Author: Vladimir I. Arnold

Publisher: Springer-Verlag

ISBN: 3540350314

Category: Mathematics

Page: 174

View: 562

Nach seinem bekannten und viel verwendeten Buch über gewöhnliche Differentialgleichungen widmet sich der berühmte Mathematiker Vladimir Arnold nun den partiellen Differentialgleichungen in einem neuen Lehrbuch. In seiner unnachahmlich eleganten Art führt er über einen geometrischen, anschaulichen Weg in das Thema ein, und ermöglicht den Lesern so ein vertieftes Verständnis der Natur der partiellen Differentialgleichungen. Für Studierende der Mathematik und Physik ist dieses Buch ein Muss. Wie alle Bücher Vladimir Arnolds ist dieses Buch voller geometrischer Erkenntnisse. Arnold illustriert jeden Grundsatz mit einer Abbildung. Das Buch behandelt die elementarsten Teile des Fachgebiets and beschränkt sich hauptsächlich auf das Cauchy-Problem und das Neumann-Problems für die klassischen Lineargleichungen der mathematischen Physik, insbesondere auf die Laplace-Gleichung und die Wellengleichung, wobei die Wärmeleitungsgleichung und die Korteweg-de-Vries-Gleichung aber ebenfalls diskutiert werden. Die physikalische Intuition wird besonders hervorgehoben. Eine große Anzahl von Problemen ist übers ganze Buch verteilt, und ein ganzer Satz von Aufgaben findet sich am Ende. Was dieses Buch so einzigartig macht, ist das besondere Talent Arnolds, ein Thema aus einer neuen, frischen Perspektive zu beleuchten. Er lüftet gerne den Schleier der Verallgemeinerung, der so viele mathematische Texte umgibt, und enthüllt die im wesentlichen einfachen, intuitiven Ideen, die dem Thema zugrunde liegen. Das kann er besser als jeder andere mathematische Autor.
Read More

Physics and Engineering at the Nanoscale

Author: John Weiner,Frederico Nunes

Publisher: Oxford University Press

ISBN: 0198796668

Category:

Page: 448

View: 8936

Light-matter interaction is pervasive throughout the disciplines of optical and atomic physics, condensed matter physics, electrical engineering, and now increasingly in biology and medicine with frequency and length scales extending over many orders of magnitude. Deep earth and sea communications use frequencies of a few tens of Hz, and X-ray imaging requires sources oscillating at hundreds of petaHz. This book provides advanced undergraduates, graduate students and researchers from diverse disciplines with the principal tools required to understand and contribute to rapidly advancing developments in light-matter interaction, centred at optical frequencies and length scales from a few hundred nanometres to a few hundredths of a nanometre. This book deploys an arsenal of powerful analytic tools to render this multidisciplinary subject in unique form, not encountered in standard Physics or Electrical Engineering text books. This new edition has been substantially expanded with almost 200 pages of new material. Several new and extended chapters treat momentum flow between fields and matter, metamaterials, and atom-optical forces applied to atomic and molecular cooling and trapping.
Read More

Author: Arnold Sommerfeld

Publisher: Springer Science & Business Media

ISBN: 0817681965

Category: Mathematics

Page: 157

View: 624

A. Sommerfeld's "Mathematische Theorie der Diffraction" marks a milestone in optical theory, full of insights that are still relevant today. In a stunning tour de force, Sommerfeld derives the first mathematically rigorous solution of an optical diffraction problem. Indeed, his diffraction analysis is a surprisingly rich and complex mix of pure and applied mathematics, and his often-cited diffraction solution is presented only as an application of a much more general set of mathematical results. This complete translation, reflecting substantial scholarship, is the first publication in English of Sommerfeld's original work. The extensive notes by the translators are rich in historical background and provide many technical details for the reader.
Read More

Author: Michael Griebel,Marc Alexander Schweitzer

Publisher: Springer Science & Business Media

ISBN: 3642329799

Category: Computers

Page: 244

View: 5464

Meshfree methods are a modern alternative to classical mesh-based discretization techniques such as finite differences or finite element methods. Especially in a time-dependent setting or in the treatment of problems with strongly singular solutions their independence of a mesh makes these methods highly attractive. This volume collects selected papers presented at the Sixth International Workshop on Meshfree Methods held in Bonn, Germany in October 2011. They address various aspects of this very active research field and cover topics from applied mathematics, physics and engineering. ​
Read More

