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.
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.
Rezensionen / Stimmen
From the reviews of the second edition:
"This book is a good complement to existing textbooks on vector calculus and shows a different view on classic material. It should be helpful to both physicists and mathematicians as an introduction to first concepts of the basic tools of modern theoretical physics, differential geometry, and topology." (Vladislav Nikolaevich Dumachev, zbMATH, Vol. 1266, 2013)
Auflage
Sprache
Verlagsort
Zielgruppe
Für Beruf und Forschung
Lower undergraduate
Editions-Typ
Illustrationen
43
43 s/w Abbildungen
XVI, 156 p. 43 illus.
Maße
Höhe: 241 mm
Breite: 160 mm
Dicke: 14 mm
Gewicht
ISBN-13
978-0-8176-8303-0 (9780817683030)
DOI
10.1007/978-0-8176-8304-7
Schweitzer Klassifikation
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.
