This is an undergraduate-level course on Complex Analysis.
Lecturer: Prof. Bing Wang
TA: 林晓烁
Textbook: Complex Analysis, Elias M. Stein and Rami Shakarchi. I am updating an Errata to this book.
Time: 14:00–15:35, Tuesday; 09:45–12:10, Thursday
Classroom: 5106
All written assignments are Exercises / Problems from the textbook unless otherwise noted.
HW 1 (Due: 03-06) 1.4.2, 1.4.4, 1.4.5, 1.4.6, 1.4.7, 1.4.9, 1.4.15, 1.4.16 Solutions
HW 2 (Due: 03-13) 2.6.1, 2.6.2, 2.6.3, 2.6.4, 2.6.5, 2.6.6, 2.6.7 Solutions
HW 3 (Due: 03-20) 2.6.9 (One should add the condition that \(\Omega\) is connected), 2.6.11, 2.6.13, 2.6.15, 2.7.3, 2.7.4 Solutions
HW 4 (Due: 03-27) 3.8.1, 3.8.2, 3.8.3, 3.8.4, 3.8.5, 3.8.6, 3.8.7, 3.8.13. Additional exercise: Show that \[\int_{-\infty}^{\infty}e^{-2\pi\mathrm{i}x\xi}\frac{\sin\pi a}{\cosh\pi x+\cos\pi a}\,\mathrm{d}x=\frac{2\sinh2\pi a\xi}{\sinh2\pi\xi}\] whenever \(0 < a < 1\) and \(\xi\in\mathbb{R}\). Solutions
HW 5 (Due: 04-03) 3.8.8, 3.8.9, 3.8.10, 3.8.14, 3.8.15, 3.8.16, 3.8.17. Additional exercises: (i) The stereographic projection. (ii) Show that an integer-valued function on \([0,1]\) is constant if it is continuous. (Used in the proof of Rouché’s theorem.)
HW 6 (Due: 04-10) 3.8.11, 3.8.12, 3.8.19. Additional exercise: In Theorem 6.1 (iii) of Chapter 3, do we have \(F(r)=\log r\) for all \(r\in\Omega\cap\mathbb{R}_{>0}\)? Justify your answer.