A Modern Introduction to Classical Electrodynamics
A Modern Introduction to Classical Electrodynamics

Author: Michele Maggiore

Publisher: Oxford University Press

Published: 2023-08-28

Total Pages: 465

ISBN-13: 0192867423

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A Modern Introduction to Classical Electrodynamics is suitable for undergraduate students with some background knowledge of the subject and for graduate students, while more advanced topics make it a useful resource for PhD students and researchers. The book places much emphasis on the formal structure of the theory; beginning with Maxwell's equations in the vacuum, it emphasises the central role of gauge invariance and Special Relativity. After introductory chapters which include rederivations of elementary results of electrostatics and magnetostatics, and the multipole expansion, Special Relativity is introduced, and most of the subsequent derivations are performed using covariant formalism and gauge potentials, allowing for greater conceptual and technical clarity compared to more traditional treatments. The second part of the book covers electrodynamics in material media. This includes Maxwell's equations in material media, frequency dependent response of materials and Kramers-Kronig relations, electromagnetic waves in materials, and scattering of electromagnetic radiation. Finally, the text also includes advanced topics, such as the field-theoretical treatment of classical electrodynamics as a modern treatment of radiation reaction. These parts are meant for the advanced reader and are clearly marked, and can be skipped without loss of continuity.

Special Relativity
Special Relativity

Author: N.M.J. Woodhouse

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 214

ISBN-13: 1447100832

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This book provides readers with the tools needed to understand the physical basis of special relativity and will enable a confident mathematical understanding of Minkowski's picture of space-time. It features a large number of examples and exercises, ranging from the rather simple through to the more involved and challenging. Coverage includes acceleration and tensors and has an emphasis on space-time diagrams.

SEC Docket
SEC Docket

Author: United States. Securities and Exchange Commission

Publisher:

Published: 1982

Total Pages: 1116

ISBN-13:

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Classical And Computational Solid Mechanics
Classical And Computational Solid Mechanics

Author: Pin Tong

Publisher: World Scientific Publishing Company

Published: 2001-06-29

Total Pages: 952

ISBN-13: 9813102829

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This invaluable book has been written for engineers and engineering scientists in a style that is readable, precise, concise, and practical. It gives first priority to the formulation of problems, presenting the classical results as the gold standard, and the numerical approach as a tool for obtaining solutions. The classical part is a revision of the well-known text Foundations of Solid Mechanics, with a much-expanded discussion on the theories of plasticity and large elastic deformation with finite strains. The computational part is all new and is aimed at solving many major linear and nonlinear boundary-value problems.

Principles of Fourier Analysis
Principles of Fourier Analysis

Author: Kenneth B. Howell

Publisher: CRC Press

Published: 2016-12-12

Total Pages: 805

ISBN-13: 1498734081

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Fourier analysis is one of the most useful and widely employed sets of tools for the engineer, the scientist, and the applied mathematician. As such, students and practitioners in these disciplines need a practical and mathematically solid introduction to its principles. They need straightforward verifications of its results and formulas, and they need clear indications of the limitations of those results and formulas. Principles of Fourier Analysis furnishes all this and more. It provides a comprehensive overview of the mathematical theory of Fourier analysis, including the development of Fourier series, "classical" Fourier transforms, generalized Fourier transforms and analysis, and the discrete theory. Much of the author's development is strikingly different from typical presentations. His approach to defining the classical Fourier transform results in a much cleaner, more coherent theory that leads naturally to a starting point for the generalized theory. He also introduces a new generalized theory based on the use of Gaussian test functions that yields an even more general -yet simpler -theory than usually presented. Principles of Fourier Analysis stimulates the appreciation and understanding of the fundamental concepts and serves both beginning students who have seen little or no Fourier analysis as well as the more advanced students who need a deeper understanding. Insightful, non-rigorous derivations motivate much of the material, and thought-provoking examples illustrate what can go wrong when formulas are misused. With clear, engaging exposition, readers develop the ability to intelligently handle the more sophisticated mathematics that Fourier analysis ultimately requires.

The Application of Mathematics to the Sciences of Nature
The Application of Mathematics to the Sciences of Nature

Author: Claudio Pellegrini

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 292

ISBN-13: 1461505917

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The historical and epistemological reflection on the applications of mathematical techniques to the Sciences of Nature - physics, biology, chemistry, and geology - today generates attention and interest because of the increasing use of mathematical models in all sciences and their high level of sophistication. The goal of the meeting and the papers collected in this proceedings volume is to give physicists, biologists, mathematicians, and historians of science the opportunity to share information on their work and reflect on the and mathematical models are used in the natural sciences today and in way mathematics the past. The program of the workshop combines the experience of those working on current scientific research in many different fields with the historical analysis of previous results. We hope that some novel interdisciplinary, philosophical, and epistemological considerations will follow from the two aspects of the workshop, the historical and the scientific· This proceedings includes papers presented at the meeting and some of the results of the discussions that took place during the workshop. We wish to express our gratitude to Sergio Monteiro for all his work, which has been essential for the successful publication of these proceedings. We also want to thank the editors of Kluwer AcademidPlenum Publishers for their patience and constant help, and in particular Beth Kuhne and Roberta Klarreich. Our thanks to the fallowing institutions: -Amministrazione Comunale di Arcidosso -Comunita Montana del Monte Amiata ·Center for the History of Physics, UCLA -Centre F.

