Aris R. Vectors, Tensors, and the Basic Equations of Fluid Mechanics

Dover Publications, 1989. 314 p. ISBN: 0486661105

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 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.
Many exercises throughout the text.

Introduction
Cartesian Vectors and Tensors: Their Algebra
Cartesian Vectors and Tensors: Their Calculus
Equations for Reacting Fluids
Appendix A. Resume of Three-dimensional Coordinate Geometry and Matrix Theory
Appendix B. Implicit Functions and Jacobians
Index