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A Geometric Approach to Differential Forms
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Librairie Eyrolles - Paris 5e
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A Geometric Approach to Differential Forms

A Geometric Approach to Differential Forms

David Bachman

133 pages, parution le 31/10/2006

Résumé

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.

Sommaire

  • Guide to the Reader.-Multivariable Calculus
  • Parameterizations
  • Introduction to Forms
  • Forms
  • Differential Forms
  • Differentiation of Forms
  • Stokes' Theorem
  • Applications
  • Manifolds
  • Non-linear Forms
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Caractéristiques techniques

  PAPIER
Éditeur(s) Birkhäuser
Auteur(s) David Bachman
Parution 31/10/2006
Nb. de pages 133
Format 15 x 23
Couverture Broché
Poids 272g
Intérieur Noir et Blanc
EAN13 9780817644994
ISBN13 978-0-8176-4499-4

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