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Physical scientists are problem solvers. They are comfortable "doing" science: they find problems, solve them, and explain their solutions. Roger Newton believes that his fellow physicists might be too comfortable with their roles as solvers of problems. He argues that physicists should spend more time thinking about physics. If they did, he believes, they would become even more skilled at solving problems and "doing" science. As Newton points out in this thought-provoking book, problem solving is always influenced by the theoretical assumptions of the problem solver. Too often, though, he believes, physicists haven't subjected their assumptions to thorough scrutiny. Newton's goal is to provide a framework within which the fundamental theories of modern physics can be explored, interpreted, and understood. "Surely physics is more than a collection of experimental results, assembled to satisfy the curiosity of appreciative experts," Newton writes. Physics, according to Newton, has moved beyond the describing and naming of curious phenomena, which is the goal of some other branches of science. Physicists have spent a great part of the twentieth century searching for explanations of experimental findings. Newton agrees that experimental facts are vital to the study of physics, but only because they lead to the development of a theory that can explain them. Facts, he argues, should undergird theory. Newton's explanatory sweep is both broad and deep. He covers such topics as quantum mechanics, classical mechanics, field theory, thermodynamics, the role of mathematics in physics, and the concepts of probability and causality. For Newton the fundamental entity in quantum theory is the field, from which physicists can explain the particle-like and wave-like properties that are observed in experiments. He grounds his explanations in the quantum field. Although this is not designed as a stand-alone textbook, it is essential reading for advanced undergraduate students, graduate students, professors, and researchers. This is a clear, concise, up-to-date book about the concepts and theories that underlie the study of contemporary physics. Readers will find that they will become better-informed physicists and, therefore, better thinkers and problem solvers too.

Physics --- Philosophy. --- Bayesian probabilities. --- Bell experiments. --- Copenhagen interpretation. --- Dirac equation. --- EPR experiment. --- Gamma-space. --- Higgs boson. --- KdV equation. --- Kuhn, Thomas. --- Lorentz transformation. --- Newtonian laws. --- absorber theory. --- accidental degeneracy. --- action at a distance. --- active tranformation. --- angular momentum. --- anthropic principle. --- associated production. --- axial vector. --- beta decay. --- butterfly effect. --- causality. --- coarse graining. --- configuration space. --- conventionalist stratagem. --- cosmological constant. --- density operator. --- deterministic chaos. --- electromagnetic radiation. --- exponential decay law. --- ferromagnetism. --- fluid dynamics. --- gauge invariance. --- gravitational constant. --- group representations. --- harmonic oscillator. --- idealism. --- infrared divergencies. --- integral equations. --- intrinsic parity. --- lattice field theory. --- laws of motion. --- local theories. --- macrostate. --- microstates. --- nuclear physics. --- paradigm shift. --- paradigm. --- perturbation theory. --- predissociation. --- probability. --- propensity. --- pseudo-scalar.

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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.

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For centuries, astronomers have been interested in the motions of the planets and in methods to calculate their orbits. Since Newton, mathematicians have been fascinated by the related N-body problem. They seek to find solutions to the equations of motion for N masspoints interacting with an inverse-square-law force and to determine whether there are quasi-periodic orbits or not. Attempts to answer such questions have led to the techniques of nonlinear dynamics and chaos theory. In this book, a classic work of modern applied mathematics, Jürgen Moser presents a succinct account of two pillars of the theory: stable and chaotic behavior. He discusses cases in which N-body motions are stable, covering topics such as Hamiltonian systems, the (Moser) twist theorem, and aspects of Kolmogorov-Arnold-Moser theory. He then explores chaotic orbits, exemplified in a restricted three-body problem, and describes the existence and importance of homoclinic points. This book is indispensable for mathematicians, physicists, and astronomers interested in the dynamics of few- and many-body systems and in fundamental ideas and methods for their analysis. After thirty years, Moser's lectures are still one of the best entrées to the fascinating worlds of order and chaos in dynamics.

Celestial mechanics. --- Accuracy and precision. --- Action-angle coordinates. --- Analytic function. --- Bounded variation. --- Calculation. --- Chaos theory. --- Coefficient. --- Commutator. --- Constant term. --- Continuous embedding. --- Continuous function. --- Coordinate system. --- Countable set. --- Degrees of freedom (statistics). --- Degrees of freedom. --- Derivative. --- Determinant. --- Differentiable function. --- Differential equation. --- Dimension (vector space). --- Discrete group. --- Divergent series. --- Divisor. --- Duffing equation. --- Eigenfunction. --- Eigenvalues and eigenvectors. --- Elliptic orbit. --- Energy level. --- Equation. --- Ergodic theory. --- Ergodicity. --- Euclidean space. --- Even and odd functions. --- Existence theorem. --- Existential quantification. --- First-order partial differential equation. --- Forcing function (differential equations). --- Fréchet derivative. --- Gravitational constant. --- Hamiltonian mechanics. --- Hamiltonian system. --- Hessian matrix. --- Heteroclinic orbit. --- Homoclinic orbit. --- Hyperbolic partial differential equation. --- Hyperbolic set. --- Initial value problem. --- Integer. --- Integrable system. --- Integration by parts. --- Invariant manifold. --- Inverse function. --- Invertible matrix. --- Iteration. --- Jordan curve theorem. --- Klein bottle. --- Lie algebra. --- Linear map. --- Linear subspace. --- Linearization. --- Maxima and minima. --- Monotonic function. --- Newton's method. --- Nonlinear system. --- Normal bundle. --- Normal mode. --- Open set. --- Parameter. --- Partial differential equation. --- Periodic function. --- Periodic point. --- Perturbation theory (quantum mechanics). --- Phase space. --- Poincaré conjecture. --- Polynomial. --- Probability theory. --- Proportionality (mathematics). --- Quasiperiodic motion. --- Rate of convergence. --- Rational dependence. --- Regular element. --- Root of unity. --- Series expansion. --- Sign (mathematics). --- Smoothness. --- Special case. --- Stability theory. --- Statistical mechanics. --- Structural stability. --- Symbolic dynamics. --- Symmetric matrix. --- Tangent space. --- Theorem. --- Three-body problem. --- Uniqueness theorem. --- Unitary matrix. --- Variable (mathematics). --- Variational principle. --- Vector field. --- Zero of a function.