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| Author | : Anne Boutet de Monvel |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 471 |
| Release | : 2013-11-11 |
| Genre | : Science |
| ISBN | : 940170693X |
Proceedings of the Kaciveli Summer School, Crimea, Ukraine, 1993
| Author | : Paolo Gibilisco |
| Publisher | : Cambridge University Press |
| Total Pages | : 447 |
| Release | : 2010 |
| Genre | : Mathematics |
| ISBN | : 0521896193 |
An up-to-date account of algebraic statistics and information geometry, which also explores the emerging connections between these two disciplines.
| Author | : G. Giachetta |
| Publisher | : World Scientific |
| Total Pages | : 715 |
| Release | : 2005 |
| Genre | : Science |
| ISBN | : 9812701265 |
In the last decade, the development of new ideas in quantum theory, including geometric and deformation quantization, the non-Abelian Berry''s geometric factor, super- and BRST symmetries, non-commutativity, has called into play the geometric techniques based on the deep interplay between algebra, differential geometry and topology. The book aims at being a guide to advanced differential geometric and topological methods in quantum mechanics. Their main peculiarity lies in the fact that geometry in quantum theory speaks mainly the algebraic language of rings, modules, sheaves and categories. Geometry is by no means the primary scope of the book, but it underlies many ideas in modern quantum physics and provides the most advanced schemes of quantization.
| Author | : Galina Filipuk |
| Publisher | : Birkhäuser |
| Total Pages | : 472 |
| Release | : 2017-06-23 |
| Genre | : Mathematics |
| ISBN | : 3319528424 |
This volume consists of invited lecture notes, survey papers and original research papers from the AAGADE school and conference held in Będlewo, Poland in September 2015. The contributions provide an overview of the current level of interaction between algebra, geometry and analysis and demonstrate the manifold aspects of the theory of ordinary and partial differential equations, while also pointing out the highly fruitful interrelations between those aspects. These interactions continue to yield new developments, not only in the theory of differential equations but also in several related areas of mathematics and physics such as differential geometry, representation theory, number theory and mathematical physics. The main goal of the volume is to introduce basic concepts, techniques, detailed and illustrative examples and theorems (in a manner suitable for non-specialists), and to present recent developments in the field, together with open problems for more advanced and experienced readers. It will be of interest to graduate students, early-career researchers and specialists in analysis, geometry, algebra and related areas, as well as anyone interested in learning new methods and techniques.
| Author | : Bernard F. Schutz |
| Publisher | : Cambridge University Press |
| Total Pages | : 272 |
| Release | : 1980-01-28 |
| Genre | : Science |
| ISBN | : 1107268141 |
In recent years the methods of modern differential geometry have become of considerable importance in theoretical physics and have found application in relativity and cosmology, high-energy physics and field theory, thermodynamics, fluid dynamics and mechanics. This textbook provides an introduction to these methods - in particular Lie derivatives, Lie groups and differential forms - and covers their extensive applications to theoretical physics. The reader is assumed to have some familiarity with advanced calculus, linear algebra and a little elementary operator theory. The advanced physics undergraduate should therefore find the presentation quite accessible. This account will prove valuable for those with backgrounds in physics and applied mathematics who desire an introduction to the subject. Having studied the book, the reader will be able to comprehend research papers that use this mathematics and follow more advanced pure-mathematical expositions.
| Author | : Charles Nash |
| Publisher | : Courier Corporation |
| Total Pages | : 302 |
| Release | : 2013-08-16 |
| Genre | : Mathematics |
| ISBN | : 0486318362 |
Written by physicists for physics students, this text assumes no detailed background in topology or geometry. Topics include differential forms, homotopy, homology, cohomology, fiber bundles, connection and covariant derivatives, and Morse theory. 1983 edition.
| Author | : W. V. D. Hodge |
| Publisher | : Cambridge University Press |
| Total Pages | : 350 |
| Release | : 1994-05-19 |
| Genre | : Mathematics |
| ISBN | : 0521467756 |
All three volumes of Hodge and Pedoe's classic work have now been reissued. Together, these books give an insight into algebraic geometry that is unique and unsurpassed.
| Author | : Maria Ulan |
| Publisher | : Springer Nature |
| Total Pages | : 231 |
| Release | : 2021-02-12 |
| Genre | : Mathematics |
| ISBN | : 3030632539 |
This volume presents lectures given at the Wisła 19 Summer School: Differential Geometry, Differential Equations, and Mathematical Physics, which took place from August 19 - 29th, 2019 in Wisła, Poland, and was organized by the Baltic Institute of Mathematics. The lectures were dedicated to symplectic and Poisson geometry, tractor calculus, and the integration of ordinary differential equations, and are included here as lecture notes comprising the first three chapters. Following this, chapters combine theoretical and applied perspectives to explore topics at the intersection of differential geometry, differential equations, and mathematical physics. Specific topics covered include: Parabolic geometry Geometric methods for solving PDEs in physics, mathematical biology, and mathematical finance Darcy and Euler flows of real gases Differential invariants for fluid and gas flow Differential Geometry, Differential Equations, and Mathematical Physics is ideal for graduate students and researchers working in these areas. A basic understanding of differential geometry is assumed.
| Author | : Theodore Frankel |
| Publisher | : Cambridge University Press |
| Total Pages | : 749 |
| Release | : 2011-11-03 |
| Genre | : Mathematics |
| ISBN | : 1139505610 |
This book provides a working knowledge of those parts of exterior differential forms, differential geometry, algebraic and differential topology, Lie groups, vector bundles and Chern forms that are essential for a deeper understanding of both classical and modern physics and engineering. Included are discussions of analytical and fluid dynamics, electromagnetism (in flat and curved space), thermodynamics, the Dirac operator and spinors, and gauge fields, including Yang–Mills, the Aharonov–Bohm effect, Berry phase and instanton winding numbers, quarks and quark model for mesons. Before discussing abstract notions of differential geometry, geometric intuition is developed through a rather extensive introduction to the study of surfaces in ordinary space. The book is ideal for graduate and advanced undergraduate students of physics, engineering or mathematics as a course text or for self study. This third edition includes an overview of Cartan's exterior differential forms, which previews many of the geometric concepts developed in the text.
| Author | : V.I. Arnol'd |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 530 |
| Release | : 2013-04-09 |
| Genre | : Mathematics |
| ISBN | : 1475720637 |
This book constructs the mathematical apparatus of classical mechanics from the beginning, examining basic problems in dynamics like the theory of oscillations and the Hamiltonian formalism. The author emphasizes geometrical considerations and includes phase spaces and flows, vector fields, and Lie groups. Discussion includes qualitative methods of the theory of dynamical systems and of asymptotic methods like averaging and adiabatic invariance.
