculus of variations, and integral transforms. The text is a valuable source of data for researchers wanting to study the mathematical aspects of seismology.

Spherical Sampling

Author: Willi Freeden

Publisher: Birkhäuser

Published: 2018-05-03

Total Pages: 596

ISBN-13: 3319714589

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This book presents, in a consistent and unified overview, results and developments in the field of today ́s spherical sampling, particularly arising in mathematical geosciences. Although the book often refers to original contributions, the authors made them accessible to (graduate) students and scientists not only from mathematics but also from geosciences and geoengineering. Building a library of topics in spherical sampling theory it shows how advances in this theory lead to new discoveries in mathematical, geodetic, geophysical as well as other scientific branches like neuro-medicine. A must-to-read for everybody working in the area of spherical sampling.

Book Synopsis Spherical Sampling by : Willi Freeden

Download or read book Spherical Sampling written by Willi Freeden and published by Birkhäuser. This book was released on 2018-05-03 with total page 596 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents, in a consistent and unified overview, results and developments in the field of today ́s spherical sampling, particularly arising in mathematical geosciences. Although the book often refers to original contributions, the authors made them accessible to (graduate) students and scientists not only from mathematics but also from geosciences and geoengineering. Building a library of topics in spherical sampling theory it shows how advances in this theory lead to new discoveries in mathematical, geodetic, geophysical as well as other scientific branches like neuro-medicine. A must-to-read for everybody working in the area of spherical sampling.

Metaharmonic Lattice Point Theory

Author: Willi Freeden

Publisher: CRC Press

Published: 2011-05-09

Total Pages: 467

ISBN-13: 1439861854

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Metaharmonic Lattice Point Theory covers interrelated methods and tools of spherically oriented geomathematics and periodically reflected analytic number theory. The book establishes multi-dimensional Euler and Poisson summation formulas corresponding to elliptic operators for the adaptive determination and calculation of formulas and identities of

Book Synopsis Metaharmonic Lattice Point Theory by : Willi Freeden

Download or read book Metaharmonic Lattice Point Theory written by Willi Freeden and published by CRC Press. This book was released on 2011-05-09 with total page 467 pages. Available in PDF, EPUB and Kindle. Book excerpt: Metaharmonic Lattice Point Theory covers interrelated methods and tools of spherically oriented geomathematics and periodically reflected analytic number theory. The book establishes multi-dimensional Euler and Poisson summation formulas corresponding to elliptic operators for the adaptive determination and calculation of formulas and identities of

Mathematical Methods for Geophysics and Space Physics

Author: William I. Newman

Publisher: Princeton University Press

Published: 2016-05-03

Total Pages: 266

ISBN-13: 0691170606

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An essential textbook on the mathematical methods used in geophysics and space physics Graduate students in the natural sciences—including not only geophysics and space physics but also atmospheric and planetary physics, ocean sciences, and astronomy—need a broad-based mathematical toolbox to facilitate their research. In addition, they need to survey a wider array of mathematical methods that, while outside their particular areas of expertise, are important in related ones. While it is unrealistic to expect them to develop an encyclopedic knowledge of all the methods that are out there, they need to know how and where to obtain reliable and effective insights into these broader areas. Here at last is a graduate textbook that provides these students with the mathematical skills they need to succeed in today's highly interdisciplinary research environment. This authoritative and accessible book covers everything from the elements of vector and tensor analysis to ordinary differential equations, special functions, and chaos and fractals. Other topics include integral transforms, complex analysis, and inverse theory; partial differential equations of mathematical geophysics; probability, statistics, and computational methods; and much more. Proven in the classroom, Mathematical Methods for Geophysics and Space Physics features numerous exercises throughout as well as suggestions for further reading. Provides an authoritative and accessible introduction to the subject Covers vector and tensor analysis, ordinary differential equations, integrals and approximations, Fourier transforms, diffusion and dispersion, sound waves and perturbation theory, randomness in data, and a host of other topics Features numerous exercises throughout Ideal for students and researchers alike An online illustration package is available to professors

Book Synopsis Mathematical Methods for Geophysics and Space Physics by : William I. Newman

Download or read book Mathematical Methods for Geophysics and Space Physics written by William I. Newman and published by Princeton University Press. This book was released on 2016-05-03 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: An essential textbook on the mathematical methods used in geophysics and space physics Graduate students in the natural sciences—including not only geophysics and space physics but also atmospheric and planetary physics, ocean sciences, and astronomy—need a broad-based mathematical toolbox to facilitate their research. In addition, they need to survey a wider array of mathematical methods that, while outside their particular areas of expertise, are important in related ones. While it is unrealistic to expect them to develop an encyclopedic knowledge of all the methods that are out there, they need to know how and where to obtain reliable and effective insights into these broader areas. Here at last is a graduate textbook that provides these students with the mathematical skills they need to succeed in today's highly interdisciplinary research environment. This authoritative and accessible book covers everything from the elements of vector and tensor analysis to ordinary differential equations, special functions, and chaos and fractals. Other topics include integral transforms, complex analysis, and inverse theory; partial differential equations of mathematical geophysics; probability, statistics, and computational methods; and much more. Proven in the classroom, Mathematical Methods for Geophysics and Space Physics features numerous exercises throughout as well as suggestions for further reading. Provides an authoritative and accessible introduction to the subject Covers vector and tensor analysis, ordinary differential equations, integrals and approximations, Fourier transforms, diffusion and dispersion, sound waves and perturbation theory, randomness in data, and a host of other topics Features numerous exercises throughout Ideal for students and researchers alike An online illustration package is available to professors