The Now Mighty Theoretical Physics, 1870 to 1925

Author: Christa Jungnickel,Russell McCormmach

Publisher: University of Chicago Press

ISBN: 9780226415857

Category: Reference

Page: 435

View: 5464

Winner of the 1987 Pfizer Award of the History of Science Society "A majestic study of a most important spoch of intellectual history."—Brian Pippard, Times Literary Supplement "The authors' use of archival sources hitherto almost untouched gives their story a startling vividness. These volumes are among the finest works produced by historians of physics."—Jed Z. Buchwald, Isis "The authors painstakingly reconstruct the minutiae of laboratory budgets, instrument collections, and student numbers; they disentangle the intrigues of faculty appointments and the professional values those appointments reflected; they explore collegial relationships among physicists; and they document the unending campaign of scientists to wring further support for physics from often reluctant ministries."—R. Steven Turner, Science "Superbly written and exhaustively researched."—Peter Harman, Nature
Read More

lecture notes in pure and applied mathematics

Author: Giuseppe Da Prato,Jean-Paul Zolesio

Publisher: CRC Press

ISBN: 1482273616

Category: Mathematics

Page: 352

View: 2093

"Based on the International Federatiojn for Information Processing WG 7.2 Conference, held recently in Pisa, Italy. Provides recent results as well as entirely new material on control theory and shape analysis. Written by leading authorities from various desciplines."
Read More

Author: E. C. Zachmanoglou,Dale W. Thoe

Publisher: Courier Corporation

ISBN: 048613217X

Category: Mathematics

Page: 432

View: 6857

This text explores the essentials of partial differential equations as applied to engineering and the physical sciences. Discusses ordinary differential equations, integral curves and surfaces of vector fields, the Cauchy-Kovalevsky theory, more. Problems and answers.
Read More

Eine Einführung

Author: Walter A. Strauss

Publisher: Springer-Verlag

ISBN: 366312486X

Category: Mathematics

Page: 458

View: 2643

Dieses Buch ist eine umfassende Einführung in die klassischen Lösungsmethoden partieller Differentialgleichungen. Es wendet sich an Leser mit Kenntnissen aus einem viersemestrigen Grundstudium der Mathematik (und Physik) und legt seinen Schwerpunkt auf die explizite Darstellung der Lösungen. Es ist deshalb besonders auch für Anwender (Physiker, Ingenieure) sowie für Nichtspezialisten, die die Methoden der mathematischen Physik kennenlernen wollen, interessant. Durch die große Anzahl von Beispielen und Übungsaufgaben eignet es sich gut zum Gebrauch neben Vorlesungen sowie zum Selbststudium.
Read More

Functional Analytic Methods

Author: Friedrich Sauvigny

Publisher: Springer Science & Business Media

ISBN: 9783540344629

Category: Mathematics

Page: 392

View: 6512

This encyclopedic work covers the whole area of Partial Differential Equations - of the elliptic, parabolic, and hyperbolic type - in two and several variables. Emphasis is placed on the connection of PDEs and complex variable methods. This second volume addresses Solvability of operator equations in Banach spaces; Linear operators in Hilbert spaces and spectral theory; Schauder's theory of linear elliptic differential equations; Weak solutions of differential equations; Nonlinear partial differential equations and characteristics; Nonlinear elliptic systems with differential-geometric applications. While partial differential equations are solved via integral representations in the preceding volume, this volume uses functional analytic solution methods.
Read More

The Metz Surveys 3

Author: Michel Chipot,J Saint Jean Paulin,I Shafrir

Publisher: CRC Press

ISBN: 9780582253803

Category: Mathematics

Page: 240

View: 6297

Presents some recent advances in various important domains of partial differential equations and applied mathematics including harmonic maps, Ginzburg - Landau energy, liquid crystals, superconductivity, homogenization and oscillations, dynamical systems and inertial manifolds. These topics are now part of various areas of science and have experienced tremendous development during the last decades.
Read More

Author: Roger Temam

Publisher: Springer Science & Business Media

ISBN: 9780387948669

Category: Mathematics

Page: 650

View: 5229

In this book the author presents the dynamical systems in infinite dimension, especially those generated by dissipative partial differential equations. This book attempts a systematic study of infinite dimensional dynamical systems generated by dissipative evolution partial differential equations arising in mechanics and physics and in other areas of sciences and technology. This second edition has been updated and extended.
Read More