Introductory Differential Geometry For Physicists - Tapa dura

"... the book is very suitable for advanced undergraduates or researchers in other areas interested in an introduction to the subject ... A very interesting feature of this book is that all the examples and exercises are motivated by important physical theories. Therefore the book is also of interest to mathematicians." Jair Koiller Mathematical Reviews "The present book certainly provides the basic tools in an easily digestible form and with plenty of concrete mathematical detail. As such I am sure it will be found useful by a research student intending to take up research in this area, or someone needing to brush up on a particular topic ... it should prove useful for a postgraduate lecture course." G W Gibbons Contemporary Physics "The many complements and exercises and their connections to physics are the strong point of this book; they are due to the author's philosophy that an abstract introduction of mathematical concepts should be motivated to students in physics by examples and applications while a purely intuitive and heuristic differential geometric education of physicists is not sufficient." U Simon Mathematics Abstracts

This book develops the mathematics of differential geometry in a way more intelligible to physicists and other scientists interested in this field. This book is basically divided into 3 levels; level 0, the nearest to intuition and geometrical experience, is a short summary of the theory of curves and surfaces; level 1 repeats, comments and develops upon the traditional methods of tensor algebra analysis and level 2 is an introduction to the language of modern differential geometry. A final chapter (chapter IV) is devoted to fibre bundles and their applications to physics. Exercises are provided to amplify the text material.