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Mathematical methods for 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 m...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Princeton, New Jersey ; Oxford :
Princeton University Press,
[2016]
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| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 100 | 1 | |a Newman, William I., |e author. | |
| 245 | 1 | 0 | |a Mathematical methods for geophysics and space physics / |c William I. Newman. |
| 264 | 1 | |a Princeton, New Jersey ; |a Oxford : |b Princeton University Press, |c [2016] | |
| 264 | 4 | |c ©2016 | |
| 300 | |a 1 online resource (xiv, 250 pages) : |b illustrations | ||
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| 504 | |a Includes bibliographical references and index. | ||
| 588 | 0 | |a Print version record. | |
| 505 | 0 | |a Mathematical preliminaries -- Ordinary differential equations -- Evaluation of integrals and integral transform methods -- Partial differential equations of mathematical geophysics -- Probability, statistics, and computational methods. | |
| 520 | |a 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. | ||
| 546 | |a In English. | ||
| 590 | |a JSTOR |b Books at JSTOR All Purchased | ||
| 590 | |a JSTOR |b Books at JSTOR Demand Driven Acquisitions (DDA) | ||
| 590 | |a JSTOR |b Books at JSTOR Evidence Based Acquisitions | ||
| 650 | 0 | |a Geophysics |x Mathematics. | |
| 650 | 0 | |a Cosmic physics |x Mathematics. | |
| 650 | 6 | |a Géophysique |x Mathématiques. | |
| 650 | 6 | |a Physique spatiale |x Mathématiques. | |
| 650 | 7 | |a MATHEMATICS |x General. |2 bisacsh | |
| 650 | 7 | |a Geophysics |x Mathematics |2 fast | |
| 776 | 0 | 8 | |i Print version: |a Newman, William I. |t Mathematical methods for geophysics and space physics. |d Princeton, New Jersey ; Oxford : Princeton University Press, [2016] |z 9780691170602 |w (DLC) 2015040966 |w (OCoLC)930462870 |
| 856 | 4 | 0 | |u https://jstor.uam.elogim.com/stable/10.2307/j.ctvc77m0n |z Texto completo |
| 880 | 0 | |6 505-00/(S |a Cover -- Title -- Copyright -- Contents -- Preface -- 1 Mathematical Preliminaries -- 1.1 Vectors, Indicial Notation, and Vector Operators -- 1.2 Cylindrical and Spherical Geometry -- 1.3 Theorems of Gauss, Green, and Stokes -- 1.4 Rotation and Matrix Representation -- 1.5 Tensors, Eigenvalues, and Eigenvectors -- 1.6 Ramp, Heaviside, and Dirac δ Functions -- 1.7 Exercises -- 2 Ordinary Differential Equations -- 2.1 Linear First-Order Ordinary Differential Equations -- 2.2 Second-Order Ordinary Differential Equations -- 2.2.1 Linear Second-Order Differential Equations -- 2.2.2 Green's Functions -- 2.2.3 LRC Circuits and Visco-Elastic Solids -- 2.2.4 Driven Oscillators, Resonance, and Variation of Constants -- 2.2.5 JWKB Method, Riccati Equation, and Adiabatic Invariants -- 2.2.6 Nonlinearity and Perturbation Theory -- 2.3 Special Functions, Laplacians, and Separation of Variables -- 2.3.1 Cartesian Coordinates and Separation of Variables -- 2.3.2 Polar and Cylindrical Coordinates and Separation of Variables -- Bessel and Generating Functions -- 2.3.3 Spherical Coordinates and Separation of Variables -- Green's and Generating Function -- Spherical Harmonics -- 2.4 Nonlinear Ordinary Differential Equations -- 2.4.1 Bullard's Homopolar Dynamo -- 2.4.2 Poincaré-Bendixson Theorem and the Van der Pol Oscillator -- 2.4.3 Lorenz Attractor, Perturbation Theory, and Chaos -- 2.4.4 Fractals -- 2.4.5 Maps and Period Doubling -- 2.5 Exercises -- 3 Evaluation of Integrals and Integral Transform Methods -- 3.1 Integration Methods, Approximations, and Special Cases -- 3.1.1 Elementary Methods and Asymptotic Methods -- 3.1.2 Steepest Descent Methods -- 3.1.3 Special Problems in Geophysics -- Elliptic Integrals -- 3.2 Complex Analysis and Elementary Contour Integration -- 3.3 Fourier Transforms and Analysis Methods. | |
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