Introduction to Tensor Analysis and the Calculus of Moving Surfaces

4.21 avg rating
( 14 ratings by Goodreads )
 
9781461478669: Introduction to Tensor Analysis and the Calculus of Moving Surfaces

This textbook is distinguished from other texts on the subject by the depth of the presentation and the discussion of the calculus of moving surfaces, which is an extension of tensor calculus to deforming manifolds.

 

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.

 

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 author’s 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 consistent level of rigor, it takes great care to avoid formalizing the subject.

 

The last part of the textbook is devoted to the Calculus of Moving Surfaces. It is the first textbook exposition of this important technique and is one of the gems of this text. A number of exciting applications of the calculus are presented including shape optimization, boundary perturbation of boundary value problems and dynamic fluid film equations developed by the author in recent years. Furthermore, the moving surfaces framework is used to offer new derivations of classical results such as the geodesic equation and the celebrated Gauss-Bonnet theorem.

"synopsis" may belong to another edition of this title.

From the Back Cover:

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 reader’s 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 author’s 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.

 The last part of the textbook is devoted to the calculus of moving surfaces. It is the first textbook exposition of this important technique and is one of the gems of this text. A number of exciting applications of the calculus are presented including shape optimization, boundary perturbation of boundary value problems, and dynamic fluid film equations developed by the author in recent years. Furthermore, the moving surfaces framework is used to offer new derivations of classical results such as the geodesic equation and the celebrated Gauss–Bonnet theorem.

 

About the Author:

Pavel Grinfeld is currently a professor of mathematics at Drexel University, teaching courses in linear algebra, tensor analysis, numerical computation, and financial mathematics. Drexel is interested in recording Grinfeld's lectures on tensor calculus and his course is becoming increasingly popular. Visit Professor Grinfeld's series of lectures on tensor calculus on YouTube's playlist: http://bit.ly/1lc2JiY http://bit.ly/1lc2JiY  

Also view the author's Forum/Errata/Solution Manual (Coming soon): http://bit.ly/1nerfEf

The author has published in a number of journals including 'Journal of Geometry and Symmetry in Physics' and 'Numerical Functional Analysis and Optimization'. Grinfeld received his PhD from MIT under Gilbert Strang.

"About this title" may belong to another edition of this title.

Top Search Results from the AbeBooks Marketplace

1.

Pavel Grinfeld
ISBN 10: 1461478669 ISBN 13: 9781461478669
New Quantity Available: 3
Seller:
Books_Universe
(Sugarland, TX, U.S.A.)
Rating
[?]

Book Description Book Condition: New. Brand New. US Edition Book. We do not ship to Military Addresses. Fast Shipping with Order Tracking. For Standard Shipping 7-8 business days & Expedite Shipping 4-6 business days, after shipping. Bookseller Inventory # 1461478669-RMX

More Information About This Seller | Ask Bookseller a Question

Buy New
US$ 51.86
Convert Currency

Add to Basket

Shipping: FREE
Within U.S.A.
Destination, Rates & Speeds

2.

Pavel Grinfeld
Published by Springer (2013)
ISBN 10: 1461478669 ISBN 13: 9781461478669
New Hardcover Quantity Available: 1
Seller:
Irish Booksellers
(Rumford, ME, U.S.A.)
Rating
[?]

Book Description Springer, 2013. Hardcover. Book Condition: New. book. Bookseller Inventory # M1461478669

More Information About This Seller | Ask Bookseller a Question

Buy New
US$ 51.87
Convert Currency

Add to Basket

Shipping: FREE
Within U.S.A.
Destination, Rates & Speeds

3.

Pavel Grinfeld
Published by Springer-Verlag New York Inc., United States (2013)
ISBN 10: 1461478669 ISBN 13: 9781461478669
New Hardcover Quantity Available: 10
Seller:
The Book Depository US
(London, United Kingdom)
Rating
[?]

Book Description Springer-Verlag New York Inc., United States, 2013. Hardback. Book Condition: New. 2013 ed.. Language: English . Brand New Book. This textbook is distinguished from other texts on the subject by the depth of the presentation and the discussion of the calculus of moving surfaces, which is an extension of tensor calculus to deforming manifolds. 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. 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 author s 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 consistent level of rigor, it takes great care to avoid formalizing the subject. The last part of the textbook is devoted to the Calculus of Moving Surfaces. It is the first textbook exposition of this important technique and is one of the gems of this text. A number of exciting applications of the calculus are presented including shape optimization, boundary perturbation of boundary value problems and dynamic fluid film equations developed by the author in recent years. Furthermore, the moving surfaces framework is used to offer new derivations of classical results such as the geodesic equation and the celebrated Gauss-Bonnet theorem. Bookseller Inventory # SPR9781461478669

More Information About This Seller | Ask Bookseller a Question

Buy New
US$ 52.00
Convert Currency

Add to Basket

Shipping: FREE
From United Kingdom to U.S.A.
Destination, Rates & Speeds

4.

Pavel Grinfeld
Published by Springer-Verlag New York Inc., United States (2013)
ISBN 10: 1461478669 ISBN 13: 9781461478669
New Hardcover Quantity Available: 10
Seller:
The Book Depository
(London, United Kingdom)
Rating
[?]

