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Differential Forms in Mathematical Physics

Differential Forms in Mathematical Physics PDF Author: Cornelius von Westenholz
Publisher: North Holland
ISBN:
Category : Science
Languages : en
Pages : 610

Book Description


Differential Forms in Mathematical Physics

Differential Forms in Mathematical Physics PDF Author: Cornelius von Westenholz
Publisher: North Holland
ISBN:
Category : Science
Languages : en
Pages : 610

Book Description


Differential Geometry and Mathematical Physics

Differential Geometry and Mathematical Physics PDF Author: Gerd Rudolph
Publisher: Springer Science & Business Media
ISBN: 9400753454
Category : Science
Languages : en
Pages : 766

Book 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.

Geometrical Methods of Mathematical Physics

Geometrical Methods of Mathematical Physics PDF Author: Bernard F. Schutz
Publisher: Cambridge University Press
ISBN: 1107268141
Category : Science
Languages : en
Pages : 272

Book Description
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.

Differential Forms with Applications to the Physical Sciences

Differential Forms with Applications to the Physical Sciences PDF Author: Harley Flanders
Publisher: Courier Corporation
ISBN: 0486139611
Category : Mathematics
Languages : en
Pages : 226

Book Description
"To the reader who wishes to obtain a bird's-eye view of the theory of differential forms with applications to other branches of pure mathematics, applied mathematic and physics, I can recommend no better book." — T. J. Willmore, London Mathematical Society Journal. This excellent text introduces the use of exterior differential forms as a powerful tool in the analysis of a variety of mathematical problems in the physical and engineering sciences. Requiring familiarity with several variable calculus and some knowledge of linear algebra and set theory, it is directed primarily to engineers and physical scientists, but it has also been used successfully to introduce modern differential geometry to students in mathematics. Chapter I introduces exterior differential forms and their comparisons with tensors. The next three chapters take up exterior algebra, the exterior derivative and their applications. Chapter V discusses manifolds and integration, and Chapter VI covers applications in Euclidean space. The last three chapters explore applications to differential equations, differential geometry, and group theory. "The book is very readable, indeed, enjoyable — and, although addressed to engineers and scientists, should be not at all inaccessible to or inappropriate for ... first year graduate students and bright undergraduates." — F. E. J. Linton, Wesleyan University, American Mathematical Monthly.

A Visual Introduction to Differential Forms and Calculus on Manifolds

A Visual Introduction to Differential Forms and Calculus on Manifolds PDF Author: Jon Pierre Fortney
Publisher: Springer
ISBN: 3319969927
Category : Mathematics
Languages : en
Pages : 470

Book Description
This book explains and helps readers to develop geometric intuition as it relates to differential forms. It includes over 250 figures to aid understanding and enable readers to visualize the concepts being discussed. The author gradually builds up to the basic ideas and concepts so that definitions, when made, do not appear out of nowhere, and both the importance and role that theorems play is evident as or before they are presented. With a clear writing style and easy-to- understand motivations for each topic, this book is primarily aimed at second- or third-year undergraduate math and physics students with a basic knowledge of vector calculus and linear algebra.

Electricity and Magnetism for Mathematicians

Electricity and Magnetism for Mathematicians PDF Author: Thomas A. Garrity
Publisher: Cambridge University Press
ISBN: 1107435161
Category : Mathematics
Languages : en
Pages : 297

Book Description
Maxwell's equations have led to many important mathematical discoveries. This text introduces mathematics students to some of their wonders.

Global Analysis

Global Analysis PDF Author: Ilka Agricola
Publisher: American Mathematical Soc.
ISBN: 0821829513
Category : Mathematics
Languages : en
Pages : 362

Book Description
The final third of the book applies the mathematical ideas to important areas of physics: Hamiltonian mechanics, statistical mechanics, and electrodynamics." "There are many classroom-tested exercises and examples with excellent figures throughout. The book is ideal as a text for a first course in differential geometry, suitable for advanced undergraduates or graduate students in mathematics or physics."--BOOK JACKET.

Differential Forms and Connections

Differential Forms and Connections PDF Author: R. W. R. Darling
Publisher: Cambridge University Press
ISBN: 9780521468008
Category : Mathematics
Languages : en
Pages : 288

Book Description
Introducing the tools of modern differential geometry--exterior calculus, manifolds, vector bundles, connections--this textbook covers both classical surface theory, the modern theory of connections, and curvature. With no knowledge of topology assumed, the only prerequisites are multivariate calculus and linear algebra.

Differential Geometry, Gauge Theories, and Gravity

Differential Geometry, Gauge Theories, and Gravity PDF Author: M. Göckeler
Publisher: Cambridge University Press
ISBN: 9780521378215
Category : Mathematics
Languages : en
Pages : 248

Book Description
Cambridge University Press is committed to keeping scholarly work in print for as long as possible. A short print-run of this academic paperback has been produced using digital technology. This technology has enabled Cambridge to keep the book in print for specialists and students when traditional methods of reprinting would not have been feasible. While the new digital cover differs from the original, the text content is identical to that of previous printings.

Differential Forms in Mathematical Physics

Differential Forms in Mathematical Physics PDF Author:
Publisher: Elsevier
ISBN: 0080875246
Category : Mathematics
Languages : en
Pages : 504

Book Description
Differential Forms in Mathematical Physics