Is functional analysis part of real analysis?

That said, functional analysis is pretty much universally taught as a continuation of real analysis—real analysis gives you the foundation to think about limits and metric spaces, which then gets used in complex analysis, measure theory, and functional analysis.

Do you need real analysis before complex analysis?

A usual course in complex analysis does not require a course in real analysis, although it might need advanced calculus.

Is functional analysis difficult?

Functional analysis is conceptually more difficult (starts off with point set topology) and has both real and complex analysis as prerequisites.

What is the main concept of functional analysis?

Functional analysis is a methodology that is used to explain the workings of a complex system. The basic idea is that the system is viewed as computing a function (or, more generally, as solving an information processing problem).

What is functional analysis in math?

Functional analysis is, for a large part, linear algebra on a infinite dimensional vector space over the real or complex numbers.

What is the best book to start learning linear functional analysis?

Linear Functional Analysis by Rynne and Youngson (Springer Undergraduate) is really understandable if you don’t have many prerequisites, comparable to Kreyzig’s book. It doesn’t cover that much material, but all the basics are there, with all details filled in. We used Conway (about 3/4th) of the book for functional analysis.

What are the requirements for the first functional analysis course?

Not to scare you, but list of requirements for a first course in functional analysis is rather long: Arzelà-Ascoli (how else will you show that an operator is compact?) Measure theory — or at least be ready to accept that you have to learn some while reading functional analysis.

What are some of the best books on infinite dimensional analysis?

Inner product spaces, including the Riesz representation theorem, normed/metric spaces and topological spaces. Granted, the Hahn-Banach theorem isn’t introduced until chapter 11 but the text is mostly self-contained and very easy to read. One unconventional book is Infinite Dimensional Analysis: A Hitchiker’s Guide by Aliprantis and Border.