Math 132 (Fall 2024)
Instructor: Professor Hyunki Min
Discussion Section Location: MS 5127
TA Office Hours: Thursdays 12:00 – 1:30 PM in MS 2961 or by appointment.
You can find a course description through UCLA’s registrar. Official course materials are available on BruinLearn.
The aim of this course is to apply the theory of complex analysis to perform otherwise difficult computations, many of which have practical relevance in applications. The most intimidating and hence most famous examples would be contour integrals, such as \(\int _{-\infty}^{\infty} \frac{\log \left\lvert x+i \right\rvert}{x^2+4} dx\). The aim of discussion sections will be to get some guided practise on these sorts of computations, and hopefully this will in turn refresh the underlying theory along the way.
We’ll be using the textbook Complex Analysis by Gamelin, which is available for free to UCLA students at the previous link. I’ll be uploading my discussion notes and additional resources to this page as we go, so don’t worry if you have to miss a discussion!
- 1. Week 1: Complex Numbers, Alone and in Packs
- 2. Week 2: More on \(\exp\) and \(\log\)
- 3. Week 3: Complex Derivatives
- 4. Week 4: Conformal Mappings
- 5. Week 5: Estimating and Sometimes Computing Path Integrals
- 6. Week 6: The Fundamental Theorems of Complex Analysis
- 7. Week 7: Power Series
- 8. Week 8: Orders of Zeroes
- 9. Week 9: Laurent Series and Singularities
- 10. Week 10: Contour Integration