| Tensor Analysis on Manifolds (Dover Books on Mathematics) | ||||||||||||||||||||||
|
Well-written text • • • • • (bewertet mit 5 von 5 Punkten) Alle meine Rezensionen ansehen (REAL NAME) Rezension bezieht sich auf: Tensor Analysis on Manifolds (Dover Books on Mathematics) (Taschenbuch) This is a terse treatment of differential geometry. It is perhaps too sophisticated to serve as an introduction to modern differential geometry. The beginner probably needs to see examples of two dimensional surfaces embedded in Euclidean 3-space and to do calculations with reference to such surfaces. For example,the use of coordinate patches to cover the 2-sphere. And then seeing how the change of coordinates in overlapping patches affects geometric objects such as vectors, 1-forms, and the metric tensor. This provides some grounding for the abstract treatment of manifolds and the tensors defined on them. Also a leisurely introduction to the geometry of curved surfaces, either classically, using the first and second fundamental forms, or the modern way, using the shape operator (which is equivalent). This motivates the more abstract treatment of connections, which become necessary when there is no underlying space to embed the surface in (Euclidean 3-space provides a notion of connection (i.e. covariant derivative) that is geometrically clear; we have to axiomatize this notion when there's no natural space to embed in). Though the book may not be suitable as a first text, it can be used in conjunction with a more elementary text. Alternatively, it could be used for a graduate course. Though there are now a plethora of other good treatments around, this book remains one of the classics,and furthermore its price makes it particularly appealing. Eine Rezension von Ein Kunde vom 31. März 2000 | ||||||||||||||||||||||
| ||||||||||||||||||||||
| Zur Übersicht ... | ||||||||||||||||||||||
| | | | | | |||||||||||||||||
| Angebote zu , , ab 1 Euro! | ||||||||||||||||||||||
| Siehe auch folgende Artikel: | ||||||||||||||||||||||
 | Tensor Calculus (Dover Pictorial Archives) Partial Differential Equations for Scientis... Lectures on Classical Differential Geometry:... Differential Forms with Applications to the P... Quantum Mechanics and Path Integrals (Dove... The Variational Principles of Mechanics (Do... | |||||||||||||||||||||
| Mehr zu Vektoranalyse | ||||||||||||||||||||||
| Home ..., , Begleitseite ... | ||||||||||||||||||||||
| Herausgeber dieser Seite ist DomainLoc.com GmbH - Partner von | ||||||||||||||||||||||
Copyright © DomainLoc.com GmbH (Impressum) | ||||||||||||||||||||||