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

Introductory text for engineers, physicists and applied mathematicians applies mathematics of Cartesian and general tensors to physical field theories, demonstrating them chiefly in terms of the theory of fluid mechanics. Many exercises throughout the text. Index. Preface. Appendixes. 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. 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 anddemonstrates them chiefly in terms of the theory of fluid mechanics. Numerous exercises appear throughout the text. 1962 edition. this is really a nice book if you want to work on fluid mechanics. it provides you the equations of fluid mechanics in different coordinate system.