Spherical Functions of Mathematical Geosciences - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Spherical Functions of Mathematical Geosciences write by Willi Freeden. This book was released on 2022. Spherical Functions of Mathematical Geosciences available in PDF, EPUB and Kindle. This book is an enlarged second edition of a monograph published in the Springer AGEM2-Series, 2009. It presents, in a consistent and unified overview, a setup of the theory of spherical functions of mathematical (geo-)sciences. The content shows a twofold transition: First, the natural transition from scalar to vectorial and tensorial theory of spherical harmonics is given in a coordinate-free context, based on variants of the addition theorem, Funk-Hecke formulas, and Helmholtz as well as Hardy-Hodge decompositions. Second, the canonical transition from spherical harmonics via zonal (kernel) functions to the Dirac kernel is given in close orientation to an uncertainty principle classifying the space/frequency (momentum) behavior of the functions for purposes of data analysis and (geo-)application. The whole palette of spherical functions is collected in a well-structured form for modeling and simulating the phenomena and processes occurring in the Earth's system. The result is a work which, while reflecting the present state of knowledge in a time-related manner, claims to be of largely timeless significance in (geo-)mathematical research and teaching.
Spherical Functions of Mathematical Geosciences
Spherical Functions of Mathematical Geosciences - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Spherical Functions of Mathematical Geosciences write by Willi Freeden. This book was released on 2008-12-14. Spherical Functions of Mathematical Geosciences available in PDF, EPUB and Kindle. 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.
Spherical Sampling
Spherical Sampling - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Spherical Sampling write by Willi Freeden. This book was released on 2018-05-03. Spherical Sampling available in PDF, EPUB and Kindle. 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.
A Primer on Radial Basis Functions with Applications to the Geosciences
A Primer on Radial Basis Functions with Applications to the Geosciences - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook A Primer on Radial Basis Functions with Applications to the Geosciences write by Bengt Fornberg. This book was released on 2015-09-30. A Primer on Radial Basis Functions with Applications to the Geosciences available in PDF, EPUB and Kindle. ?Adapted from a series of lectures given by the authors, this monograph focuses on radial basis functions (RBFs), a powerful numerical methodology for solving PDEs to high accuracy in any number of dimensions. This method applies to problems across a wide range of PDEs arising in fluid mechanics, wave motions, astro- and geosciences, mathematical biology, and other areas and has lately been shown to compete successfully against the very best previous approaches on some large benchmark problems. Using examples and heuristic explanations to create a practical and intuitive perspective, the authors address how, when, and why RBF-based methods work.? The authors trace the algorithmic evolution of RBFs, starting with brief introductions to finite difference (FD) and pseudospectral (PS) methods and following a logical progression to global RBFs and then to RBF-generated FD (RBF-FD) methods. The RBF-FD method, conceived in 2000, has proven to be a leading candidate for numerical simulations in an increasingly wide range of applications, including seismic exploration for oil and gas, weather and climate modeling, and electromagnetics, among others.? This is the first survey in book format of the RBF-FD methodology and is suitable as the text for a one-semester first-year graduate class.
Special Functions of Mathematical (Geo-)Physics
Special Functions of Mathematical (Geo-)Physics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Special Functions of Mathematical (Geo-)Physics write by Willi Freeden. This book was released on 2013-02-15. Special Functions of Mathematical (Geo-)Physics available in PDF, EPUB and Kindle. 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.
