MATH2230B - Complex Variables with Applications - 2020/21
Announcement
- ZOOM links for lectures and tutorials will be announced on Blackboard.
- The tutorial class starts from the second week.
- Homework assignments should be submitted via Blackboard.
- Homework 1 has been posted and is due on Jan. 25.
- The midterm exam is scheduled on March 3.
- Homework 2 has been posted and is due on Feb. 1.
- Homework 3 has been posted and is due on Feb. 8.
- Homework 4 has been posted and is due on Feb. 15.
- Homework 5 has been posted and is due on Mar. 1.
- Our midterm is scheduled on Mar. 3 online at the regular lecture time (17:30-18:15). Midterm cover topics from lecture 1 to lecture 12. Please join the zoom class 5-10 mins before the lecture time to adjust your camera. Your upper body including shoulders, arms and two hands should be shown in the screen. During the exam, no books and notes are allowed to use. After the exam, you have 10 mins to prepare submission. Please submit all your solutions via Blackboard. Your camera should still be in function during all your submission process.
- For the midterm exam, please use paper and pen to answer, and scan your answers for submission.
- Homework 6 has been posted and is due on Mar. 15.
- Homework 7 has been posted and is due on Mar. 22.
- Homework 8 has been posted and is due on Mar. 29.
General Information
Lecturer
-
Chia-Yu HSIEH
- Office: LSB 232A
- Email:
- Office Hours: by appointment
Teaching Assistant
-
Kaihui LUO
- Office: LSB 232
- Email:
-
Tianhan YI
- Office: LSB G08
- Email:
Time and Venue
- Lecture: Mo 12:30PM - 2:15PM; We 5:30PM - 6:15PM
- Tutorial: We 3:30PM - 4:15PM
Course Description
This course is to introduce the basic properties of complex functions and analytic functions and to illustrate the important use of these theories to other branches of mathematics and sciences. Topics include: complex numbers; limits, continuity and derivatives, Cauchy-Riemann equations, analytic functions; elementary functions; mapping by elementary functions; Contours integrals, Cauchy-Goursat theorem, Cauchy integral formula, Morera’s theorem, maximum moduli of functions, the fundamental theorem of algebra; Taylor series and Laurent’s series; residues and poles, evaluation of infinite real integrals.
Textbooks
- Complex Variables and Applications, Ninth Edition, by James Ward Brown / Ruel V. Churchill
References
- Complex Analysis, Princeton Lectures in Analysis II, by Elias M. Stein / Rami Shakarchi
- Complex Analysis: An Introduction to the Theory of Analytic Functions of One Complex Variable, Third Edition, by Lars V. Ahlfors
Lecture Notes
- Lecture 1
- Lecture 2
- Lecture 3
- Lecture 4
- Lecture 5
- Lecture 6
- Lecture 7
- Lecture 8
- Lecture 9
- Lecture 10
- Lecture 11
- Lecture 12
- Lecture 13
- Lecture 14 (revised) (there are typos in the theorem of term-by-term differentiation for power series in the previous version in f'(z) and g(z))
- Lecture 15
- Lecture 16
- Lecture 17
- Lecture 18
- Lecture 19
Tutorial Notes
Assignments
- Homework Set 1 (due on Jan. 25)
- Homework Set 2 (due on Feb. 1)
- Homework Set 3 (due on Feb. 8)
- Homework Set 4 (due on Feb. 15)
- Homework Set 5 (due on Mar. 1)
- Homework Set 6 (due on Mar. 15)
- Homework Set 7 (due on Mar. 22)
- Homework Set 8 (due on Mar. 29)
Solutions
Assessment Scheme
| Homework | 10% | |
| Midterm | 40% | |
| Final | 50% |
Useful Links
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.
Assessment Policy Last updated: March 22, 2021 19:15:28