|About the Book|
This book is intended to be an introduction to tensors for anyone who has had differential and integral calculus. It should be understandable to upper-class college students in the physical sciences and engineering as well as to faculty and researchMoreThis book is intended to be an introduction to tensors for anyone who has had differential and integral calculus. It should be understandable to upper-class college students in the physical sciences and engineering as well as to faculty and research scientists. It was written specifically as an aid to anyone interested in the subject of cosmology (where an understanding of tensor analysis is indispensable) but not limited thereto. The starting point is the simplest possible - plane vectors as directed line segments. It progresses step by step from rectilinear coordinates in two dimensions to curvilinear coordinates in two dimensions, then rectilinear coordinates in three dimensions, curvilinear coordinates in three dimensions, and finally rectilinear and curvilinear coordinates in four or more dimensions. This progression allows the student to become familiar with the concepts and notation in a rational and graduated fashion, assisted at every step by relevant applications from geometry, physics, astronomy and cosmology. The ritual abracadabra of conventional vector and tensor courses is replaced by discussions with logical and intuitive appeal. The emphasis is at all times upon the utilitarian aspects of tensors. perhaps the most novel feature of this book is the final chapter. By the time the reader has reached this point, he will have been prepared to tackle traditional treatises on general relativistic cosmology if he so desires. This chapter, however, offers a wholly novel development of cosmology in flat space-time, inspired by E. A. Milnes kinematic relativity. It is shown that the space-time curvature is not a necessary feature of a successful theory of gravitation nor of a logically coherent model of the universe. Several of the advantages of such a treatment are pointed out and contrasted with currently accepted orthodox cosmologies.