UID:
almafu_9959237149902883
Format:
1 online resource (xiii, 281 pages) :
,
digital, PDF file(s).
Edition:
1st ed.
ISBN:
1-107-22141-2
,
1-139-12484-6
,
1-283-29859-7
,
9786613298591
,
1-139-12337-8
,
0-511-79443-6
,
1-139-11762-9
,
1-139-12828-0
,
1-139-11326-7
,
1-139-11545-6
Content:
The advent of accessible student computing packages has meant that geophysics students can now easily manipulate datasets and gain first-hand modeling experience - essential in developing an intuitive understanding of the physics of the Earth. Yet to gain a more in-depth understanding of physical theory, and to develop new models and solutions, it is necessary to be able to derive the relevant equations from first principles. This compact, handy book fills a gap left by most modern geophysics textbooks, which generally do not have space to derive all of the important formulae, showing the intermediate steps. This guide presents full derivations for the classical equations of gravitation, gravity, tides, earth rotation, heat, geomagnetism and foundational seismology, illustrated with simple schematic diagrams. It supports students through the successive steps and explains the logical sequence of a derivation - facilitating self-study and helping students to tackle homework exercises and prepare for exams.
Note:
Title from publisher's bibliographic system (viewed on 05 Oct 2015).
,
Cover; Title; Copyright; Dedication; Contents; Preface; Acknowledgments; 1 Mathematical background; 1.1 Cartesian and spherical coordinates; 1.2 Complex numbers; 1.3 Vector relationships; 1.3.1 Scalar and vector products; 1.3.2 Vector differential operations; 1.4 Matrices and tensors; 1.4.1 The rotation matrix; 1.4.2 Eigenvalues and eigenvectors; 1.4.3 Tensor notation; 1.4.4 Rotation of coordinate axes; 1.4.5 Vector differential operations in tensor notation; 1.5 Conservative force, field, and potential; 1.6 The divergence theorem (Gauss's theorem); 1.7 The curl theorem (Stokes' theorem)
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1.8 Poisson's equation1.9 Laplace's equation; 1.10 Power series; 1.10.1 MacLaurin series; 1.10.2 Taylor series; 1.10.3 Binomial series; Finite series; Infinite series; 1.10.4 Linear approximations; 1.11 Leibniz's rule; 1.12 Legendre polynomials; 1.13 The Legendre differential equation; 1.13.1 Orthogonality of the Legendre polynomials; 1.13.2 Normalization of the Legendre polynomials; 1.14 Rodrigues' formula; 1.15 Associated Legendre polynomials; 1.15.1 Orthogonality of associated Legendre polynomials; 1.15.2 Normalization of associated Legendre polynomials; 1.16 Spherical harmonic functions
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1.16.1 Normalization of spherical harmonic functions1.16.2 Zonal, sectorial, and tesseral spherical harmonics; 1.17 Fourier series, Fourier integrals, and Fourier transforms; 1.17.1 Fourier series; 1.17.2 Fourier integrals and Fourier transforms; 1.17.3 Fourier sine and cosine transforms; Further reading; 2 Gravitation; 2.1 Gravitational acceleration and potential; 2.2 Kepler's laws of planetary motion; 2.2.1 Kepler's Second Law; 2.2.2 Kepler's First Law; 2.2.3 Kepler's Third Law; 2.3 Gravitational acceleration and the potential of a solid sphere
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2.3.1 Outside a solid sphere, using Laplace's equation2.3.2 Inside a solid sphere, using Poisson's equation; 2.4 Laplace's equation in spherical polar coordinates; 2.4.1 Azimuthal (longitudinal) solution; 2.4.2 Polar (latitudinal) solution for rotational symmetry; 2.4.3 Radial solution; 2.4.4 Solution of Laplace's equation for rotational symmetry; 2.4.5 General solution of Laplace's equation; 2.5 MacCullagh's formula for the gravitational potential; 2.5.1 Gravitational potential of a spheroid; 2.5.2 MacCullagh's formula and the figure of the Earth; Further reading; 3 Gravity
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3.1 The ellipticity of the Earth's figure3.2 The geopotential; 3.2.1 Gravitational potential; 3.2.2 Centrifugal potential; 3.3 The equipotential surface of gravity; 3.3.1 Relationship of J2, J4, f, and m; 3.3.2 Inferred increase of density with depth in the Earth; 3.4 Gravity on the reference spheroid; 3.4.1 Polar component of gravity; 3.4.2 Radial component of gravity; 3.4.3 Variation of reference gravity with geocentric latitude; 3.4.4 Clairaut's formula; 3.5 Geocentric and geographic latitude; 3.5.1 Normal gravity on the reference ellipsoid; 3.6 The geoid
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3.6.1 The potential of a geoid undulation
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English
Additional Edition:
ISBN 0-521-18377-4
Additional Edition:
ISBN 1-107-00584-1
Language:
English
Subjects:
Physics
URL:
https://doi.org/10.1017/CBO9780511794438
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