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Principles of Mechanics
This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Tensor Calculus
Fundamental introduction of absolute differential calculus and for those interested in applications of tensor calculus to mathematical physics and engineering. Topics include spaces and tensors; basic operations in Riemannian space, curvature of space, more.
Principles Of Mechanics
In a sense this is a book for the beginner in mechanics, but in another sense it is not. From the time we make our first movements, crude ideas on force, mass, and motion take shape in our minds. This body of ideas might be reduced to some order at high school as crude ideas of geometry are reduced to order, but that is not the educational practice in North America. There is rather an accumulation of miscellaneous facts bearing on mechanics, some mathematical and some experimental, until a state is reached where the student is in danger of being repelled by the subject, as a chaotic jumble which is neither mathematics nor physics. This book is intended primarily for students at this stage. T...
Geometrical Optics
It is by no means easy for the applied mathematician to decide how much importance he should attach to the more abstract and aesthetic side of his work ... To all appearances, Sir William Rowan Hamilton (1850-1865) attached little importance to the practical applications of his method, and it was only with the publication of his Mathematical Papers that it was possible to form a more correct and balanced judgement of Hamilton as an applied mathematician.
Relativity
Essential tensor formulae for Riemannian space-time -- The world-function [omega] -- Chronometry in Riemannian space-time -- The material continuum -- Some properties of Einstein fields -- Integral conservation laws and equations of motion -- Fields with spherical symmetry -- Some special universes -- Gravitational waves -- Electromagnetism -- Geometrical optics.
Relativistic Geodesy
Due to steadily improving experimental accuracy, relativistic concepts – based on Einstein’s theory of Special and General Relativity – are playing an increasingly important role in modern geodesy. This book offers an introduction to the emerging field of relativistic geodesy, and covers topics ranging from the description of clocks and test bodies, to time and frequency measurements, to current and future observations. Emphasis is placed on geodetically relevant definitions and fundamental methods in the context of Einstein’s theory (e.g. the role of observers, use of clocks, definition of reference systems and the geoid, use of relativistic approximation schemes). Further, the appl...
Relativity
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A Half-Century of Physical Asymptotics and Other Diversions
Michael Berry is a theoretical physicist who has contributed to a wide variety of areas in quantum mechanics, optics and related mathematics, linked by the geometrical aspects of waves, especially phase. This collection of his selected published and unpublished papers, reviews, tributes to other scientists, speeches and other works ranges from the technical to the popular. It is organized by the themes of his significant scientific contributions. Detailed introductions emphasize the rich connections between the different themes. An essential read for physicists, mathematicians, students and philosophers of science.
The Hypercircle in Mathematical Physics
This 1957 book was written to help physicists and engineers solve partial differential equations subject to boundary conditions. The complexities of calculation are illuminated throughout by simple, intuitive geometrical pictures. This book will be of value to anyone with an interest in solutions to boundary value problems in mathematical physics.
