This book is for physics students interested in the mathematics they use and for mathematics students interested in seeing how some of the ideas of their discipline find realization in an applied setting. The presentation tries to strike a balance between formalism and application, between abstract and concrete. The interconnections among the various topics are clarified both by the use of vector spaces as a central unifying theme, recurring throughout the book, and by putting ideas into their historical context. Enough of the essential formalism is included to make the presentation self-contained.
The book is divided into eight parts: The first covers finite- dimensional vector spaces and the linear operators defined on them. The second is devoted to infinite-dimensional vector spaces, and includes discussions of the classical orthogonal polynomials and of Fourier series and transforms. The third part deals with complex analysis, including complex series and their convergence, the calculus of residues, multivalued functions, and analytic continuation. Part IV treats ordinary differential equations, concentrating on second-order equations and discussing both analytical and numerical methods of solution. The next part deals with operator theory, focusing on integral and Sturm--Liouville operators. Part VI is devoted to Green's functions, both for ordinary differential equations and in multidimensional spaces. Parts VII and VIII contain a thorough discussion of differential geometry and Lie groups and their applications, concluding with Noether's theorem on the relationship between symmetries and conservation laws.
Intended for advanced undergraduates or beginning graduate students, this comprehensive guide should also prove useful as a refresher or reference for physicists and applied mathematicians. Over 300 worked-out examples and more than 800 problems provide valuable learning aids.
Numerous enhancements and revision are incorporated into this new edition. For example, fiber bundle techniques are used to introduce differential geometry. This more elegant and intuitive approach naturally connects differential geometry with not only the general theory of relativity, but also gauge theories of fundamental forces.
Some praise for the previous edition:
PAGEOPH Pure and Applied Geophysics]
Review by Daniel Wojcik, University of Maryland
"This volume should be a welcome addition to any collection. The book is well written and explanations are usually clear. Lives of famous mathematicians and physicists are scattered within the book. They are quite extended, often amusing, making nice interludes. Numerous exercises help the student practice the methods introduced. ... I have recently been using this book for an extended time and acquired a liking for it. Among all the available books treating mathematical methods of physics this one certainly stands out and assuredly it would suit the needs of many physics readers."
ZENTRALBLATT MATH
Review by G.Roepstorff, University of Aachen, Germany
..". Unlike most existing texts with the same emphasis and audience, which are merely collections of facts and formulas, the present book is more systematic, self-contained, with a level of presentation that tends to be more formal and abstract. This entails proving a large number of theorems, lemmas, and corollaries, deferring most of the applications that physics students might be interested in to the example sections in small print. Indeed, there are 350 worked-out examples and about 850 problems. ... A very nice feature is the way the author intertwines the formalism with the life stories and anecdotes of some mathematicians and physicists, leading at their times. As is often the case, the historical view point helps to understand and appreciate the ideas presented in the text. ... For the physics studen
Автор: Peter A. Fejer; Dan A. Simovici Название: Mathematical Foundations of Computer Science ISBN: 1461277922 ISBN-13(EAN): 9781461277927 Издательство: Springer Рейтинг: Цена: 11173.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Mathematical Foundations of Computer Science, Volume I is the first of two volumes presenting topics from mathematics (mostly discrete mathematics) which have proven relevant and useful to computer science.
Автор: Eduard Feireisl; John Ball; Eduard Feireisl; Elisa Название: Mathematical Thermodynamcis of Complex Fluids ISBN: 3319675990 ISBN-13(EAN): 9783319675992 Издательство: Springer Рейтинг: Цена: 6288.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The main goal of this book is to provide an overview of the state of the art in the mathematical modeling of complex fluids, with particular emphasis on its thermodynamical aspects.
Автор: Michel Deville; Thomas B. Gatski Название: Mathematical Modeling for Complex Fluids and Flows ISBN: 3642435602 ISBN-13(EAN): 9783642435607 Издательство: Springer Рейтинг: Цена: 15372.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Mathematical Modeling for Complex Fluids and Flows provides researchers and engineering practitioners encountering fluid flows with state-of-the-art knowledge in continuum concepts and associated fluid dynamics.
Автор: Ali Sanayei; Otto E. R?ssler; Ivan Zelinka Название: ISCS 2014: Interdisciplinary Symposium on Complex Systems ISBN: 3319107585 ISBN-13(EAN): 9783319107585 Издательство: Springer Рейтинг: Цена: 19591.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The book starts with a comprehensive overview and classification of complexity problems entitled Physics in the world of ideas: Complexity as Energy" , followed by chapters about complexity measures and physical principles, its observation, modeling and its applications, to solving various problems including real-life applications.
Автор: Kazuyuki Aihara; Jun-ichi Imura; Tetsushi Ueta Название: Analysis and Control of Complex Dynamical Systems ISBN: 4431550127 ISBN-13(EAN): 9784431550129 Издательство: Springer Рейтинг: Цена: 18284.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book is the first to report on theoretical breakthroughs on control of complex dynamical systems developed by collaborative researchers in the two fields of dynamical systems theory and control theory.
