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Celestial mechanics is the branch of mathematical astronomy devoted to studying the motions of celestial bodies subject to the Newtonian law of gravitation. This mathematical introductory textbook reveals that even the most basic question in celestial mechanics, the Kepler problem, leads to a cornucopia of geometric concepts: conformal and projective transformations, spherical and hyperbolic geometry, notions of curvature, and the topology of geodesic flows. For advanced undergraduate and beginning graduate students, this book explores the geometric concepts underlying celestial mechanics and is an ideal companion for introductory courses. The focus on the history of geometric ideas makes it perfect supplementary reading for students in elementary geometry and topology. Numerous exercises, historical notes and an extensive bibliography provide all the contextual information required to gain a solid grounding in celestial mechanics.

Celestial mechanics. --- Kepler's laws.

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Nonlinear theories --- Mathematical physics --- Mathematical physics. --- Nonlinear theories. --- Nonlinear problems --- Nonlinearity (Mathematics) --- Calculus --- Mathematical analysis --- Physical mathematics --- Physics --- Mathematics --- applied mathematics --- nonlinear science --- dynamical systems --- celestial mechanics --- graph theory --- fractional calculus

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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

Geophysics --- Cosmic physics --- Physics --- Space sciences --- Mathematics. --- Analytical mechanics. --- Applied mathematics. --- Atmospheric physics. --- Bessel function. --- Bifurcation theory. --- Calculation. --- Calculus of variations. --- Cartesian coordinate system. --- Cauchy's theorem (geometry). --- Celestial mechanics. --- Central limit theorem. --- Chaos theory. --- Classical electromagnetism. --- Classical mechanics. --- Classical physics. --- Convolution theorem. --- Deformation (mechanics). --- Degeneracy (mathematics). --- Diagram (category theory). --- Differential equation. --- Drag (physics). --- Earth science. --- Eigenvalues and eigenvectors. --- Einstein notation. --- Elliptic integral. --- Elliptic orbit. --- Equation. --- Expectation value (quantum mechanics). --- Figure of the Earth. --- Forcing function (differential equations). --- Fourier series. --- Fourier transform. --- Fractal dimension. --- Function (mathematics). --- Gaussian function. --- Geochemistry. --- Geochronology. --- Geodesics in general relativity. --- Geometry. --- Geophysics. --- Gravitational acceleration. --- Gravitational constant. --- Gravitational potential. --- Gravitational two-body problem. --- Hamiltonian mechanics. --- Handbook of mathematical functions. --- Harmonic oscillator. --- Helmholtz equation. --- Hilbert transform. --- Hyperbolic partial differential equation. --- Integral equation. --- Isotope geochemistry. --- Lagrangian (field theory). --- Laplace transform. --- Laplace's equation. --- Laws of thermodynamics. --- Limit (mathematics). --- Line (geometry). --- Lorenz system. --- Mathematical analysis. --- Mathematical geophysics. --- Mathematical physics. --- Newton's law of universal gravitation. --- Newton's laws of motion. --- Newton's method. --- Newtonian dynamics. --- Numerical analysis. --- Numerical integration. --- Operator (physics). --- Orbit. --- Orbital resonance. --- Parseval's theorem. --- Partial differential equation. --- Perturbation theory (quantum mechanics). --- Perturbation theory. --- Planetary body. --- Planetary science. --- Poisson's equation. --- Pole (complex analysis). --- Proportionality (mathematics). --- Quantum mechanics. --- Rotation (mathematics). --- Satellite geodesy. --- Scalar (physics). --- Scientific notation. --- Separatrix (mathematics). --- Sign (mathematics). --- Space physics. --- Statistical mechanics. --- Stokes' theorem. --- Three-dimensional space (mathematics). --- Transformation geometry. --- Trapezoidal rule. --- Truncation error (numerical integration). --- Two-dimensional space. --- Van der Pol oscillator. --- Variable (mathematics). --- Vector space. --- Wave equation.