Mukherjea K. Differential Calculus in Normed Linear Spaces

2nd Edition. — Hindustan Book Agency (India), 2007. — 299 p. —(Texts and Readings in Mathematics 26) — ISBN: 8185931763.This book arose out of a course on Advanced Calculus I taught several years ago to second year students of the B. Stat. programme at the In- dian Statistical Institute, Calcutta. The contents of the course had been determined, to a very large extent, by my experience of teaching Differ- ential Geometry to students at theM. Stat. level. I had found that when dealing with functions between open sets of Euclidean spaces, even the best of our students had difficulty in treating the derivative as a linear map (rather than the Jacobian matrix) and that their grasp of the In- verse/Implicit Function Theorems lacked conviction. As a result the first few weeks of my Differential Geometry lectures were always devoted to a crash course on Advanced Calculus with a geometric viewpoint; that is, without using the usual apparatus of partial derivatives, Jacobians, etc. I had found that students found it easier to grasp the essence of results x like the Inverse Function Theorem in this kind of geometric treatment of Advanced Calculus.Preliminaries
Linear Spaces: New Spaces for Old
Normed Linear Spaces, Metric Spaces
Calculus
Existence Theorems
Applications: Stationary values
Appendix: Green's Theorem