Vectors, Tensors and the Basic Equations of Fluid Mechanics (Dover Books on Mathematics)
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This superb text develops and utilizes mathematical concepts to light up 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 on the subject of the theory of fluid mechanics.
Essentially an introductory text, intended for readers with some acquaintance with the calculus of partial differentiation and a couple of integration, it first reviews the important 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 glide in Euclidean space.
The concluding chapters discuss the geometry of surfaces in space, the equations of surface glide and equations for reacting fluids. Two invaluable appendixes present a resume of 3-dimensional coordinate geometry and matrix theory and some other of implicit functions and Jacobians. A generous collection of exercises are an integral a part of the presentation, providing a lot of opportunities for manipulation and extension of the concepts presented.
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