Introductory to Functional Analysis

In summary, the conversation is about finding online resources for functional analysis, specifically a free PDF. One person suggests a website and another recommends purchasing Kreyszig's book. The person asking for resources also has questions about notations and LaTeX. The conversation ends with a suggestion for a tutorial on LaTeX and a positive review of Kreyszig's book.
  • #1
bugatti79
794
1
Folks,

I am starting a module in functional analysis undergrad level. I have been suggested introductory functional analysis by Kreyszig, but in instead of buying another expensive book is there a good online source like a pdf on in this topic that I could avail of?

Any help will be appreciated.

Kind regards
Eddie
 
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  • #3
Kreyszig (700 pages from 1978) is VERY good and provides you with a lot of information. If you're really interested in this topic of maths, make an effort & get it.
 
  • #4
Thank you guys. I got my hands on Kreyszig.

What I am missing now some useful link detailing

1) all the notations used in Functional analysis like the symbol for 'subset', 'is an element if', 'for all' etc etc. I see kreyszig has some notation but its not completely definitive?

2) A link to the equivalent Latex notation so i can write on this forum.

Thanks
 
  • #5
1) I don't understand. Check his page 609 where he starts an appendix on set theory and has all the notations listed. What do you mean definitive ? Are there any inconsistencies ?

2) You can type on this forum using TEX/LATEX code. Search this forum or the internet for tutorials.

EDIT: Here's a free tutorial I found in my computer.
 

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  • #6
ok, thanks dextercioby although I am waiting for that attachment to be approved that last few days :-)
 
  • #7
bugatti79 said:
2) A link to the equivalent Latex notation so i can write on this forum.

Thanks

https://www.physicsforums.com/showthread.php?t=8997

& the kreyszig book is great. it does basic functional analysis & keeps the measure & topology to a minimum. the only topology that I remember off the top of my head is sequential compactness.
 
Last edited:

1. What is Functional Analysis?

Functional Analysis is a branch of mathematics that studies vector spaces and linear operators between them, with a focus on infinite-dimensional spaces. It provides a framework for analyzing and solving problems in diverse areas such as physics, engineering, economics, and more.

2. What are the key concepts in Functional Analysis?

The key concepts in Functional Analysis include vector spaces, linear operators, Banach spaces, Hilbert spaces, and functionals. Other important topics include topological vector spaces, duality, and the Hahn-Banach theorem.

3. How is Functional Analysis different from other branches of mathematics?

Functional Analysis is unique in its focus on infinite-dimensional spaces and the study of linear operators between them. It also has applications in many other fields, making it a highly interdisciplinary branch of mathematics.

4. What are some real-world applications of Functional Analysis?

Functional Analysis has numerous real-world applications, including in physics (quantum mechanics, fluid dynamics), engineering (signal processing, control theory), economics (game theory, optimization), and more. It also plays a crucial role in the development of modern data science and machine learning algorithms.

5. What are some useful resources for learning Functional Analysis?

Some useful resources for learning Functional Analysis include textbooks such as "Introductory Functional Analysis with Applications" by Kreyszig and "Functional Analysis" by Rudin. Online resources such as lecture notes, video lectures, and problem sets are also available on various university websites and educational platforms like Coursera and edX.

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