Modern Geometry-Methods and Applications, Part I The Geometry of Surfaces, Transformation Groups, and Fields

This is the first volume of a three-volume introduction to modern geometry, with emphasis on applications to other areas of mathematics and theoretical physics. Topics covered include tensors and their differential calculus, the calculus of variations in one and several dimensions, and geometric field theory. This material is explained in as simple and concrete a language as possible, in a terminology acceptable to physicists. The text for the second edition has been substantially revised.Dubrovin, B. A. is the author of 'Modern Geometry-Methods and Applications, Part I The Geometry of Surfaces, Transformation Groups, and Fields', published 1991 under ISBN 9780387976631 and ISBN 0387976639.