Vector and Tensor Analysis with Applications By A. I. Borisenko
This concise introduction to a basic branch of applied mathematics is indispensable to mathematicians, physicists and engineers. Eminently readable, it covers the elements of vector and tensor analysis, with applications of the theory to specific physics and engineering problems. It lays particular stress on the applications of the theory to fluid dynamics. Download Vector and Tensor Analysis with Applications Book.
The authors begin with a definition of vectors and a discussion of algebraic operations on vectors. The vector concept is then generalized in a natural way, leading to the concept of a tensor. Chapter Three considers algebraic operations on tensors. Next, the authors turn to a systematic study of the differential and integral calculus of vector and tensor functions of space and time. Finally, vector and tensor analysis is considered from both a rudimentary standpoint, and in its fuller ramifications, concluding the volume.