A geometric approach to differential forms
The modern subject of differential forms subsumes classical vector calculus. This text presents differential forms from a geometric perspective accessible at the undergraduate level. The book begins with basic concepts such as partial differentiation and multiple integration and gently develops the...
Gespeichert in:
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| Format: | Livre numérique |
| Sprache: | Anglais |
| Veröffentlicht: |
Boston, MA :
Birkhäuser Boston
[20..].
Cham : Springer Nature |
| Schlagworte: | |
| Online Zugang: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Anmerkung: |
Description d'après consultation du 1er mars 2011 Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • A geometric approach to differential forms, David Bachman, 2006, Boston, Birkhauser, 1 vol. (XVI-133 p.), 978-0-8176-4499-4 |
| Zusammenfassung: | The modern subject of differential forms subsumes classical vector calculus. This text presents differential forms from a geometric perspective accessible at the 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 vector calculus; while the third targets advanced undergraduates and beginning graduate students in physics or mathematics, touching on 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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| Beschreibung: | Description d'après consultation du 1er mars 2011 Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Bibliographie: | Bibliogr. Index |
| ISBN: | 0817645209 9780817645205 |
| Zugangseinschränkungen: | Accès en ligne pour les établissements français bénéficiaires des licences nationales Accès soumis à abonnement pour tout autre établissement Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 |