Geometrical Methods Of Mathematical Physics
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| 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 | : Bernard F. Schutz |
| Publisher | : Cambridge University Press |
| Total Pages | : 272 |
| Release | : 1980-01-28 |
| Genre | : Mathematics |
| ISBN | : 9780521298872 |
For physicists and applied mathematicians working in the fields of relativity and cosmology, high-energy physics and field theory, thermodynamics, fluid dynamics and mechanics. This book provides an introduction to the concepts and techniques of modern differential theory, particularly Lie groups, Lie forms and differential forms.
| Author | : Peter Szekeres |
| Publisher | : Cambridge University Press |
| Total Pages | : 620 |
| Release | : 2004-12-16 |
| Genre | : Mathematics |
| ISBN | : 9780521829601 |
This textbook, first published in 2004, provides an introduction to the major mathematical structures used in physics today.
| 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 | : Sadri Hassani |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 1052 |
| Release | : 2002-02-08 |
| Genre | : Science |
| ISBN | : 9780387985794 |
For physics students interested in the mathematics they use, and for math students interested in seeing how some of the ideas of their discipline find realization in an applied setting. The presentation strikes 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.
| 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.
| Author | : Jürgen Jost |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 226 |
| Release | : 2009-08-17 |
| Genre | : Mathematics |
| ISBN | : 3642005411 |
"Geometry and Physics" addresses mathematicians wanting to understand modern physics, and physicists wanting to learn geometry. It gives an introduction to modern quantum field theory and related areas of theoretical high-energy physics from the perspective of Riemannian geometry, and an introduction to modern geometry as needed and utilized in modern physics. Jürgen Jost, a well-known research mathematician and advanced textbook author, also develops important geometric concepts and methods that can be used for the structures of physics. In particular, he discusses the Lagrangians of the standard model and its supersymmetric extensions from a geometric perspective.
| Author | : Marián Fecko |
| Publisher | : Cambridge University Press |
| Total Pages | : 11 |
| Release | : 2006-10-12 |
| Genre | : Science |
| ISBN | : 1139458035 |
Covering subjects including manifolds, tensor fields, spinors, and differential forms, this textbook introduces geometrical topics useful in modern theoretical physics and mathematics. It develops understanding through over 1000 short exercises, and is suitable for advanced undergraduate or graduate courses in physics, mathematics and engineering.
| Author | : Dariusz Chruscinski |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 346 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 0817681760 |
Several well-established geometric and topological methods are used in this work in an application to a beautiful physical phenomenon known as the geometric phase. This book examines the geometric phase, bringing together different physical phenomena under a unified mathematical scheme. The material is presented so that graduate students and researchers in applied mathematics and physics with an understanding of classical and quantum mechanics can handle the text.
| 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.
