Tensor Analysis on Manifolds

Nonfiction, Science & Nature, Mathematics, Vector Analysis
Cover of the book Tensor Analysis on Manifolds by Samuel I. Goldberg, Richard L. Bishop, Dover Publications
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Samuel I. Goldberg, Richard L. Bishop ISBN: 9780486139234
Publisher: Dover Publications Publication: April 26, 2012
Imprint: Dover Publications Language: English
Author: Samuel I. Goldberg, Richard L. Bishop
ISBN: 9780486139234
Publisher: Dover Publications
Publication: April 26, 2012
Imprint: Dover Publications
Language: English

"This is a first-rate book and deserves to be widely read." — American Mathematical Monthly
Despite its success as a mathematical tool in the general theory of relativity and its adaptability to a wide range of mathematical and physical problems, tensor analysis has always had a rather restricted level of use, with an emphasis on notation and the manipulation of indices. This book is an attempt to broaden this point of view at the stage where the student first encounters the subject. The authors have treated tensor analysis as a continuation of advanced calculus, striking just the right balance between the formal and abstract approaches to the subject.
The material proceeds from the general to the special. An introductory chapter establishes notation and explains various topics in set theory and topology. Chapters 1 and 2 develop tensor analysis in its function-theoretical and algebraic aspects, respectively. The next two chapters take up vector analysis on manifolds and integration theory. In the last two chapters (5 and 6) several important special structures are studied, those in Chapter 6 illustrating how the previous material can be adapted to clarify the ideas of classical mechanics. The text as a whole offers numerous examples and problems.
A student with a background of advanced calculus and elementary differential equation could readily undertake the study of this book. The more mature the reader is in terms of other mathematical knowledge and experience, the more he will learn from this presentation.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

"This is a first-rate book and deserves to be widely read." — American Mathematical Monthly
Despite its success as a mathematical tool in the general theory of relativity and its adaptability to a wide range of mathematical and physical problems, tensor analysis has always had a rather restricted level of use, with an emphasis on notation and the manipulation of indices. This book is an attempt to broaden this point of view at the stage where the student first encounters the subject. The authors have treated tensor analysis as a continuation of advanced calculus, striking just the right balance between the formal and abstract approaches to the subject.
The material proceeds from the general to the special. An introductory chapter establishes notation and explains various topics in set theory and topology. Chapters 1 and 2 develop tensor analysis in its function-theoretical and algebraic aspects, respectively. The next two chapters take up vector analysis on manifolds and integration theory. In the last two chapters (5 and 6) several important special structures are studied, those in Chapter 6 illustrating how the previous material can be adapted to clarify the ideas of classical mechanics. The text as a whole offers numerous examples and problems.
A student with a background of advanced calculus and elementary differential equation could readily undertake the study of this book. The more mature the reader is in terms of other mathematical knowledge and experience, the more he will learn from this presentation.

More books from Dover Publications

Cover of the book Classic French Fashions of the Twenties by Samuel I. Goldberg, Richard L. Bishop
Cover of the book Norse Mythology by Samuel I. Goldberg, Richard L. Bishop
Cover of the book Ancient European Costume and Fashion by Samuel I. Goldberg, Richard L. Bishop
Cover of the book Idylls of the King by Samuel I. Goldberg, Richard L. Bishop
Cover of the book The First American Cookbook by Samuel I. Goldberg, Richard L. Bishop
Cover of the book The Cruise of the Dazzler by Samuel I. Goldberg, Richard L. Bishop
Cover of the book Young Goodman Brown and Other Short Stories by Samuel I. Goldberg, Richard L. Bishop
Cover of the book Dogs of Character by Samuel I. Goldberg, Richard L. Bishop
Cover of the book Indian and Oriental Arms and Armour by Samuel I. Goldberg, Richard L. Bishop
Cover of the book Fairy Tales from Shakespeare by Samuel I. Goldberg, Richard L. Bishop
Cover of the book The Psychology of the Mystics by Samuel I. Goldberg, Richard L. Bishop
Cover of the book The Arts of the Sailor by Samuel I. Goldberg, Richard L. Bishop
Cover of the book Beardsley's Le Morte Darthur by Samuel I. Goldberg, Richard L. Bishop
Cover of the book Invitation to Dynamical Systems by Samuel I. Goldberg, Richard L. Bishop
Cover of the book How to Play the Chess Openings by Samuel I. Goldberg, Richard L. Bishop
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy