Vectors and Tensors in Engineering and Physics Second Edition by D.A. Danielson. 
This text develops the calculus of tensor fields and uses this mathematics to model the physical world. This new edition includes expanded derivations and solutions, and new applications. The book provides equations for predicting the rotations of gyroscopes and other axisymmetric solids, derived from Euler's equations for the motion of rigid bodies; the temperature decays in quenched forgings, derived from the heat equation; the deformed shapes of twisted rods and bent beams, derived from the Navier equations of elasticity; the flow fields in cylindrical pipes, derived from the Navier-Stokes equations of fluid mechanics; The book also features over 100 illustrations, complete solutions to over 400 examples and problems, Cartesian components, general components, and components-free notations, lists of notations used by other authors, boxes to highlight key equations, historical notes, and an extensive.