Book Description Springer-Verlag New York Inc., United States, 2013. Hardback. Book Condition: New. 2013 ed.. Language: English . Brand New Book. This textbook is distinguished from other texts on the subject by the depth of the presentation and the discussion of the calculus of moving surfaces, which is an extension of tensor calculus to deforming manifolds. 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. 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 author s 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 consistent level of rigor, it takes great care to avoid formalizing the subject. The last part of the textbook is devoted to the Calculus of Moving Surfaces. It is the first textbook exposition of this important technique and is one of the gems of this text. A number of exciting applications of the calculus are presented including shape optimization, boundary perturbation of boundary value problems and dynamic fluid film equations developed by the author in recent years. Furthermore, the moving surfaces framework is used to offer new derivations of classical results such as the geodesic equation and the celebrated Gauss-Bonnet theorem. Bookseller Inventory # SPR9781461478669

More Information About This Seller | Ask Bookseller a Question

Buy New
US$ 53.30
Convert Currency

Add to Basket

Shipping: FREE
From United Kingdom to U.S.A.
Destination, Rates & Speeds

5.

Pavel Grinfeld, Pavel Greenfield
Published by Springer 2013-09-24 (2013)
ISBN 10: 1461478669 ISBN 13: 9781461478669
New Quantity Available: 5
Seller:
Chiron Media
(Wallingford, United Kingdom)
Rating
[?]

Book Description Springer 2013-09-24, 2013. Book Condition: New. Brand new book, sourced directly from publisher. Dispatch time is 24-48 hours from our warehouse. Book will be sent in robust, secure packaging to ensure it reaches you securely. Bookseller Inventory # NU-GRD-05036685

More Information About This Seller | Ask Bookseller a Question

Buy New
US$ 50.64
Convert Currency

Add to Basket

Shipping: US$ 3.98
From United Kingdom to U.S.A.
Destination, Rates & Speeds

6.

Pavel Grinfeld
ISBN 10: 1461478669 ISBN 13: 9781461478669
New Quantity Available: 3
Seller:
Speedy Hen LLC
(Sunrise, FL, U.S.A.)
Rating
[?]

Book Description Book Condition: New. Bookseller Inventory # ST1461478669. Bookseller Inventory # ST1461478669

More Information About This Seller | Ask Bookseller a Question

Buy New
US$ 58.01
Convert Currency

Add to Basket

Shipping: FREE
Within U.S.A.
Destination, Rates & Speeds

7.

Pavel Grinfeld
Published by Springer New York 2013-09-24, New York (2013)
ISBN 10: 1461478669 ISBN 13: 9781461478669
New Hardcover Quantity Available: > 20
Seller:
Blackwell's
(Oxford, OX, United Kingdom)
Rating
[?]

Book Description Springer New York 2013-09-24, New York, 2013. hardback. Book Condition: New. Bookseller Inventory # 9781461478669

More Information About This Seller | Ask Bookseller a Question

Buy New
US$ 50.33
Convert Currency

Add to Basket

Shipping: US$ 7.99
From United Kingdom to U.S.A.
Destination, Rates & Speeds

8.

Grinfeld, Pavel
Published by Springer-Verlag New York Inc. (2013)
ISBN 10: 1461478669 ISBN 13: 9781461478669
New Quantity Available: 7
Seller:
Books2Anywhere
(Fairford, GLOS, United Kingdom)
Rating
[?]

Book Description Springer-Verlag New York Inc., 2013. HRD. Book Condition: New. New Book. Shipped from UK in 4 to 14 days. Established seller since 2000. Bookseller Inventory # GB-9781461478669

More Information About This Seller | Ask Bookseller a Question

Buy New
US$ 47.50
Convert Currency

Add to Basket

Shipping: US$ 11.99
From United Kingdom to U.S.A.
Destination, Rates & Speeds

9.

Pavel Grinfeld
Published by Springer
ISBN 10: 1461478669 ISBN 13: 9781461478669
New Hardcover Quantity Available: 2
Seller:
THE SAINT BOOKSTORE
(Southport, United Kingdom)
Rating
[?]

Book Description Springer. Hardcover. Book Condition: New. New copy - Usually dispatched within 2 working days. Bookseller Inventory # B9781461478669

More Information About This Seller | Ask Bookseller a Question

Buy New
US$ 52.42
Convert Currency

Add to Basket

Shipping: US$ 9.24
From United Kingdom to U.S.A.
Destination, Rates & Speeds

10.

Pavel Grinfeld, Pavel Greenfield
Published by Springer 2013-09-24 (2013)
ISBN 10: 1461478669 ISBN 13: 9781461478669
New Quantity Available: 3
Seller:
Chiron Media
(Wallingford, United Kingdom)
Rating
[?]

Book Description Springer 2013-09-24, 2013. Book Condition: New. Brand new book, sourced directly from publisher. Dispatch time is 24-48 hours from our warehouse. Book will be sent in robust, secure packaging to ensure it reaches you securely. Bookseller Inventory # NU-LBR-01231323

More Information About This Seller | Ask Bookseller a Question

Buy New
US$ 58.38
Convert Currency

Add to Basket

Shipping: US$ 3.98
From United Kingdom to U.S.A.
Destination, Rates & Speeds

There are more copies of this book

View all search results for this book