On this page I give links to the complete set of (streaming video) screencasts from the 2009-10 edition of my fourth-year module G14FUN Functional Analysis (University of Nottingham).

**New!** The complete set of videos, lecture notes, question sheets and solutions, etc., can now be viewed or downloaded (1.9 Gb) from

http://unow.nottingham.ac.uk/resources/resource.aspx?hid=c9eec1dc-8c27-9949-dc16-2728edf6c994

as part of the University of Nottingham Open Courseware Repository U-NoW (http://unow.nottingham.ac.uk).

Similarly, the 2006-7 and 2007-8 versions of this module, including the printed notes and slides and audio recordings, and many other module materials, are available from

http://unow.nottingham.ac.uk/resources/resource.aspx?hid=bd32d53b-3c12-ac19-176b-d9e112731951

In the screencasts below, the quality of the picture-in-picture video of me in the corner was mostly poor for the first few lectures,** but improved a lot once I started using a desk lamp for additional illumination from lecture 8 onwards.
**

- Lecture 1 (introductory material on
**totally ordered sets and partially ordered sets**) - Lecture 2 (
**Chapter 1: Complete metric spaces**, printed slides 1-8) - Lecture 3 (
**revision of Metric and Topological Spaces**) - Lecture 4 (printed slides 7-9)
- Lecture 5, part a (printed slide 9 to end of Chapter 1)
- Lecture 5, part b (
**Chapter 2: Infinite products and Tychonoff’s theorem**, printed slides 13-14) - Lecture 6 (
**discussion session on totally ordered sets and partially ordered sets**) - Lecture 7 (printed slides 13-25)
- Lecture 8 (printed slides 20-27)
- Lecture 9, part a (printed slide 26 to end of Chapter2)
- Lecture 9, part b (
**Section 3.1: Normed spaces and Banach spaces**, printed slides 28-31) - Lecture 10 (printed slides 31-34)
- Lecture 11, part a (printed slides 33-34 continued, completeness of the uniform norm)
- Lecture 11, part b (Interlude on
**pointwise convergence and uniform convergence**) - Lecture 12 (printed slides 33-34 concluded, and printed slides 35-37)
- Lecture 13, part a (final discussion of Section 3.1)
- Lecture 13, part b (
**Section 3.2: Equivalence of norms**, whole of Section 3.2 discussed, including discussion of facts needed to prove Theorem 3.8) - Lecture 14, part a (recap of
- Lecture 14, part b (“conclusion” of Section 3.2, including the proofs of Theorems 3.8 and 3.10)
- Lecture 15, part a (final discussion of Section 3.2).
- Lecture 15, part b (
**Section 3.3: Linear maps**, printed slides 41-43) - Lecture 16, part a (Conclusion of Section 3.3 including recap, printed slide 44, connections with Lipschitz continuity)
- Lecture 16, part b (
**Section 3.4: Sequence spaces**, printed slides 45-48) - Lecture 17 (Recap of Section 3.4 and proof of part of Theorem 3.15)
- Lecture 18, part a (Conclusion of Section 3.4)
- Lecture 18, part b (
**Section 3.5: Isomorphisms**, printed slides 49-51) - Lecture 19, part a (Conclusion of Section 3.5: printed slides 51-54)
- Lecture 19, part b (
**Section 3.6: Sums and quotients of vector spaces**, printed slides 55-57) - Lecture 20, part a (Conclusion of Section 3.6, printed slides 57-60)
- Lecture 20, part b (
**Section 3.7: Dual spaces**, printed slides 61-64) - Lecture 21 (Section 3.7, printed slides 64-65)
- Lecture 22 (Conclusion of Section 3.7 and brief introduction to Section 3.8).
- Lecture 23 (All of Section 3.8,
**Extensions of linear maps**) - Lecture 24 (All of Section 3.9,
**Completions, quotients and Riesz’s Lemma**) - Lecture 25 (All of
**Chapter 4,****The Weak-* Topology and the Banach-Alaoglu Theorem**) - Lecture 26 (
**Chapter 5: Open Mappings and their Applications**, printed slides 93-96) - Lecture 27 (Chapter 5, printed slides 97-102)
- Lecture 28, part a (Recap concerning convex sets which are symmetric about 0, laptop running on battery power)
- Lecture 28, part b (Chapter 5, printed slides 102-108,
**note a ‘typo’ in the proof of Lemma 5.8 where one A should be an E**) - Lecture 29, part a (Recap, and proof of the Closed Graph Theorem)
- Lecture 29, part b (All of
**Chapter 6, The Uniform Boundedness Principle/Banach-Steinhaus**) - Lecture 30 (
**Commutative Banach Algebras**, printed slides 1-19) - Lecture 31 (Commutative Banach Algebras, printed slides 19-29)
- Lecture 32 (Discussion session on measure theory material)

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Those lectures are excellent! Highly recommend them 🙂

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Dear Dr. Joel,

I’m an MBA student. First of all, I want to thank you about these excellent Lectures.I understood a lot of things from it.

Secondly, I have some problems in proving Bernstein Theorem. If you please can help me with it. I read a lot from the internet and books, but i found it difficult to understand. Is there a simple way to understand the prove !!!

Thanks in Advance.

Regards,

Nehad

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