By Pavel Grinfeld
This textbook is unusual from different texts at the topic by way of the intensity of the presentation and the dialogue of the calculus of relocating surfaces, that is an extension of tensor calculus to deforming manifolds.
Designed for complicated undergraduate and graduate scholars, this article invitations its viewers to take a clean examine formerly realized fabric throughout the prism of tensor calculus. as soon as the framework is mastered, the coed is brought to new fabric including differential geometry on manifolds, form optimization, boundary perturbation and dynamic fluid movie equations.
The language of tensors, initially championed via Einstein, is as basic because the languages of calculus and linear algebra and is person who each technical scientist should converse. The tensor strategy, invented on the flip of the 20th century, is now thought of classical. but, because the writer exhibits, it continues to be remarkably important and appropriate. The author’s expert lecturing services are obtrusive via the inclusion of insightful examples and a plethora of workouts. loads of fabric is dedicated to the geometric basics, the mechanics of switch of variables, the right kind use of the tensor notation and the dialogue of the interaction among algebra and geometry. The early chapters have many phrases and few equations. The definition of a tensor comes merely in bankruptcy 6 – whilst the reader is prepared for it. whereas this article keeps a constant point of rigor, it takes nice care to prevent formalizing the subject.
The final a part of the textbook is dedicated to the Calculus of relocating Surfaces. it's the first textbook exposition of this crucial approach and is among the gemstones of this article. a few fascinating functions of the calculus are provided together with form optimization, boundary perturbation of boundary price difficulties and dynamic fluid movie equations constructed by means of the writer lately. in addition, the relocating surfaces framework is used to supply new derivations of classical effects resembling the geodesic equation and the prestigious Gauss-Bonnet theorem.
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Additional resources for Introduction to Tensor Analysis and the Calculus of Moving Surfaces
Introduction to Tensor Analysis and the Calculus of Moving Surfaces by Pavel Grinfeld