This book develops and utilizes mathematical concepts to illuminate physical theories. 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. 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. Numerous exercises appear throughout the text.Content:Front Matter Preface Table of Contents1. Introduction2. Cartesian Vectors and Tensors: Their Algebra3. Cartesian Vectors and Tensors: Their Calculus4. The Kinematics of Fluid Motion5. Stress in Fluids6. Equations of Motion and Energy in Cartesian Coordinates7. Tensors8. The Equations of Fluid Flow in Euclidean Space9. The Geometry of Surfaces in Space10. The Equations of Surface Flow11. Equations for Reacting FluidsAppendicesIndex