Spain Barry. Tensor Calculus

3rd ed. — Oliver & Boyd, 1960. — 124 p.The object of this book is to provide a compact exposition of the fundamental results in the theory of tensors and also to illustrate the power of the tensor technique by applications to differential geometry, elasticity, and relativity. In the first five chapters the mathematical concepts are developed without undue stress on rigour. The remaining three chapters are independent of one another except that sections 38 and 39 of chapter VI, which treats Euclidean three-dimensional differential geometry, are necessary for a proper understanding of chapter VII which contains the theory of cartesian tensors and elasticity. Finally, chapter VIII is devoted both to the special and general theories of relativity. In the limited space available it is impossible to do justice to the physical principles underlying both these theories. But in order to help the reader unacquainted with relativity some explanatory matter has been incorporated into the text.The presentation owes much to the authors listed in the bibliography, especially to McConnell, Synge and Schild. In particular, I wish to express my thanks to Dr. D. E. Rutherford for numerous suggestions and helpful criticisms during the manuscript and proof stages. Lastly I wish to thank my wife for her help with the proofreading.