Differential Geometry and Mathematical Physics: Part I. Manifolds, Lie Groups an

Description: Differential Geometry and Mathematical Physics by Gerd Rudolph, Matthias Schmidt 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. FORMAT Hardcover LANGUAGE English CONDITION Brand New Publisher Description 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. Notes Provides profound yet compact knowledge in manifolds, tensor fields, differential forms, Lie groups, G-manifolds and symplectic algebra and geometry for theoretical physicistsPrepares the reader to access the research literature in Hamiltonian mechanics and related areasComplete account to Marsden-Weinstein reduction, including the singular caseDetailed examples for all methods Back Cover 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. Table of Contents 1 Differentiable manifolds.- 2 Vector bundles.- 3 Vector fields.- 4 Differential forms.- 5 Lie groups.- 6 Lie group actions.- 7 Linear symplectic algebra.- 8 Symplectic geometry.- 9 Hamiltonian systems.- 10 Symmetries.- 11 Integrability.- 12 Hamilton-Jacobi theory.- References Review From the reviews:"The book is the first of two volumes on differential geometry and mathematical physics. The present volume deals with manifolds, Lie groups, symplectic geometry, Hamiltonian systems and Hamilton-Jacobi theory. … There are several examples and exercises scattered throughout the book. The presentation of material is well organized and clear. The reading of the book gives real satisfaction and pleasure since it reveals deep interrelations between pure mathematics and theoretical physics." (Tomasz Rybicki, Mathematical Reviews, October, 2013) Review Quote From the reviews: "The book is the first of two volumes on differential geometry and mathematical physics. The present volume deals with manifolds, Lie groups, symplectic geometry, Hamiltonian systems and Hamilton-Jacobi theory. ... There are several examples and exercises scattered throughout the book. The presentation of material is well organized and clear. The reading of the book gives real satisfaction and pleasure since it reveals deep interrelations between pure mathematics and theoretical physics." (Tomasz Rybicki, Mathematical Reviews, October, 2013) Feature Provides profound yet compact knowledge in manifolds, tensor fields, differential forms, Lie groups, G-manifolds and symplectic algebra and geometry for theoretical physicists Prepares the reader to access the research literature in Hamiltonian mechanics and related areas Complete account to Marsden-Weinstein reduction, including the singular case Detailed examples for all methods Includes supplementary material: sn.pub/extras Details ISBN9400753446 Author Matthias Schmidt Short Title DIFFERENTIAL GEOMETRY & MATHEM Publisher Springer Series Theoretical and Mathematical Physics Language English ISBN-10 9400753446 ISBN-13 9789400753440 Media Book Format Hardcover Year 2012 Imprint Springer Place of Publication Dordrecht Country of Publication Netherlands Publication Date 2012-11-10 DEWEY 516.36 Pages 762 Edition 2013th Illustrations XIV, 762 p. DOI 10.1007/978-94-007-5345-7 Edition Description 2013 ed. Subtitle Part I. Manifolds, Lie Groups and Hamiltonian Systems Alternative 9789401781985 Audience Professional & Vocational We've got this At The Nile, if you're looking for it, we've got it. With fast shipping, low prices, friendly service and well over a million items - you're bound to find what you want, at a price you'll love! TheNile_Item_ID:96398988;

Price: 281.08 AUD

Location: Melbourne

End Time: 2025-02-06T19:43:27.000Z

Shipping Cost: 19.47 AUD