A Geometrical Approach to Physics, Burton, David A ; Noble, Adam
Автор: Burton, David A ; Noble, Adam Название: A Geometrical Approach to Physics ISBN: 1032133805 ISBN-13(EAN): 9781032133805 Издательство: Taylor&Francis Рейтинг: Цена: 19906.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Автор: Aldrovandi Ruben & Pereira Jose Geraldo Название: Introduction To Geometrical Physics, An (Second Edition) ISBN: 9813146818 ISBN-13(EAN): 9789813146815 Издательство: World Scientific Publishing Цена: 11563.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
"The book contains a very large amount of material and is useful for students and specialists as a reference book."
Zentralblatt MATH
This book focuses on the unifying power of the geometrical language in bringing together concepts from many different areas of physics, ranging from classical physics to the theories describing the four fundamental interactions of Nature -- gravitational, electromagnetic, strong nuclear, and weak nuclear.
The book provides in a single volume a thorough introduction to topology and differential geometry, as well as many applications to both mathematical and physical problems. It is aimed as an elementary text and is intended for first year graduate students.
In addition to the traditional contents of books on special and general relativities, this book discusses also some recent advances such as de Sitter invariant special relativity, teleparallel gravity and their implications in cosmology for those wishing to reach a higher level of understanding.
Автор: Aldrovandi Ruben & Pereira Jose Geraldo Название: Introduction To Geometrical Physics, An (Second Edition) ISBN: 981314680X ISBN-13(EAN): 9789813146808 Издательство: World Scientific Publishing Цена: 42768.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
"The book contains a very large amount of material and is useful for students and specialists as a reference book."
Zentralblatt MATH
This book focuses on the unifying power of the geometrical language in bringing together concepts from many different areas of physics, ranging from classical physics to the theories describing the four fundamental interactions of Nature -- gravitational, electromagnetic, strong nuclear, and weak nuclear.
The book provides in a single volume a thorough introduction to topology and differential geometry, as well as many applications to both mathematical and physical problems. It is aimed as an elementary text and is intended for first year graduate students.
In addition to the traditional contents of books on special and general relativities, this book discusses also some recent advances such as de Sitter invariant special relativity, teleparallel gravity and their implications in cosmology for those wishing to reach a higher level of understanding.
Автор: Paul Steinmann Название: Geometrical Foundations of Continuum Mechanics ISBN: 3662464594 ISBN-13(EAN): 9783662464595 Издательство: Springer Рейтинг: Цена: 20896.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Geometrical Foundations of Continuum Mechanics
This textbook is a short comprehensive and intuitive introduction to Lie group analysis of ordinary and partial differential equations. This practical-oriented material contains a large number of examples and problems accompanied by detailed solutions and figures. In comparison with the known beginner guides to Lie group analysis, the book is oriented toward students who are interested in financial mathematics, mathematical finance and economics.
We provide the results of the Lie group analysis of actual models in Financial Mathematics using recent publications. These models are usually formulated as nonlinear partial differential equations and are rather difficult to make use of. With the help of Lie group analysis it is possible to describe some important properties of these models and to obtain interesting reductions in a clear and understandable algorithmic way.
The book can serve as a short introduction for a further study of modern geometrical analysis applied to models in financial mathematics. It can also be used as textbook in a master's program, in an intensive compact course, or for self study.
The textbook with a large number of examples will be useful not only for students who are interested in Financial Mathematics but also for people who are working in other areas of research that are not directly connected with Physics (for instance in such areas of Applied Mathematics like mathematical economy, bio systems, coding theory, etc.).
