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Vectors, Tensors and the Basic Equations of Fluid Mechanics (Dover Books on Mathematics), by Rutherford Aris, Mathematics
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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.
- Sales Rank: #185113 in Books
- Published on: 1990-01-01
- Released on: 1990-01-01
- Original language: English
- Number of items: 1
- Dimensions: 8.48" h x .64" w x 5.40" l, .73 pounds
- Binding: Paperback
- 320 pages
Most helpful customer reviews
52 of 55 people found the following review helpful.
Mathematical Foundations of Fluid Mechanics
By Utah Blaine
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.
17 of 22 people found the following review helpful.
Not for the weakhearted!
By Vivek Sharma
This is one of those pithy classics that one needs to tread through very very carefully. The book is an uphill task, wherein rests its utility and fun. Fluid Mechanics in its simplified diluted version is served in many OTHER textbooks. This one serves it in its raw mathematical glory, and as the author says in the preface of the book, any serious engineer and fluid mechanician must realize that math must be befriended and mastered. The author makes very terse, and powerful introduction to the field. I would recommend a physicist to supplement it with a text by Faber, for Chemical Engineer to study it after the famous BSL (Transport Phenomenon), for a mathematician to pick it on any day, and for everyone in general to approach it with determination required to climb a rocky terrain. (Ah! I guess I would write an even better review if and when I finish reading it:)
17 of 18 people found the following review helpful.
Very complete introduction to tensor analysis in 3 dimensions.
By Daverz
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
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