Описание: In his bestselling work of popular science, Sir Roger Penrose takes us on a fascinating tour through the basic principles of physics, cosmology, mathematics, and philosophy to show that human thinking can never be emulated by a machine.
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: Bengtsson Ingemar Название: Geometry of Quantum States ISBN: 1107026253 ISBN-13(EAN): 9781107026254 Издательство: Cambridge Academ Рейтинг: Цена: 13779.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The second edition of a book that has become a standard reference for researchers working on geometric aspects of quantum entanglement and quantum theory of information. Its comprehensive style makes it suitable for students of physics, information science, and mathematics wishing to learn more about quantum mechanics and quantum entanglement.
Автор: Alexander S. Holevo Название: Quantum Systems, Channels, Information: A Mathematical Introduction ISBN: 311027325X ISBN-13(EAN): 9783110273250 Издательство: Walter de Gruyter Цена: 16916.00 р. 24166.00-30% Наличие на складе: Есть (1 шт.) Описание: The main emphasis of this work is the mathematical theory of quantum channels and their entropic and information characteristics. Quantum information theory is one of the key research areas, since it leads the way to vastly increased computing speeds by using quantum systems to store and process information. Quantum cryptography allows for secure communication of classified information. Research in the field of quantum informatics, including quantum information theory, is in progress in leading scientific centers throughout the world.The past years were marked with impressive progress made by several researchers in solution of some difficult problems, in particular, the additivity of the entropy characteristics of quantum channels. This suggests a need for a book that not only introduces the basic concepts of quantum information theory, but also presents in detail some of the latest achievements.
Автор: Wazwaz Abdul-Majid Название: First Course In Integral Equations, A (Second Edition) ISBN: 9814675121 ISBN-13(EAN): 9789814675123 Издательство: World Scientific Publishing Рейтинг: Цена: 6336.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This second edition integrates the newly developed methods with classical techniques to give both modern and powerful approaches for solving integral equations.
Автор: Ihor Lubashevsky Название: Physics of the Human Mind ISBN: 3319517058 ISBN-13(EAN): 9783319517056 Издательство: Springer Рейтинг: Цена: 15372.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Modeling of Human Behavior as Individual Branch of Physics and Mathematics.- Why Laws of Classical Physics Have Their Form.- Fodor-Kim Dilemma.- Strong Emergence via Constitutive Fields.- Non-Cartesian Dualism and Meso-Relational Media.- Modeling of Human Behavior Within the Paradigm of Modern Physics.- Emergent Phenomena Caused by Bounded Capacity of Human Cognition.- Epilog: Physics and Human Mind.- References.- Index.
Описание: This book considers the interaction of physical and non-physical causation in complex systems such as living beings, and in particular in the human brain, relating this to the emergence of higher levels of complexity with real causal powers.
Автор: Donald Merlin Название: A Mind So Rare: The Evolution of Human Consciousness ISBN: 0393323196 ISBN-13(EAN): 9780393323191 Издательство: Wiley Рейтинг: Цена: 2929.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: In this masterful rebuttal to the prevailing neuroscientific arguments that seek to explain away consciousness, Merlin Donald presents "a sophisticated conception of a multilayered consciousness drawing much of its power from its cultural matrix" (Booklist). Donald makes "a persuasive case...for consciousness as the central player in the drama of mind" (Peter Dodwell), as he details the forces, both cultural and neuronal, that power our distinctively human modes of awareness. He proposes that the human mind is a hybrid product, interweaving a super-complex form of matter (the brain) with an invisible symbolic web (culture) to form a "distributed" cognitive network.
This hybrid mind, he argues, is our main evolutionary advantage, for it allowed humanity as a species to break free of the limitations of the mammalian brain. "Donald transcends the simplistic claims of Evolutionary Psychology,...offering a true Darwinian perspective on the evolution of consciousness."-Philip Lieberman
Описание: What every neuroscientist should know about the mathematical modeling of excitable cells. Combining empirical physiology and nonlinear dynamics, this text provides an introduction to the simulation and modeling of dynamic phenomena in cell biology and neuroscience. It introduces mathematical modeling techniques alongside cellular electrophysiology. Topics include membrane transport and diffusion, the biophysics of excitable membranes, the gating of voltage and ligand-gated ion channels, intracellular calcium signalling, and electrical bursting in neurons and other excitable cell types. It introduces mathematical modeling techniques such as ordinary differential equations, phase plane, and bifurcation analysis of single-compartment neuron models. With analytical and computational problem sets, this book is suitable for life sciences majors, in biology to neuroscience, with one year of calculus, as well as graduate students looking for a primer on membrane excitability and calcium signalling.
Автор: Al-Mutairi Название: The Minimalist Program ISBN: 1107041341 ISBN-13(EAN): 9781107041349 Издательство: Cambridge Academ Рейтинг: Цена: 15840.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This evaluation of Chomsky`s work from the perspectives of linguistics, evolution of language, history of physics, and philosophy of mind is interdisciplinary. It encourages linguists to reflect on the foundations of their discipline, and invites non-linguists to appreciate the complexity of human language and its place in the world.
Описание: Quantum physics, unlike classical physics, suggests a non-physicalistic metaphysics. Whereas physicalism implies a reductive position in the philosophy of mind, quantum physics is compatible with non-reductionism, and actually seems to support it. The essays in this book explore, from various points of view, the possibilities of basing a non-reductive philosophy of mind on quantum physics.
Автор: M. Esfeld Название: Holism in Philosophy of Mind and Philosophy of Physics ISBN: 9048157110 ISBN-13(EAN): 9789048157112 Издательство: Springer Рейтинг: Цена: 27251.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The Scope of the Project The concept of holism is at the centre of far-reaching changes in various areas of philosophy in the second half of the twentieth century. Holism in epistemology and the philosophy of mind is seen as an alternative to what is known as the Cartesian tradition, which dominated modem thought down to logical empiricism.
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