## Math 131BH (Spring 2024)

Instructor: Professor Michael Hitrik

Discussion Section Location: LaKretz 120

TA Office Hours: Tuesdays 10:00 AM - 11:00 AM; Thursdays 11:00 AM - 12:00 PM in MS 2943

You can find a course description through UCLA’s registrar. Official course materials are available on BruinLearn.

This is very loosely a continuation of Math 131AH from last quarter. Welcome back if you were here last quarter, and welcome if you weren’t! We will studying some properties of spaces of functions — how can we describe the closed and compact subsets of these spaces with respect to various notions of convergence? We’ll also be studying analytic functions and their Taylor series alongside some applications and generalisations of the integral from last quarter.

You will find detailed notes for whatever I plan to cover for my discussion sections on this page, alongside some other notes and resources I may write along the way.

**Week 5 Announcement**: Due to current events and university policy, the Thursday discussion and office hours have been moved online.

**Week 6 Announcement**: Due to continuing current events, this week’s office hours and discussions have all been moved online.

- 1. Compactness, Uniform Convergence, and the Weierstrass M-Test
- 2. The Diagonalisation Argument and Equicontinuity
- 3. Weierstrass' Approximation Theorem and Convolutions
- 4. Integration Review
- 5. Comments on Homework 2, Problem 3
- 6. Differentiating Power Series, Taylor Series
- 7. Comments on Homework 3
- 8. Convolutions
- 9. Multivariable Calculus Refresher
- 10. The Inverse Function Theorem and More
- 11. A Generalisation of the Implicit Function Theorem
- 12. Some Final Practise Problems