Ebook: Friendly Approach To Functional Analysis, A

Intro; Contents; Preface; 1. Normed and Banach spaces; 1.1 Vector spaces; 1.2 Normed spaces; 1.3 Topology of normed spaces; 1.4 Sequences in a normed space; Banach spaces; 1.5 Compact sets; 2. Continuous and linear maps; 2.1 Linear transformations; 2.2 Continuous maps; 2.3 The normed space CL(X, Y); 2.4 Composition of continuous linear transformations; 2.5 (â#x80;Ø) Open Mapping Theorem; 2.6 Spectral Theory; 2.7 (â#x80;Ø) Dual space and the Hahn-Banach Theorem; 3. Differentiation; 3.1 Definition of the derivative; 3.2 Fundamental theorems of optimisation; 3.3 Euler-Lagrange equation.