# Real / Functional Analysis Video Lectures?

## Main Question or Discussion Point

Does anybody know of any good resources for this? Specifically for real analysis, I'm looking for something that covers calculus on manifolds, differential forms, Lebesgue integration, etc. and for functional analysis: metric spaces, Banach spaces, Hilbert spaces, Fourier series, etc. Thanks!

I don't think you'll find any videos on the subject except for some very short ones taken here and there in the classroom or out to explain or not some obsolete concept of RA.

I look forward to taking this course next Fall or Winter and was hoping to find something so I can get a feel of what's at hand but alas to no avail.

A book I found at my university's library for functional analysis is

Functional Analysis Vol. I: A Gentle Introduction
by Dzung Minh Ha

Information here

http://matrixeditions.com/FunctionalAnalysisVol1.html

This book helped me a lot, and it explains things well. Unfortunately it's not listed at half.com or amazon.com. At least I can't find it there. Might be worth taking a look at.

Edit - Sorry, I didn't realize this post was asking for videos.

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Maybe you found what you were searching for, but I wanted to link you a you-tube channel I find interesting...

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For Lebesgue, I suggest Stein and Shakarchi's book Real Analysis which also goes through Hilbert Spaces and their many examples. Royden's Real Analysis is also very good. Rudin has two small chapter introducing Lebesgue integration and differential forms in his Principles of Mathematical Analysis. Rudin also goes through all the necessary things on metric spaces. This is the standard text in introductory analysis classes.

Rudin also has a book on Functional Analysis but I prefer Conway's.

For differential forms and calculus on manifolds, Munkres has a book on Analysis on Manifolds. I have not personally read this book. If you are advanced enough, I would suggest Lee's Introduction to Smooth Manifolds, which covers topics from differential topology and introduces differential forms in a very abstract way. This is the book I used and I highly recommend it if you have the necessary requirements. Also, Richard Bishop's Tensor Analysis on Manifolds (this book is very dense) and Spivak's Calculus on Manifolds (haven't read this but hear good things) are excellent.

You will find the original videos here:
http://www.uccs.edu/~math/vidarchive.html

The basic Analysis courses on that page are good, too.
This looks like a great resource. What browser did you use to view them? Every time I've tried, the streaming has been impossibly slow and staccato. Their viewing tips page says to right click on the video links to download them. But when I right click nothing happens, not in Firefox, nor in IE9.

This looks like a great resource. What browser did you use to view them? Every time I've tried, the streaming has been impossibly slow and staccato. Their viewing tips page says to right click on the video links to download them. But when I right click nothing happens, not in Firefox, nor in IE9.
It looks like they have changed their website for the worse. It is difficult to get the video files directly now. I looked at the page source and the MOV files are still available if you do a little hand-writing of addresses.

For example, if this is the course you want:
Code:
[PLAIN]http://cmes.uccs.edu/Fall2011/Math313/archive.php
[/PLAIN] [Broken]

The videos are listed as this (with the appropriate number):
Code:
[PLAIN]http://cmes.uccs.edu/Fall2011/Math313/Videos/Math313Lecture1.mov
[/PLAIN] [Broken]

You could email their feedback address saying that the streaming is poor and ask for an easy download link as well. It would actually save them bandwidth in the long run.

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Thank you, Sankaku, that's really made my day! I've been trying to find a way to watch those for ages. Let's just hope they don't disable it any time soon. I've notified them about the problem.

Astronuc
Staff Emeritus
Not a video lecture, but an online set of notes.

http://www.mathcs.org/analysis/reals/index.html

MathCS said:
Interactive Real Analysis is an online, interactive textbook for Real Analysis or Advanced Calculus in one real variable. It deals with sets, sequences, series, continuity, differentiability, integrability (Riemann and Lebesgue), topology, power series, and more.

td21
Gold Member
there's one from Harvey Mudd 4 years ago.... i think it's still on the internet. But low resolution.