Advertisement
Published in:
2014 | OriginalPaper | Chapter
12. Differentiation and Integration
Author : Joseph Muscat
Published in: Functional Analysis
Publisher: Springer International Publishing
Activate our intelligent search to find suitable subject content or patents.
Select sections of text to find matching patents with Artificial Intelligence. powered by
Select sections of text to find additional relevant content using AI-assisted search. powered by
Abstract
Although the continuous linear operators are of paramount importance as the morphisms of normed spaces, much can be deduced about ‘locally linear’ maps, otherwise known as differentiable functions. Particular consideration is given to generalizations of the Fundamental Theorem of Calculus, the Mean Value Theorem, and Taylor’s theorem to Banach spaces. The theory is applied to the Newton Raphson iteration method of solving equations. Complex differentiable functions, known as analytic functions, have distinctively more rigid properties, borne out by a string of results proved by Cauchy, including the Cauchy’s Residue theorem and Integral Formula.