Classical and Computational Solid Mechanics
Classical and Computational Solid Mechanics

Author: Yuan-cheng Fung

Publisher: World Scientific

Published: 2001

Total Pages: 954

ISBN-13: 9789810241247

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This invaluable book has been written for engineers and engineering scientists in a style that is readable, precise, concise, and practical. It gives first priority to the formulation of problems, presenting the classical results as the gold standard, and the numerical approach as a tool for obtaining solutions. The classical part is a revision of the well-known text Foundations of Solid Mechanics, with a much-expanded discussion on the theories of plasticity and large elastic deformation with finite strains. The computational part is all new and is aimed at solving many major linear and nonlinear boundary-value problems.

Topics in Applied Continuum Mechanics
Topics in Applied Continuum Mechanics

Author: J.L. Zeman

Publisher: Springer Science & Business Media

Published: 2013-11-11

Total Pages: 230

ISBN-13: 3709141885

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THE FOUNDATIONS OF THERMOELASTICITY-EXPERIMENTS AND THEORY (A. PHILLIPS) 1. Introduction 2. The initial yield surface 4 3. The subsequent yield surface 6 4. Some theoretical consequences 10 References 13 ON THE PHYSICS AND MATHEMATICS OF SELF-STRESSES (E. KRONER) 1. Introduction 22 2. The physical origin of the self-stresses 23 3. Formulation of the mathematical problem of self-stresses 27 4. The method of modified Green's functions 30 5. Concluding remarks 35 References 38 DISTORTION IN MICROPOLAR ELASTICITY (W. NOWACKI) 1. Fundamental relations and equations 39 2. Principle of virtual work 42 3. Theorem of minimum of the complimentary work 43 • 4. Reciprocity theorem 44 5. Equations in displacements and rotations 47 6. Compatibility equations 51 References 57 THE YIELD CRITERION IN THE GENERAL CASE OF NONHOMOGENEOUS STRESS AND DEFORMATION FIELDS (J. A. KONIG and W. OLSZAK) 1. Introduction 58 2. The plasticity condition 61 3. Special cases of the yield condition 62 4. Example: Pure bending 63 5. Criteria for neutral, passive and active processes 65 VI 6. The flow law 67 References 69 ELECTRO-MAGNETO-ELASTICITY (J. B. ALBLAS) 1. Introduction 71 2. Balance equations 77 3. The jump and boundary conditions 85 4. The constitutive equations 91 5. Linearization of the magnetic problem 95 6. Magneto-elastic waves in the infinite space and in the half-space 105 References 114 PLASTICITY AND CREEP THEORY IN ENGINEERING MECHANICS (J. F • BESSE LING) 1. Introduction 115 2. Limit analysis 117 3.

The Mathematics of Fluid Flow Through Porous Media
The Mathematics of Fluid Flow Through Porous Media

Author: Myron B. Allen, III

Publisher: John Wiley & Sons

Published: 2021-06-08

Total Pages: 226

ISBN-13: 1119663873

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Master the techniques necessary to build and use computational models of porous media fluid flow In The Mathematics of Fluid Flow Through Porous Media, distinguished professor and mathematician Dr. Myron B. Allen delivers a one-stop and mathematically rigorous source of the foundational principles of porous medium flow modeling. The book shows readers how to design intelligent computation models for groundwater flow, contaminant transport, and petroleum reservoir simulation. Discussions of the mathematical fundamentals allow readers to prepare to work on computational problems at the frontiers of the field. Introducing several advanced techniques, including the method of characteristics, fundamental solutions, similarity methods, and dimensional analysis, The Mathematics of Fluid Flow Through Porous Media is an indispensable resource for students who have not previously encountered these concepts and need to master them to conduct computer simulations. Teaching mastery of a subject that has increasingly become a standard tool for engineers and applied mathematicians, and containing 75 exercises suitable for self-study or as part of a formal course, the book also includes: A thorough introduction to the mechanics of fluid flow in porous media, including the kinematics of simple continua, single-continuum balance laws, and constitutive relationships An exploration of single-fluid flows in porous media, including Darcy’s Law, non-Darcy flows, the single-phase flow equation, areal flows, and flows with wells Practical discussions of solute transport, including the transport equation, hydrodynamic dispersion, one-dimensional transport, and transport with adsorption A treatment of multiphase flows, including capillarity at the micro- and macroscale Perfect for graduate students in mathematics, civil engineering, petroleum engineering, soil science, and geophysics, The Mathematics of Fluid Flow Through Porous Media also belongs on the bookshelves of any researcher who wishes to extend their research into areas involving flows in porous media.