Introduction to Theoretical Geophysics

Author: C. B. Officer

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 389

ISBN-13: 3642657311

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It has been my intention in this book to give a coordinated treatment of the whole of theoretical geophysics. The book assumes a mathematical back ground through calculus and differential equations. It also assumes a reason able background in physics and in elementary vector analysis. The level of the book is commensurate with that of a senior undergraduate or first year graduate course. Its aim is to provide the reader with a survey of the whole of theoretical geophysics. The emphasis has been on the basic and the elementary. The expert in any one of the several disciplines covered here will find much lacking from his particular area of investigation; no apology is made for that. In order to treat all aspects in a coordinated manner, the simplest type of mathematical nota tion for the various physical problems has been used, namely, that of scalars, three-dimensional vectors, and the vector operators, gradient, curl, divergence, etc. It is appreciated that this elementary notation often may not be the most conducive to the solution of some of the more complex geophysical problems. The derivations are, in almost every case, carried through in considerable detail. Sometimes the particulars of the algebra and calculus have been omitted and relegated to one of the problems following the section. The emphasis has been on the physics of the derivations and on explaining the various physical principles important in geophysics, such as continuity, mixing, diffusion, conduction, convection, precession, wobble, rays, waves, dispersion, and potential theory.

Book Synopsis Introduction to Theoretical Geophysics by : C. B. Officer

Download or read book Introduction to Theoretical Geophysics written by C. B. Officer and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: It has been my intention in this book to give a coordinated treatment of the whole of theoretical geophysics. The book assumes a mathematical back ground through calculus and differential equations. It also assumes a reason able background in physics and in elementary vector analysis. The level of the book is commensurate with that of a senior undergraduate or first year graduate course. Its aim is to provide the reader with a survey of the whole of theoretical geophysics. The emphasis has been on the basic and the elementary. The expert in any one of the several disciplines covered here will find much lacking from his particular area of investigation; no apology is made for that. In order to treat all aspects in a coordinated manner, the simplest type of mathematical nota tion for the various physical problems has been used, namely, that of scalars, three-dimensional vectors, and the vector operators, gradient, curl, divergence, etc. It is appreciated that this elementary notation often may not be the most conducive to the solution of some of the more complex geophysical problems. The derivations are, in almost every case, carried through in considerable detail. Sometimes the particulars of the algebra and calculus have been omitted and relegated to one of the problems following the section. The emphasis has been on the physics of the derivations and on explaining the various physical principles important in geophysics, such as continuity, mixing, diffusion, conduction, convection, precession, wobble, rays, waves, dispersion, and potential theory.

Mathematical Geophysics

Author: Jean-Yves Chemin

Publisher: Oxford University Press on Demand

Published: 2006-04-13

Total Pages: 263

ISBN-13: 019857133X

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Aimed at graduate students and researchers in mathematics, engineering, oceanography, meteorology and mechanics, this text provides a detailed introduction to the physical theory of rotating fluids, a significant part of geophysical fluid dynamics. The Navier-Stokes equations are examined in both incompressible and rapidly rotating forms.

Book Synopsis Mathematical Geophysics by : Jean-Yves Chemin

Download or read book Mathematical Geophysics written by Jean-Yves Chemin and published by Oxford University Press on Demand. This book was released on 2006-04-13 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt: Aimed at graduate students and researchers in mathematics, engineering, oceanography, meteorology and mechanics, this text provides a detailed introduction to the physical theory of rotating fluids, a significant part of geophysical fluid dynamics. The Navier-Stokes equations are examined in both incompressible and rapidly rotating forms.

Mathematical Geophysics

Author: Jean-Yves Chemin

Publisher: Clarendon Press

Published: 2006-04-13

Total Pages: 264

ISBN-13: 019151389X

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Aimed at graduate students, researchers and academics in mathematics, engineering, oceanography, meteorology and mechanics, this text provides a detailed introduction to the physical theory of rotating fluids, a significant part of geophysical fluid dynamics. The text is divided into four parts, with the first part providing the physical background of the geophysical models to be analysed. Part II is devoted to a self contained proof of the existence of weak (or strong) solutions to the incompressible Navier-Stokes equations. Part III deals with the rapidly rotating Navier-Stokes equations, first in the whole space, where dispersion effects are considered. The case where the domain has periodic boundary conditions is then analysed, and finally rotating Navier-Stokes equations between two plates are studied, both in the case of periodic horizontal coordinates and those in R2. In Part IV the stability of Ekman boundary layers, and boundary layer effects in magnetohydrodynamics and quasigeostrophic equations are discussed. The boundary layers which appear near vertical walls are presented and formally linked with the classical Prandlt equations. Finally spherical layers are introduced, whose study is completely open.

Book Synopsis Mathematical Geophysics by : Jean-Yves Chemin

Download or read book Mathematical Geophysics written by Jean-Yves Chemin and published by Clarendon Press. This book was released on 2006-04-13 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: Aimed at graduate students, researchers and academics in mathematics, engineering, oceanography, meteorology and mechanics, this text provides a detailed introduction to the physical theory of rotating fluids, a significant part of geophysical fluid dynamics. The text is divided into four parts, with the first part providing the physical background of the geophysical models to be analysed. Part II is devoted to a self contained proof of the existence of weak (or strong) solutions to the incompressible Navier-Stokes equations. Part III deals with the rapidly rotating Navier-Stokes equations, first in the whole space, where dispersion effects are considered. The case where the domain has periodic boundary conditions is then analysed, and finally rotating Navier-Stokes equations between two plates are studied, both in the case of periodic horizontal coordinates and those in R2. In Part IV the stability of Ekman boundary layers, and boundary layer effects in magnetohydrodynamics and quasigeostrophic equations are discussed. The boundary layers which appear near vertical walls are presented and formally linked with the classical Prandlt equations. Finally spherical layers are introduced, whose study is completely open.