Modern Geometrical Machinery; 1 .1 Introduction; 1 .2 Smooth Manifolds; 1.2.1 Intuition Behind a Smooth Manifold; 1.2.2 Definition of a Smooth Manifold; 1.2.3 Smooth Maps Between Manifolds; 1.2.4 (Co)Tangent Bundles of a Smooth Manifold; 1.2.5 Tensor Fields and Bundles of a Smooth Manifold; 1.2.6 Lie Derivative on a Smooth Manifold; 1.2.7 Lie Groups and Associated Lie Algebras; 1.2.8 Lie Symmetries and Prolongations on Manifolds;1.2.9 Riemannian Manifolds; 1.2.10 Finsler Manifolds; 1.2.11 Symplectic Manifolds; 1.2.12 Complex and Kдhler Manifolds; 1.2.13 Conformal Killing-Riemannian Geometry; 1.3 Fibre Bundles; 1.3.1 Intuition Behind a Fibre Bundle; 1.3.2 Definition of a Fibre Bundle;1.3.3 Vector and Affine Bundles; 1.3.4 Principal Bundles; 1.3.5 Multivector-Fields and Tangent-Valued Forms; 1.4 Jet Spaces; 1.4.1 Intuition Behind a Jet Space; 1.4.2 Definition of a 1-Jet Space; 1.4.3 Connections as Jet Fields; 1.4.4 Definition of a 2-Jet Space; 1.4.5 Higher-Order Jet Spaces; 1.4.6 Jets in Mechanics;1.4.7 Jets and Action Principle; 1.5 Path Integrals: Extending Smooth Geometrical Machinery; 1.5.1 Intuition Behind a Path Integral; 1.5.2 Path Integral History; 1.5.3 Standard Path-Integral Quantization; 1.5.4 Sum over Geometries/Topologies; 1.5.5 TQFT and Stringy Path Integrals; 2 Dynamics of High-Dimensional Nonlinear Systems; 2.1 Mechanical Systems; 2.1.1 Autonomous Lagrangian/Hamiltonian Mechanics; 2.1.2 Non-Autonomous Lagrangian/Hamiltonian Mechanics; 2.1.3 Semi-Riemannian Geometrical Dynamics; 2.1.4 Relativistic and Multi-Time Rheonomic Dynamics; 2.1.5 Geometrical Quantization; 2.2 Physical Field Systems; 2.2.1 n-Categorical Framework; 2.2.2 Lagrangian Field Theory on Fibre Bundles; 2.2.3 Finsler-Lagrangian Field Theory; 2.2.4 Hamiltonian Field Systems: Path-Integral Quantization; 2.2.5 Gauge Fields on Principal Connections; 2.2.6 Modern Geometrodynamics; 2.2.7 Topological Phase Transitions and Hamiltonian Chaos; 2.2.8 Topological Superstring Theory; 2.2.9 Turbulence and Chaos Field Theory; 2.3 Nonlinear Control Systems; 2.3.1 The Basis of Modern Geometrical Control;2.3.2 Geometrical Control of Mechanical Systems;2.3.3 Hamiltonian Optimal Control and Maximum Principle; 2.3.4 Path-Integral Optimal Control of Stochastic Systems; 2.4 Human-Like Biomechanics; 2.4.1 Lie Groups and Symmetries in Biomechanics; 2.4.2 Muscle-Driven Hamiltonian Biomechanics; 2.4.3 Biomechanical Functors; 2.4.4 Biomechanical Topology; 2.5 Neurodynamics; 2.5.1 Microscopic Neurodynamics and Quantum Brain; 2.5.2 Macroscopic Neurodynamics; 2.5.3 Oscillatory Phase Neurodynamics;2.5.4 Neural Path-Integral Model for the Cerebellum; 2.5.5 Intelligent Robot Control; 2.5.6 Brain-Like Control Functor in Biomechanics; 2.5.7 Concurrent and Weak Functorial Machines; 2.5.8 Brain-Mind Functorial Machines; 26 Psycho-Socio-Economic Dynamics; 2.6.1 Force-Field Psychodynamics; 2.6.2 Geometrical Dynamics of Human Crowd; 2.6.3 Dynamical Games on Lie Groups; 2.6.4 Nonlinear Dynamics of Option Pricing; 2.6.5 Command/Control in Human-Robot Interactions; 2.6.6 Nonlinear Dynamics of Complex Nets; 2.6.7 Complex Adaptive Systems: Common Characteristics; 2.6.8 FAM Functors and Real-Life Games; 2.6.9 Riemann-Finsler Approach to Information Geometry; 3 Appendix: Tensors and Functors; 3.1 Elements of Classical Tensor Analysis; 3.1.1 Transformation of Coordinates and Elementary Tensors; 3.1.2 Euclidean Tensors; 3. 1 .3 Tensor Derivatives on Riemannian Manifolds; 3.1.4 Tensor Mechanics in Brief; 3.1.5 The Covariant Force Law in Robotics and Biomechanics; 3.2 Categories and Functors; 3.2.1 Maps; 3.2.2 Categories; 3.2.3 Functors; 3.2.4 Natural Transformations; 3.2.5 Limits and Colimits; 3.2.6 The Adjunction; 3.2.7 ri-Categories; 3.2.8 Abelian Functorial Algebra; References; Index.
