Modern Geometry - Methods and Applications

The first 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. Throughout the book, the authors have adhered to a principle of minimal abstractness of exposition and terminology, giving preference to geometric intuition over excessive rigour, and significant examples over general theorems.