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Reprint of the original, first published in 1873.
Excerpt from An Essay on the Mathematical Principles of Physics: With Reference To; The Study The contents of this work are devoted almost exclusively to discussing the principles and the reasoning appropriate to the theoretical department of Natural Philosophy, and the mutual relation between this and the experimental department. The discoveries in recent times of new facts and physical laws by experimental means have been so remarkable and abundant, and have given rise to so much speculation, that there seemed to be reason to apprehend that the part of philosophy which is properly theoretical might be either set aside or wholly misunderstood. The purpose of this Essay is to endeavour to counteract this tendency. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
Excerpt from An Essay on the Mathematical Principles of Physics: With Reference To; The Study With the view of assisting to form a judgment on its essential character, and on the necessity arising therefrom for adopting it, I propose to make in this Introduction some brief remarks on the antecedent history and actual state of the theoretical department of Physics. All theoretical investigation is carried on by means of calculation, and the calculation is not simply algebraic, but consists essentially of the formation, according to given conditions, of differential equations, and the solutions of them by the rules of analysis. Newton is therefore to be regarded as the founder of theoretical philosophy, having in his Principia, by reasoning of which there had been no previous example, virtually formed and solved the differential equations which are necessary for calculating the motions of the Moon, the Earth, and the Planets with their satellites. And because these calculations rested on the hypothesis of an attractive force varying with distance according to the law of the inverse square, the motions, by being thus calculated, were referred to an operative cause. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
You will marvel at these principles of mathematical physics written by Henri Poincare, one of the most famous French mathematicians. Contents: History of Mathematical Physics, The Present Crisis of Mathematical Physics, The Future of Mathematical Physics.
This Is A New Release Of The Original 1881 Edition.
A modern classic, this clearly written, incisive textbook provides a comprehensive, detailed survey of the functions of mathematical physics, a field of study straddling the somewhat artificial boundary between pure and applied mathematics. In the 18th and 19th centuries, the theorists who devoted themselves to this field — pioneers such as Gauss, Euler, Fourier, Legendre, and Bessel — were searching for mathematical solutions to physical problems. Today, although most of the functions have practical applications, in areas ranging from the quantum-theoretical model of the atom to the vibrating membrane, some, such as those related to the theory of discontinuous groups, still remain of purely mathematical interest. Chapters One and Two examine orthogonal polynomials, with sections on such topics as the recurrence formula, the Christoffel-Darboux formula, the Weierstrass approximation theorem, and the application of Hermite polynomials to quantum mechanics. Chapter Three is devoted to the principal properties of the gamma function, including asymptotic expansions and Mellin-Barnes integrals. Chapter Four covers hypergeometric functions, including a review of linear differential equations with regular singular points, and a general method for finding integral representations. Chapters Five and Six are concerned with the Legendre functions and their use in the solutions of Laplace's equation in spherical coordinates, as well as problems in an n-dimension setting. Chapter Seven deals with confluent hypergeometric functions, and Chapter Eight examines, at length, the most important of these — the Bessel functions. Chapter Nine covers Hill's equations, including the expansion theorems.