عنوان

Introduction to tensor analysis and the calculus of moving surfaces /

(Number (ISBN

1461478677 (electronic bk.)

(Number (ISBN

9781461478676 (electronic bk.)

Erroneous ISBN

9781461478669

Number

dltt

Title Proper

Introduction to tensor analysis and the calculus of moving surfaces /

General Material Designation

[Book]

First Statement of Responsibility

Pavel Grinfeld

Specific Material Designation and Extent of Item

1 online resource

Text of Note

Includes bibliographical references and index

Text of Note

This text is meant to deepen its readers understanding of vector calculus, differential geometry and related subjects in applied mathematics. Designed for advanced undergraduate and graduate students, this text invites its audience to take a fresh look at previously learned material through the prism of tensor calculus. Once the framework is mastered, the student is introduced to new material which includes differential geometry on manifolds, shape optimization, boundary perturbation, and dynamic fluid film equations. Tensor calculus is a powerful tool that combines the geometric and analytical perspectives and enables us to take full advantage of the computational utility of coordinate systems. The tensor approach can be of benefit to members of all technical sciences including mathematics and all engineering disciplines. If calculus and linear algebra are central to the readers scientific endeavors, tensor calculus is indispensable. The language of tensors, originally championed by Einstein, is as fundamental as the languages of calculus and linear algebra and is one that every technical scientist ought to speak. The tensor technique, invented at the turn of the 20th century, is now considered classical. Yet, as the author shows, it remains remarkably vital and relevant. The authors skilled lecturing capabilities are evident by the inclusion of insightful examples and a plethora of exercises. A great deal of material is devoted to the geometric fundamentals, the mechanics of change of variables, the proper use of the tensor notation, and the discussion of the interplay between algebra and geometry. The early chapters have many words and few equations. The definition of a tensor comes only in Chapter 6 when the reader is ready for it. While this text maintains a reasonable level of rigor, it takes great care to avoid formalizing the subject

Title

Introduction to tensor analysis and the calculus of moving surfaces

International Standard Book Number

1461478669

Title

OhioLINK electronic book center (Online)

Title

SpringerLink

Calculus of tensors

Vector analysis

Number

Edition

Class number

Class number

Grinfeld, Pavel

Ohio Library and Information Network

Date of Transaction

20210107091104.0

Cataloguing Rules (Descriptive Conventions))

pn

Electronic name

[Book]

270410

Y