Vectors, Tensors and the Basic Equations of Fluid Mechanics (Dover Books on Mathematics) [Paperback]

Rutherford Aris (Author), Mathematics (Author)

Book Description

ISBN-10: 0486661105 | ISBN-13: 978-0486661100 | Publication Date: January 1, 1990

This introductory text is geared toward engineers, physicists, and applied mathematicians at the advanced undergraduate and graduate levels. It applies the mathematics of Cartesian and general tensors to physical field theories and demonstrates them chiefly in terms of the theory of fluid mechanics. Numerous exercises appear throughout the text. 1962 edition.

Product Details

• Paperback: 320 pages
• Publisher: Dover Publications (January 1, 1990)
• Language: English
• ISBN-10: 0486661105
• ISBN-13: 978-0486661100
• Product Dimensions: 8.5 x 5.4 x 0.6 inches
• Shipping Weight: 11.2 ounces (View shipping rates and policies)
• Average Customer Review: 4.6 out of 5 stars  See all reviews (13 customer reviews)
• Amazon Best Sellers Rank: #48,307 in Books (See Top 100 in Books)
  • #29 in Books > Professional & Technical > Professional Science > Physics > Mechanics

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Customer Reviews

Most Helpful Customer Reviews

22 of 23 people found the following review helpful:

4.0 out of 5 stars Mathematical Foundations of Fluid Mechanics, May 6, 2007

By 

Utah Blaine (Somewhere on Trexalon in District 268) - See all my reviews

This review is from: Vectors, Tensors and the Basic Equations of Fluid Mechanics (Dover Books on Mathematics) (Paperback)

The title and many of the Amazon reviews of this book are misleading in my opinion. This book should have been titled `The Mathematical Foundation of Fluid Mechanics'. This book describes, in gory detail, the fundamental mathematics of viscous fluid flow. The text is, obviously, heavy on vector and tensor calculus. The first few chapters review the basic theorems of vector and tensor calcular relevent to fluid dynamics. The basic equations of fluid dynamics are then derived, and the analysis is extended to viscous flow. Finally, Aris discusses coordinate transformation and tensor analysis (that is really more of a lead-in to GR than fluid dynamics, although it is interesting to see how this all ties together!). This is NOT a `complete' text in hydrodynamics. There is no discussion of turbulence, supersonic flow, instabilities, etc. This is a text on the mathematical (and geometrical) foundations of hydrodynamics. As such, I view this as an advanced text for a researcher who wants to understand hydrodynamics at it's most complete, fundamental mathematical level. If you are searching for any other type of hydrodynamics text, just move on. The reason that I only gave this book four stars was because I feel that hydrodynamics is a much richer discipline than what is contained within this book. Some of the most enthusiastic reviews greatly overstate the value of working through this book. You will learn quite a bit by going through this book, and it is a great text IF you want to study the foundations of hydrodynamics in great detail, but you will need (alot) more if you want to begin to appreciate fluid mechanics.

11 of 12 people found the following review helpful:

5.0 out of 5 stars Very complete introduction to tensor analysis in 3 dimensions., September 28, 2006

By 

Daverz - See all my reviews

Amazon Verified Purchase

This review is from: Vectors, Tensors and the Basic Equations of Fluid Mechanics (Dover Books on Mathematics) (Paperback)

This would make a good introduction to tensors for physics students (e.g. for General Relativity), though the approach is a completely classical, using index notation; you won't find anything on manifolds or differential forms here. An interesting feature is an extensive chapter on local surface theory (e.g. Gaussian curvature, but only after introducing the full Riemann tensor), which is good for building intuition about curvature in higher dimensions. While the applications are all in n <= 3 dimensions, the mathematics is done in a way that easily generalizes to higher dimensions.

28 of 37 people found the following review helpful:

5.0 out of 5 stars Too good!, March 17, 2000

By 

"rishiputra" - See all my reviews

This review is from: Vectors, Tensors and the Basic Equations of Fluid Mechanics (Dover Books on Mathematics) (Paperback)

Well, I don't want to go into an endless list of superlatives which this book really deserves. I'd rather point out some of its features. It's terse, sometimes awfully so & therefore, this's not the best book to learn the "basics". Don't expect any elementary physics of fluid flow. I've only read the first half of the book and in those less-than-hundred pages, I've appreciated fluid mechanics much more than I've by any other means. However, I must say that the so-called "indices" notation for vectors and tensors can be extremely frustrating and even confusing. This notation is so extensively used in the book that it can become possibly the only reason to put the book down. The order of presentation is quite nice.

There are few problems to solve which mostly seem to fill in the details of presentation. The last chapter on mass transport is a disappointment, with nothing close to what one would expect in a book of this stature. It is however included only because "it would be unpardonable not to do so, for a book coming from Chemical Engineering dept".

The author says in his preface that the time has come to go beyond the notion that engineers don't need rigorous applied mathematics and he proves his point in every page of his book. It's a pleasure to read and work on, especially the second half of the book. With patience, paper and pencil (lots of them), one can gain a real mastery over the subject. A true graduate-level book!