Category: Mathematical Physics

By Vladimir I. Arnold, T. Damm

Nach seinem bekannten und viel verwendeten Buch ?ber gew?hnliche Differentialgleichungen widmet sich der ber?hmte Mathematiker Vladimir Arnold nun den partiellen Differentialgleichungen in einem neuen Lehrbuch. In seiner unnachahmlich eleganten paintings f?hrt er ?ber einen geometrischen, anschaulichen Weg in das Thema ein, und erm?glicht den Lesern so ein vertieftes Verst?ndnis der Natur der partiellen Differentialgleichungen. F?r Studierende der Mathematik und Physik ist dieses Buch ein Muss.

Wie alle B?cher Vladimir Arnolds ist dieses Buch voller geometrischer Erkenntnisse. Arnold illustriert jeden Grundsatz mit einer Abbildung. Das Buch behandelt die elementarsten Teile des Fachgebiets and beschr?nkt sich haupts?chlich auf das Cauchy-Problem und das Neumann-Problems f?r die klassischen Lineargleichungen der mathematischen Physik, insbesondere auf die Laplace-Gleichung und die Wellengleichung, wobei die W?rmeleitungsgleichung und die Korteweg-de-Vries-Gleichung aber ebenfalls diskutiert werden. Die physikalische instinct wird besonders hervorgehoben. Eine gro?e Anzahl von Problemen ist ?bers ganze Buch verteilt, und ein ganzer Satz von Aufgaben findet sich am Ende.

Was dieses Buch so einzigartig macht, ist das besondere expertise Arnolds, ein Thema aus einer neuen, frischen Perspektive zu beleuchten. Er l?ftet gerne den Schleier der Verallgemeinerung, der so viele mathematische Texte umgibt, und enth?llt die im wesentlichen einfachen, intuitiven Ideen, die dem Thema zugrunde liegen. Das kann er besser als jeder andere mathematische Autor.

By S. L. Sobolev

This ebook offers the speculation of services areas, referred to now as Sobolev areas, that are regular within the idea of partial differential equations, mathematical physics, and various functions. the writer additionally treats the variational approach to answer of boundary price difficulties for elliptic equations, together with people with boundary stipulations given on manifolds of other dimensions. moreover, the idea of the Cauchy challenge for second-order hyperbolic equations with variable coefficients is studied. The e-book is meant for researchers in arithmetic and mathematical physics and will be invaluable to undergraduate and graduate scholars taking complicated classes in those components.

By Michael Aizenman, Simone Warzel

This booklet offers an advent to the mathematical idea of affliction results on quantum spectra and dynamics. subject matters coated variety from the fundamental idea of spectra and dynamics of self-adjoint operators via Anderson localization—presented right here through the fractional second strategy, as much as contemporary effects on resonant delocalization. 

The subject's multifaceted presentation is equipped into seventeen chapters, every one thinking about both a particular mathematical subject or on an indication of the theory's relevance to physics, e.g., its implications for the quantum corridor influence. The mathematical chapters contain normal relatives of quantum spectra and dynamics, ergodicity and its implications, equipment for developing spectral and dynamical localization regimes, functions and homes of the golf green functionality, its relation to the eigenfunction correlator, fractional moments of Herglotz-Pick features, the part diagram for tree graph operators, resonant delocalization, the spectral records conjecture, and similar results. 

The textual content comprises notes from classes that have been offered on the authors' respective associations and attended by way of graduate scholars and postdoctoral researchers.

Readership
Graduate scholars and researchers drawn to random operator concept.

By Miki Wadati

This quantity includes chosen papers of Dr Morikazu Toda. The papers are prepared in chronological order of publishing dates. between Dr Toda's many contributions, his works on drinks and nonlinear lattice dynamics will be pointed out. The one-dimensional lattice the place nearest neighboring debris have interaction via an exponential capability is named the Toda lattice that is a miracle and certainly a jewel in theoretical physics. The papers during this quantity could be grouped into 5 topics: statistical mechanics, conception of drinks and ideas, lattice dynamics, Toda lattice and soliton idea and its purposes.

By Zhi Zong

The e-book used to be very attention-grabbing for me as my PhD thesis are attached with differential quadrature (DQ). It comprises really new informations approximately improveing of the DQM. It base on authors articles from numerous final years. The detrimental is that the articles are shorten, so occasionally you'll want to search for them within the book info base to discover information. occasionally it isn't so transparent clarify from the place the autors receive there formulation [there can be extra references to literature] - occasionally it really is attainable to discover theorems that healthy even beter to the topic. besides i'm more than happy to have this ebook because it offers me much convenient informations approximately instructions of the DQ suggestion increase.

By J. H. Heinbockel

Creation to Tensor Calculus and Continuum Mechanics is a complicated collage point arithmetic textual content. the 1st a part of the textual content introduces simple ideas, notations and operations linked to the topic quarter of tensor calculus. the fabric offered is built at a gradual velocity with a close clarification of the numerous tensor operations. the 1st 1/2 the textual content concludes with an creation to the appliance of tensor suggestions to differential geometry and relativity. the second one 1/2 the textual content provides functions of tensors to parts from continuum mechanics. Tensor calculus is utilized to the components of dynamics, elasticity, fluids, electrical energy and magnetism. a number of the simple equations from physics, engineering and technology are built which makes the textual content a good reference paintings. the second one half the textual content concludes with an advent to quaternions, multivectors and Clifford algebra. There are 4 Appendices. The Appendix A includes devices of measurements from the Système foreign d'Unitès besides a few chosen actual con stants. The Appendix B encompasses a directory of Christoffel symbols of the second one sort linked to quite a few coordinate structures. The Appendix C is a precis of use ful vector identities. The Appendix D comprises options to chose routines. The textual content has various illustrative labored examples and over 450 routines.

By Kerson Huang

Not like so much different texts at the topic, this transparent, concise creation to the idea of microscopic our bodies treats the trendy concept of serious phenomena. presents updated assurance of contemporary significant advances, together with a self-contained description of thermodynamics and the classical kinetic idea of gases, fascinating functions equivalent to superfluids and the quantum corridor impression, numerous present learn functions, The final 3 chapters are dedicated to the Landau-Wilson method of serious phenomena. Many new difficulties and illustrations were further to this version.

By W M Honig

This paintings provides mathematical innovations: non-standard logics and non-standard metrics. The suggestions are utilized to present difficulties in physics, comparable to the hidden variable challenge and the neighborhood and nonlocal difficulties.

By Descartes Rene

By J. R. Dorfman

This publication presents an creation to nonequilibrium statistical mechanics utilized to principles in chaotic dynamics. the writer illustrates how innovations in statistical mechanics can be utilized to calculate amounts which are necessary to figuring out the chaotic habit of fluid structures. starting with vital heritage info, the amount is going directly to introduce easy innovations of dynamical platforms thought via basic examples prior to explaining complex subject matters akin to SRB and Gibbs measures. it will likely be of significant curiosity to graduate scholars and researchers in condensed topic physics, nonlinear technological know-how, theoretical physics, arithmetic, and theoretical chemistry