I have taken a liking to thinking of Rutherford Aris as the Yogi Berra of science I ve quoted him often, and in many ways, he was the great American philosopher of his field However, do not let that fool you Dr Aris was an exceptional mathematician and physical scientist, and it shows in his treatment of fluid mechanics for this text.Aris begins this book with the standard introduction to the algebra of vectors and tensors, and he advances this notion early on, with his explanations involving indicial notation and a Cartesian geometry Many will find his notation to be a bit off the beaten path, but a disciplined reader will gain great insight in mathematical fluid mechanics, provided that they are willing to pay close attention to his definitions After his algebraic treatment, Aris moves into the calculus of vectors and tensors, with a bit thorough treatment than what is typically seen in a modern college course It is only after laying this strong mathematical foundation, that Aris proceeds to the advanced descriptions involving fluid mechanics.Dr Aris gets to the real meat and potatoes, so to speak, in chapters 4 and 5, where he develops the kinematics and stress for fluids In chapter 6 he derives the equations of motion and energy, while chapter 7 is dedicated solely to a advanced discussion on tensors Chapter 8 is where the reader will finally get their proper explanation pertaining to the Navier Stokes Equations, and it is arguably the standout of this text From there, Aris moves into the geometrical concepts of curved surfaces, and in chapter 10 he describes the equations of surface flow He then finishes with a chapter on reacting fluids, and of central importance to everyone is section 11.31, where Aris derives the Law of Conservation of Energy for fluids.In addition to an excellent appendix, this book also includes exercises that can help one understand problem solving techniques for fluids, but admittedly, I found it useful to keep my scratch pad handy while reading the text, and to think long and hard about the descriptions Perhaps, the only glaring omissions, are advanced theoretical descriptions pertaining to turbulence Nonetheless, considering when it was written, I am willing to forgive such imperfections I thoroughly enjoyed this book, and I would highly recommend it for anyone with an interest in vectors and tensors, as well as those who are seeking a deeper mathematical understanding of fluid mechanics. Book is fine, but the equations are scanned copies of the text and are often to small to zoom in on magnifying glass icon does no appear on the screen Problem with the paperwhite kindle not the book The guy who wrote this did it in such a way to let you know how smart he was, not to let you know how to learn the subject He skips a lot of information you need to keep up. 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. This excellent text develops and utilizes mathematical concepts to illuminate physical theories Directed primarily to engineers, physicists, and applied mathematicians at 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.Essentially an introductory text, intended for readers with some acquaintance with the calculus of partial differentiation and multiple integration, it first reviews the necessary background material, then proceeds to explore the algebra and calculus of Cartesian vectors and tensors Subsequent chapters take up the kinematics of fluid motion, stress in fluids, equations of motion and energy in Cartesian coordinates, tensors, and equations of fluid flow in Euclidean space.The concluding chapters discuss the geometry of surfaces in space, the equations of surface flow and equations for reacting fluids Two invaluable appendixes present a resume of 3 dimensional coordinate geometry and matrix theory and another of implicit functions and Jacobians A generous number of exercises are an integral part of the presentation, providing numerous opportunities for manipulation and extension of the concepts presented.Aris is affiliated with the University of Minnesota.