Tensor analysis for physicists

This book offers a valuable, yet not entirely self-contained, introduction to classical tensor analysis. As a beginner, I found the text to be too terse and was forced to consult other sources, such as Levi-Civita's "Absolute Differential Calculus" and Eisenhart's "Riemannian Geometry". Once I had gained some familiarity with the basic notions, Schouten's book became the preferred reference. The author develops an extremely precise notation which he calls the "kernel-index method" and systematically applies it as a problem solving tool throughout the book. Looking back, it is difficult to say how I ever got along without it. Unfortunately, the book's terseness is due in part to the fact that the first five chapters are basically abridged excerpts from the author's lengthier 1954 treatise, "Ricci-Calculus". In nearly every respect, the aforementioned title is more complete than the present book. In the interest of saving space for the physical applications in the second half of the text, the author omitted important details, such as an adequate definition of manifold and the role of the vector field which generates the infinitesimal transformations used in discussing Lie derivatives.