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Viser: A Geometric Approach to Differential Forms

A Geometric Approach to Differential Forms, 2. udgave
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A Geometric Approach to Differential Forms Vital Source e-bog

David Bachman
(2012)
Springer Nature
543,00 kr.
Leveres umiddelbart efter køb
A Geometric Approach to Differential Forms, 2. udgave

A Geometric Approach to Differential Forms

David Bachman
(2011)
Sprog: Engelsk
Birkhäuser Boston
646,00 kr.
Print on demand. Leveringstid vil være ca 2-3 uger.

Detaljer om varen

  • 2. Udgave
  • Vital Source searchable e-book (Fixed pages)
  • Udgiver: Springer Nature (Februar 2012)
  • ISBN: 9780817683047
The modern subject of differential forms subsumes classical vector calculus. This text presents differential forms from a geometric perspective accessible at the sophomore undergraduate level. The book begins with basic concepts such as partial differentiation and multiple integration and gently develops the entire machinery of differential forms. The author approaches the subject with the idea that complex concepts can be built up by analogy from simpler cases, which, being inherently geometric, often can be best understood visually. Each new concept is presented with a natural picture that students can easily grasp. Algebraic properties then follow. This facilitates the development of differential forms without assuming a background in linear algebra. Throughout the text, emphasis is placed on applications in 3 dimensions, but all definitions are given so as to be easily generalized to higher dimensions. A centerpiece of the text is the generalized Stokes' theorem. Although this theorem implies all of the classical integral theorems of vector calculus, it is far easier for students to both comprehend and remember. The text is designed to support three distinct course tracks: the first as the primary textbook for third semester (multivariable) calculus, suitable for anyone with a year of calculus; the second is aimed at students enrolled in sophomore-level vector calculus; while the third targets advanced undergraduates and beginning graduate students in physics or mathematics, covering more advanced topics such as Maxwell's equations, foliation theory, and cohomology. Containing excellent motivation, numerous illustrations and solutions to selected problems in an appendix, the material has been tested in the classroom along all three potential course tracks.
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Bookshelf online: 5 år fra købsdato.
Bookshelf appen: ubegrænset dage fra købsdato.

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Print: 2 sider kan printes ad gangen
Copy: højest 2 sider i alt kan kopieres (copy/paste)

Detaljer om varen

  • 2. Udgave
  • Hardback
  • Udgiver: Birkhäuser Boston (November 2011)
  • ISBN: 9780817683030

This text presents differential forms from a geometric perspective accessible at the undergraduate level. It begins with basic concepts such as partial differentiation and multiple integration and gently develops the entire machinery of differential forms. The subject is approached with the idea that complex concepts can be built up by analogy from simpler cases, which, being inherently geometric, often can be best understood visually. Each new concept is presented with a natural picture that students can easily grasp. Algebraic properties then follow. The book contains excellent motivation, numerous illustrations and solutions to selected problems.

Preface.- Guide to the Reader.-Multivariable Calculus.- Parameterizations.- Introduction to Forms.- Forms.- Differential Forms.- Differentiation of Forms.- Stokes' Theorem.- Applications.- Manifolds.- Non-linear Forms.- References.- Index.- Solutions.
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