Description
This book provides a working knowledge of those parts of exterior differential forms, differential geometry, algebraic and differential topology, Lie groups, vector bundles and Chern forms that are essential for a deeper understanding of both classical and modern physics and engineering. Included are discussions of analytical and fluid dynamics, electromagnetism (in flat and curved space), thermodynamics, the Dirac operator and spinors, and gauge fields, including Yang-Mills, the Aharonov-Bohm effect, Berry phase and instanton winding numbers, quarks and quark model for mesons. Before discussing abstract notions of differential geometry, geometric intuition is developed through a rather extensive introduction to the study of surfaces in ordinary space. The book is ideal for graduate and advanced undergraduate students of physics, engineering or mathematics as a course text or for self study. This third edition includes an overview of Cartan's exterior differential forms, which previews many of the geometric concepts developed in the text.
Provides a working knowledge of tools that are of great value in geometry and physics and in engineering.
About the Author
Theodore Frankel received his PhD from the University of California, Berkeley. He is currently Emeritus Professor of Mathematics at the University of California, San Diego.
Reviews
Review of previous edition: '... highly readable and enjoyable ... The book will make an excellent course text or self-study manual for this interesting subject.' Physics Today
Review of previous edition: 'This book provides a highly detailed account of the intricacies involved in considering geometrical concepts.' Contemporary Physics
'If you're looking for a well-written and well-motivated introduction to differential geometry, this one looks hard to beat.' Fernando Q. Gouvea, MAA Online
'... a first rate introductory textbook ... the style is lively and exposition is clear which make the text easy to read ... This book will be beneficial to students and scientists wishing to learn the foundations of differential geometry and algebraic topology as well as geometric formulations of modern physical theories.' Pure and Applied Geophysics
'... this book should not be missing in any physics or mathematics library.' European Mathematical Society
'This book is a great read and has a lot to offer to graduate students in both mathematics and physics. I wish I had had it on my desk when I began studying geometry.' AMS Review
Review of previous edition: 'The layout, the typography and the illustrations of this advanced textbook on modern mathematical methods are all very impressive and so are the topics covered in the text.' Zentralblatt fur Mathematik und ihre Grenzgebiete
'... contains a wealth of interesting material for both the beginning and the advanced levels. The writing may feel informal but it is precise - a masterful exposition. Users of this 'introduction' will be well prepared for further study of differential geometry and its use in physics and engineering ... As did earlier editions, this third edition will continue to promote the language with which mathematicians and scientists can communicate.' Jay P. Fillmore, SIAM Review
Book Information
ISBN 9781107602601
Author Theodore Frankel
Format Paperback
Page Count 748
Imprint Cambridge University Press
Publisher Cambridge University Press
Weight(grams) 1440g
Dimensions(mm) 248mm * 174mm * 33mm
Provides a working knowledge of tools that are of great value in geometry and physics and in engineering.
About the Author
Theodore Frankel received his PhD from the University of California, Berkeley. He is currently Emeritus Professor of Mathematics at the University of California, San Diego.
Reviews
Review of previous edition: '... highly readable and enjoyable ... The book will make an excellent course text or self-study manual for this interesting subject.' Physics Today
Review of previous edition: 'This book provides a highly detailed account of the intricacies involved in considering geometrical concepts.' Contemporary Physics
'If you're looking for a well-written and well-motivated introduction to differential geometry, this one looks hard to beat.' Fernando Q. Gouvea, MAA Online
'... a first rate introductory textbook ... the style is lively and exposition is clear which make the text easy to read ... This book will be beneficial to students and scientists wishing to learn the foundations of differential geometry and algebraic topology as well as geometric formulations of modern physical theories.' Pure and Applied Geophysics
'... this book should not be missing in any physics or mathematics library.' European Mathematical Society
'This book is a great read and has a lot to offer to graduate students in both mathematics and physics. I wish I had had it on my desk when I began studying geometry.' AMS Review
Review of previous edition: 'The layout, the typography and the illustrations of this advanced textbook on modern mathematical methods are all very impressive and so are the topics covered in the text.' Zentralblatt fur Mathematik und ihre Grenzgebiete
'... contains a wealth of interesting material for both the beginning and the advanced levels. The writing may feel informal but it is precise - a masterful exposition. Users of this 'introduction' will be well prepared for further study of differential geometry and its use in physics and engineering ... As did earlier editions, this third edition will continue to promote the language with which mathematicians and scientists can communicate.' Jay P. Fillmore, SIAM Review
Book Information
ISBN 9781107602601
Author Theodore Frankel
Format Paperback
Page Count 748
Imprint Cambridge University Press
Publisher Cambridge University Press
Weight(grams) 1440g
Dimensions(mm) 248mm * 174mm * 33mm
