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Vector Analysis and the Theory of Relativity
This advanced text provides a rigorous mathematical treatment of the calculus of vectors and tensors, as well as its applications to the theory of relativity and other areas of theoretical physics. Written by Francis Dominic Murnaghan, a prominent mathematician and physicist of the early 20th century, it remains an important resource for graduate students and researchers in mathematics and physics. This book will appeal to anyone interested in the history of mathematics and the foundations of modern physics. 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. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Evaluation of the Probability Integral to High Precision
The 'converging factor' for an asymptotic series representing a function f(x) is that number by which the (n + 1) term of the series must be multiplied so that the result of adding this product to the sum of the first n terms will be f(x). The determination to high precision of this factor for the asymptotic series representing the probability integral is described. Tables of this factor to 63 decimal places are included for n ranging from 2 to 64. (Author).
Lectures on Applied Mathematics
Contents: The Lagrangian function and the parametric integrand Extremal curves; The Euler-Lagrange equation Lagrangian functions which are linear in x sub t The Legendre condition for a minimal curve Proof of the Legendre condition Constrained problems; The Hamilton canonical equations The reciprocity between L and H; The transversality conditions Extremal fields; The Hilbert invariant integral The Weierstrass E-function; Positively regular problems A simple example of the construction of an extremal field; Rayleigh quotients and the method of Rayleigh-Ritz The principle of maupertuis; The propagation of waves Problems whose Lagrangian functions involve derivatives of higher order than the first Multiple-Integral problems of the calculus of variations Constrained problems; Characteristic numbers Multiple-integral problems whose Langrangian functions involve derivatives of higher order than the first The Courant maximum-minimum principle.
Recent Advances in Plasmonic Probes
This book gives a comprehensive overview of recent advancements in both theory and practical implementation of plasmonic probes. Encompassing multiple disciplines, the field of plasmonics provides a versatile and flexible platform for nanoscale sensing and imaging. Despite being a relatively young field, plasmonic probes have come a long way, with applications in chemical, biological, civil, and architectural fields as well as enabling many analytical schemes such as immunoassay, biomarkers, environmental indexing, and water quality sensing, to name but a few. The objective of the book is to present in-depth analysis of the theory and applications of novel probes based on plasmonics, with a broad selection of specially-invited chapters on the development, fabrication, functionalization, and implementation of plasmonic probes as well as their integration with current technologies and future outlook. This book is designed to cater to the needs of novice, seasoned researchers and practitioners in academia and industry, as well as medical and environmental fields.