Автор: Franck Assous; Patrick Ciarlet; Simon Labrunie Название: Mathematical Foundations of Computational Electromagnetism ISBN: 3319708414 ISBN-13(EAN): 9783319708416 Издательство: Springer Рейтинг: Цена: 16769.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book presents an in-depth treatment of various mathematical aspects of electromagnetism and Maxwell's equations: from modeling issues to well-posedness results and the coupled models of plasma physics (Vlasov-Maxwell and Vlasov-Poisson systems) and magnetohydrodynamics (MHD). These equations and boundary conditions are discussed, including a brief review of absorbing boundary conditions. The focus then moves to well?posedness results. The relevant function spaces are introduced, with an emphasis on boundary and topological conditions. General variational frameworks are defined for static and quasi-static problems, time-harmonic problems (including fixed frequency or Helmholtz-like problems and unknown frequency or eigenvalue problems), and time-dependent problems, with or without constraints. They are then applied to prove the well-posedness of Maxwell’s equations and their simplified models, in the various settings described above. The book is completed with a discussion of dimensionally reduced models in prismatic and axisymmetric geometries, and a survey of existence and uniqueness results for the Vlasov-Poisson, Vlasov-Maxwell and MHD equations. The book addresses mainly researchers in applied mathematics who work on Maxwell’s equations. However, it can be used for master or doctorate-level courses on mathematical electromagnetism as it requires only a bachelor-level knowledge of analysis.
Описание: Presents a grounding in modern nonlinear integrable dynamics theory and applications in mathematical physics, and an introduction to the developments in the field. This book begins with an introduction modern integrable dynamical systems theory, treating such topics as Liouville-Arnold and Mischenko-Fomenko integrability.
Описание: Topics include: nonlinear exaltations in condensed systems, evolution of complex systems, dynamics and structure of molecular and biomolecular systems, mathematical models of transfer processes in nonlinear systems and numerical modeling and algorithms.
Автор: Mohamed Nemiche; Mohammad Essaaidi Название: Advances in Complex Societal, Environmental and Engineered Systems ISBN: 331946163X ISBN-13(EAN): 9783319461632 Издательство: Springer Рейтинг: Цена: 18167.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book addresses recent technological progress that has led to an increased complexity in many natural and artificial systems. The resulting complexity research due to the emergence of new properties and spatio-temporal interactions among a large number of system elements - and between the system and its environment - is the primary focus of this text.This volume is divided into three parts: Part one focuses on societal and ecological systems, Part two deals with approaches for understanding, modeling, predicting and mastering socio-technical systems, and Part three includes real-life examples. Each chapter has its own special features; it is a self-contained contribution of distinguished experts working on different fields of science and technology relevant to the study of complex systems. Advances in Complex Systems of Contemporary Reality: Societal, Environmental and Engineered Systems will provide postgraduate students, researchers and managers with qualitative and quantitative methods for handling the many features of complex contemporary reality.
The scientific study of complex systems has transformed a wide range of disciplines in recent years, enabling researchers in both the natural and social sciences to model and predict phenomena as diverse as earthquakes, global warming, demographic patterns, financial crises, and the failure of materials. In this book, Didier Sornette boldly applies his varied experience in these areas to propose a simple, powerful, and general theory of how, why, and when stock markets crash.
Most attempts to explain market failures seek to pinpoint triggering mechanisms that occur hours, days, or weeks before the collapse. Sornette proposes a radically different view: the underlying cause can be sought months and even years before the abrupt, catastrophic event in the build-up of cooperative speculation, which often translates into an accelerating rise of the market price, otherwise known as a "bubble." Anchoring his sophisticated, step-by-step analysis in leading-edge physical and statistical modeling techniques, he unearths remarkable insights and some predictions--among them, that the "end of the growth era" will occur around 2050.
Sornette probes major historical precedents, from the decades-long "tulip mania" in the Netherlands that wilted suddenly in 1637 to the South Sea Bubble that ended with the first huge market crash in England in 1720, to the Great Crash of October 1929 and Black Monday in 1987, to cite just a few. He concludes that most explanations other than cooperative self-organization fail to account for the subtle bubbles by which the markets lay the groundwork for catastrophe.
Any investor or investment professional who seeks a genuine understanding of looming financial disasters should read this book. Physicists, geologists, biologists, economists, and others will welcome Why Stock Markets Crash as a highly original "scientific tale," as Sornette aptly puts it, of the exciting and sometimes fearsome--but no longer quite so unfathomable--world of stock markets.
Автор: Davron Matrasulov; H. Eugene Stanley Название: Nonlinear Phenomena in Complex Systems: From Nano to Macro Scale ISBN: 9401787077 ISBN-13(EAN): 9789401787079 Издательство: Springer Рейтинг: Цена: 10760.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Topics of complex system physics and their interdisciplinary applications to different problems in seismology, biology, economy, sociology, energy and nanotechnology are covered in this new work from renowned experts in their fields.
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