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Differential Geometry and Mathematical Physics: Part I. Manifolds, Lie Groups and Hamiltonian Systems (Theoretical and Mathematical Physics)

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Differential Geometry and Mathematical Physics: Part I. Manifolds, Lie Groups and Hamiltonian Systems (Theoretical and Mathematical Physics) Cover

 

Synopses & Reviews

Publisher Comments:

Starting from an undergraduate level, this book systematically develops the basics of • Calculus on manifolds, vector bundles, vector fields and differential forms, • Lie groups and Lie group actions, • Linear symplectic algebra and symplectic geometry, • Hamiltonian systems, symmetries and reduction, integrable systems and Hamilton-Jacobi theory. The topics listed under the first item are relevant for virtually all areas of mathematical physics. The second and third items constitute the link between abstract calculus and the theory of Hamiltonian systems. The last item provides an introduction to various aspects of this theory, including Morse families, the Maslov class and caustics. The book guides the reader from elementary differential geometry to advanced topics in the theory of Hamiltonian systems with the aim of making current research literature accessible. The style is that of a mathematical textbook,with full proofs given in the text or as exercises. The material is illustrated by numerous detailed examples, some of which are taken up several times for demonstrating how the methods evolve and interact.

Synopsis:

This book methodically covers Analysis on manifolds, Lie groups and G-manifolds; Symplectic algebra and geometry, Hamiltonian systems, symmetries and reduction; Integrable systems and Hamilton-Jacobi theory, including Morse families, the Maslov class and more.

Synopsis:

Starting from undergraduate level, this book systematically develops the basics of - Analysis on manifolds, Lie groups and G-manifolds (including equivariant dynamics) - Symplectic algebra and geometry, Hamiltonian systems, symmetries and reduction, - Integrable systems, Hamilton-Jacobi theory (including Morse families, the Maslov class and caustics). The first item is relevant for virtually all areas of mathematical physics, while the second item provides the basis of Hamiltonian mechanics. The last item introduces to important special areas. Necessary background knowledge on topology is provided in an appendix. The aim of this book is to enable the reader to access research monographs on more advanced topics. The style of this book is that of a mathematics textbook, with full proofs given in the text or as exercises. All material is illustrated by detailed examples, a number of which is taken up repeatedly for demonstrating how the methods evolve and interact.

Table of Contents

1 Differentiable manifolds.-

Product Details

ISBN:
9789400753440
Author:
Rudolph, Gerd
Publisher:
Springer
Author:
Schmidt, Matthias
Subject:
Mathematics-Differential Geometry
Subject:
Mathematical Physics
Subject:
analysis on manifolds
Subject:
Differential Geometry Applied
Subject:
Hamilton-Jacobi Theory
Subject:
Hamiltonian systems
Subject:
Integrable systems
Subject:
Lie Groups Applied
Subject:
manifold
Subject:
Symmetries and Reduction
Subject:
Symplectic geometry
Subject:
Symplectic Reduction
Subject:
mathematical methods in physics
Subject:
Global Analysis and Analysis on Manifolds
Subject:
Mechanics
Subject:
Topological Groups, Lie Groups
Subject:
Differential geometry
Copyright:
Edition Description:
2013
Series:
Theoretical and Mathematical Physics
Publication Date:
20120930
Binding:
HARDCOVER
Language:
English
Pages:
772
Dimensions:
235 x 155 mm

Related Subjects


Science and Mathematics » Biology » General
Science and Mathematics » Mathematics » Analysis General
Science and Mathematics » Mathematics » Differential Geometry
Science and Mathematics » Mathematics » Group Theory
Science and Mathematics » Physics » General
Science and Mathematics » Physics » Math

Differential Geometry and Mathematical Physics: Part I. Manifolds, Lie Groups and Hamiltonian Systems (Theoretical and Mathematical Physics) New Hardcover
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$109.25 In Stock
Product details 772 pages Springer - English 9789400753440 Reviews:
"Synopsis" by , This book methodically covers Analysis on manifolds, Lie groups and G-manifolds; Symplectic algebra and geometry, Hamiltonian systems, symmetries and reduction; Integrable systems and Hamilton-Jacobi theory, including Morse families, the Maslov class and more.
"Synopsis" by , Starting from undergraduate level, this book systematically develops the basics of - Analysis on manifolds, Lie groups and G-manifolds (including equivariant dynamics) - Symplectic algebra and geometry, Hamiltonian systems, symmetries and reduction, - Integrable systems, Hamilton-Jacobi theory (including Morse families, the Maslov class and caustics). The first item is relevant for virtually all areas of mathematical physics, while the second item provides the basis of Hamiltonian mechanics. The last item introduces to important special areas. Necessary background knowledge on topology is provided in an appendix. The aim of this book is to enable the reader to access research monographs on more advanced topics. The style of this book is that of a mathematics textbook, with full proofs given in the text or as exercises. All material is illustrated by detailed examples, a number of which is taken up repeatedly for demonstrating how the methods evolve and interact.
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