Video lectures on Real Analysis?

Question

One of the most annoying gaps in my math education is Real analysis.

I tried hard, but all I could find are either Harvey Mudd College lectures or MathDoctorBob. The latter are too short and the former are in horrendous format, I can barely make out what is written on the blackboard.

Ideally I'd like the lectures to cover topics such as proofs of continuity, differentiation, some main inequalities, $\limsup$ and $\liminf$, uniform/pointwise convergence and continuity, dominated and monotone convergence and maybe a bit more.

So if anyone knows if this material is available online, I'd be quite grateful.

Answer 1

You can try: http://www.uccs.edu/math/student-resources/video-course-archive.html

They have a Real Analysis course listed, Math 533 Real Analysis I - Fall 2007. They are good, though not that challenging.

You may need to create a [free] account to view the videos.

If you really don't want to make an account the videos start with:

http://cmes.uccs.edu/Fall2007/Math533/pages/video3.html

and go up to /video24.html. There is, for some reason, no video 1 or 2.

Answer 2

Check out these YouTube video lectures by S K Ray on real analysis.

Answer 3

Video Lectures in Mathematics , This site contains links to math videos, withch includes a lot of mathematical topics for example Topology, Algebra, Complex and real analysis and anything that you think.

Specifically, the site has 38 videos in real analysis: Analysis, Real.

Answer 4

In fact I ended up using Nottingham Uni's lectures on Youtube, like this one:

http://www.youtube.com/watch?v=mB4Yny0T3HA

Answer 5

This was basically already posted by Alex - but Joel Feistein has his 2nd year undergrad introductory course to real analysis (complete with camcasts/videos, notes, exercises and solutions) posted here http://unow.nottingham.ac.uk/resources/resource.aspx?hid=c6c045f6-286d-6b9f-b96c-36a998632fc3 and his 4th year undergrad course on functional analysis here http://unow.nottingham.ac.uk/resources/resource.aspx?hid=c9eec1dc-8c27-9949-dc16-2728edf6c994.

They are both quite good (the first one introduced me, at the time an engineering undergrad, to rigorous mathematics and how to do proofs and I cannot be happier of having watched it).

Answer 6

I was searching for the same and came across these video lectures by Dr. Jaikrishan J, Real Analysis.

As far as I know, these videos constitute one of the best lectures on the topic of Real Analysis. There are a total of 125 videos in this playlist of length varying from 2 mins to 30 mins, summing up to 1 day, 10 hours, 16 minutes, 24 seconds (~2056 minutes).

Example:

Consider this video: 7.1 Motivation for infinite series

In this video he considers the case of a chocolate bar with promotional offer on its wrappers. And goes on to show that the chocolate with the wrapper is worth more than the chocolate. By this he shows how infinite series emerges in real life situations. All of this is presented in a very logical manner.

The language of instruction is English.

Hope this helps!