# Homework Solutions Complex Analysis And Operator

### Announcement

- There will be no tutorial on the first week of class. Tutorials will start from week 2.
- The midterm will be held on Oct 20 (Thursday) in class. It'll cover Chapters 1-5 of the textbook, with the exceptions of Chapter 2.5.5 and Chapter 4.3.

### General Information

#### Lecturer

**Yung, Po Lam**

#### Teaching Assistant

#### Time and Venue

*Lecture:*Tuesdays 9:30am-10:15am, Thursdays 8:30am-10:15am, both at LSB LT4*Tutorial:*Tuesdays 8:30am-9:15am, at LSB LT4

### Course Description

This is a second course in complex analysis. Topics to be covered include the Poisson summation formula, Weierstrass infinite products, Gamma and zeta functions, the prime number theorem, the Riemann mapping theorem, elliptic functions, and time permitting the sum of two squares theorem. We assume as prerequisite a solid understanding of properties of analytic functions of one complex variable, at the level of Math 2230 or Math 3253.

### Textbooks

- E.M. Stein and R. Shakarchi, Complex Analysis, Princeton University Press, 2003.

### Pre-class Notes

### Lecture Notes

### Tutorial Notes

### Assignments

### Quizzes and Exams

### Solutions

### Assessment Scheme

Homework | 10% | |

Midterm Exam | 40% | |

Final Exam | 50% |

### Honesty in Academic Work

The Chinese University of Hong Kong places very high importance on honesty in academic work submitted by students, and adopts a policy of zero tolerance on cheating and plagiarism. Any related offence will lead to disciplinary action including termination of studies at the University. Although cases of cheating or plagiarism are rare at the University, everyone should make himself / herself familiar with the content of the following website:

http://www.cuhk.edu.hk/policy/academichonesty/and thereby help avoid any practice that would not be acceptable.

Last updated: March 01, 2017 12:26:13

**Information sheet**

**Current homework. Not to be handed in.**

**Previous assignments.**

**Projects. Due Friday, May 7, 2010.**

**Example: Chapter 4, exercise 1.**

**Test 1 review**

**Practice Tests:**2002 and 2009**Test 1 review**

**Test 2 review**

**Practice Tests:**2002 and 2009**Test 2 review**

**Final exam review**

**Practice Tests:**2001 and 2009**Final exam review**

**MATLAB M-files**

**Demo from class on 2/10/2010.**- demo_2_10_10.m. (Script m-file used in class on 2/10/2010.)
- part_sum_c.m. (Function m-file called by demo_2_10_10.m; it computes the partial sum of a Fourier series.)

**Notes on least-squares and plots in Matlab****Code from class on 2/3/2010.****Notes on Matlab M-files**- bw.m (Butterworth filter.)
- sampling_demo.m (Demostrates the sampling theorem for various values of the Nyquist rate.)
- fftcompress.m (Compression via fft.)
- compress.m (Function called by fftcompress.m to quantize FFT.)
- ft_approx.m (Computes an approximate Fourier transform from samples of a function.)
- haar_sine.m (Demonstates Haar decomposition for a chpped sine wave.)
- haar_dec.m (Demonstrates one level Haar decomposition.)

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