Автор: Angela Slavova, Petar Popivanov Название: Nonlinear Waves: A Geometrical Approach ISBN: 9813271604 ISBN-13(EAN): 9789813271609 Издательство: World Scientific Publishing Рейтинг: Цена: 12672.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
This volume provides an in-depth treatment of several equations and systems of mathematical physics, describing the propagation and interaction of nonlinear waves as different modifications of these: the KdV equation, Fornberg-Whitham equation, Vakhnenko equation, Camassa-Holm equation, several versions of the NLS equation, Kaup-Kupershmidt equation, Boussinesq paradigm, and Manakov system, amongst others, as well as symmetrizable quasilinear hyperbolic systems arising in fluid dynamics.
Readers not familiar with the complicated methods used in the theory of the equations of mathematical physics (functional analysis, harmonic analysis, spectral theory, topological methods, a priori estimates, conservation laws) can easily be acquainted here with different solutions of some nonlinear PDEs written in a sharp form (waves), with their geometrical visualization and their interpretation. In many cases, explicit solutions (waves) having specific physical interpretation (solitons, kinks, peakons, ovals, loops, rogue waves) are found and their interactions are studied and geometrically visualized. To do this, classical methods coming from the theory of ordinary differential equations, the dressing method, Hirota's direct method and the method of the simplest equation are introduced and applied. At the end, the paradifferential approach is used.
This volume is self-contained and equipped with simple proofs. It contains many exercises and examples arising from the applications in mechanics, physics, optics and, quantum mechanics.
Автор: K. Bleuler; M. Werner Название: Differential Geometrical Methods in Theoretical Physics ISBN: 9048184592 ISBN-13(EAN): 9789048184590 Издательство: Springer Рейтинг: Цена: 41647.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Proceedings of the NATO Advanced Research Workshop and the 16th International Conference, Como, Italy, August 24-29, 1987
Автор: J. Debrus Название: The Fundamental Interaction ISBN: 146159524X ISBN-13(EAN): 9781461595243 Издательство: Springer Рейтинг: Цена: 12157.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: A meeting was held at the Physics Centre in Bad Honnef from Feb. 16-20, 1987 on the subject "The Fundamental Interaction: Geometrical Trends". We are also grateful to the staff of the Physics Centre for their organizational assistance, and to the participants, whose active interest made the meeting a success.
Автор: Lin Название: Advanced Geometrical Optics ISBN: 9811022984 ISBN-13(EAN): 9789811022982 Издательство: Springer Рейтинг: Цена: 22359.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book computes the first- and second-order derivative matrices of skew ray and optical path length, while also providing an important mathematical tool for automatic optical design. This book consists of three parts. Part One reviews the basic theories of skew-ray tracing, paraxial optics and primary aberrations – essential reading that lays the foundation for the modeling work presented in the rest of this book. Part Two derives the Jacobian matrices of a ray and its optical path length. Although this issue is also addressed in other publications, they generally fail to consider all of the variables of a non-axially symmetrical system. The modeling work thus provides a more robust framework for the analysis and design of non-axially symmetrical systems such as prisms and head-up displays. Lastly, Part Three proposes a computational scheme for deriving the Hessian matrices of a ray and its optical path length, offering an effective means of determining an appropriate search direction when tuning the system variables in the system design process.
Описание: This book presents a comprehensive account of the renormalization-group (RG) method and its extension, the doublet scheme, in a geometrical point of view. It extract long timescale macroscopic/mesoscopic dynamics from microscopic equations in an intuitively understandable way rather than in a mathematically rigorous manner and introduces readers to a mathematically elementary, but useful and widely applicable technique for analyzing asymptotic solutions in mathematical models of nature. The book begins with the basic notion of the RG theory, including its connection with the separation of scales. Then it formulates the RG method as a construction method of envelopes of the naive perturbative solutions containing secular terms, and then demonstrates the formulation in various types of evolution equations. Lastly, it describes successful physical examples, such as stochastic and transport phenomena including second-order relativistic as well as nonrelativistic fluid dynamics with causality and transport phenomena in cold atoms, with extensive numerical expositions of transport coefficients and relaxation times. Requiring only an undergraduate-level understanding of physics and mathematics, the book clearly describes the notions and mathematical techniques with a wealth of examples. It is a unique and can be enlightening resource for readers who feel mystified by renormalization theory in quantum field theory.
Автор: Rajeev, S. G. (professor Of Physics And Mathematics, University Of Rochester) Название: Fluid mechanics ISBN: 0198805020 ISBN-13(EAN): 9780198805021 Издательство: Oxford Academ Рейтинг: Цена: 11246.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book emphasizes general principles of physics illustrated by simple examples in fluid mechanics. Advanced mathematics (e.g., Riemannian geometry and Lie groups) commonly used in other parts of theoretical physics (e.g. General Relativity or High Energy Physics) are explained and applied to Fluid Mechanics.
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