MATH2230A - Complex Variables with Applications - 2020/21
Announcement
- ZOOM links for Lectures and Tutorials are available on Blackboard (see Useful Links below).
- Tutorials start on the second week of the term.
- Assignments are to be submitted on Blackboard.
- HW 1 has been posted and is due on 18 Sep, Fri (see Assignments below or visit Blackboard).
- HW 2 has been posted and is due on 25 Sep, Fri.
- Our midterm is scheduled on Oct. 20 online
- HW 3 has been posted and is due on 5 Oct, Mon.
- Our midterm is scheduled on Oct. 20 online at the regular lecture time (13:30-14:15). Midterm cover topics from the lecture 1 to lecture 9. Please join the zoom class 5-10 mins before the lecture time to adjust your camera. Your upper body including shoulder, arm and two hands should be shown in the screen. During the exam, no book and notes are allowed to use. After the exam, you have 10 mins to prepare submission. Please submit all your solution via blackboard. Your camera should still be in function during all your submission process.
- HW 4 has been posted and is due on 16 Oct, Fri.
- HW 5 has been posted and is due on 23 Oct, Fri.
- HW 6 has been posted and is due on 6 Nov, Fri. (postponed).
- HW 7 has been posted and is due on 6 Nov, Fri.
- HW 8 has been posted and is due on 13 Nov, Fri.
- A Survey about the final exam is available on Blackboard. Please complete it before the last lecture, that is 3 Dec.
- HW 9 has been posted and is due on 20 Nov, Fri.
- HW 10 has been posted and is due on 27 Nov, Fri. (updated)
- FINAL EXAM IS SWITCHED ONLINE DUE TO THE CURRENT BREAKOUT OF THE PANDEMIC AND THE CASES CONFIRMED ON CAMPUS. DATE AND TIME ARE THE SAME AS SCHEDULED
- HW 11 has been posted and is due on 9 Dec, Wed
- The Exam Guideline has been updated. Please check it on Blackboard
General Information
Lecturer
-
Yong Yu
- Office: LSB214
- Tel: 39438900
- Email:
- Office Hours: By appointment
Teaching Assistant
-
Kaihui Luo
- Office: LSB 232
- Tel: 39435294
- Email:
-
KaLok LAM
- Office: LSB 222A
- Tel: 39433575
- Email:
Time and Venue
- Lecture: Tu 1:30PM - 2:15PM; Th 2:30PM - 4:15PM
- Tutorial: Tu 12:30PM - 1:15PM
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. Our first lecture will be on Sept. 8 and the last lecture will be on Dec. 3. There will be no tutorial on the first week of this term.
Textbooks
- Complex Variables and Applications (Ninth Edition by James W. Brown and Ruel V. Churchill)
References
- Complex analysis by Elias Stein
- Complex Analysis : An Introduction to The Theory of Analytic Functions of One Complex Variable by Lars Ahlfors
Lecture Notes
Tutorial Notes
- Tutorial 1 (Notes)
- Tutorial 1 (Slides, annotated)
- Tutorial 2 (Notes)
- Tutorial 2 (Slides, annotated)
- Tutorial 3(Modified)
- Tutorial 4
- Tutorial 5
Assignments
- (Due on 18 Sep) HW Set 1: P5: 2; P13-14: 3, 4, 5, 6; P23-24: 1, 2, 4, 5, 7, 9;
- (Due on 25 Sep) HW Set 2: P31: 3, 4; P35: 4, 5; P95-96: 1,2, 5; P103: 1, 2, 6; P112: 16, 17;
- (Due on 05 Oct) HW Set 3: P61: 8; P62: 9; P70-71: 1, 2, 3; P89: 3, 4, (entire in problem 4 means complexily derivable on whole complex field C), P108: 11.
- (Due on 16 Oct) HW Set 4: P119: 2, 3, 4; P133: 3, 4, 6, 7, 8, 9; P134: 11; P139: 4, 5, 6; P147: 2, 5.
- (Due on 23 Oct) HW Set 5: P159: 2, 3, 4; P161: 6, 7.
- (Due on 06 Nov) HW Set 6: P170-171: 1 (a, b, c), 2(a), 3, 7; P177: 1, 4, 6.
- (Due on 06 Nov) HW Set 7: P170-172: 1(d)(e), 2(b), 4, 5, 6, 10; P196: 5, 6, 7.
- (Due on 13 Nov) HW Set 8: P219-220: 2, 4, 5, 6, 7, 8, 10
- (Due on 20 Nov) HW Set 9: P242: 1, 2(noted that residue is the Laurant coefficient with index -1 in a Laurent series expansion of a function f), 3; P247: 3, 4, 5, 6, P253: 1, 2.
- (Updated)(Due on 27 Nov) HW Set 10: P84-85: 2, 5; P246: 1 (no need to compute residue in this homework set); P254: 5, 6 (please read residue theorem on Page: 233 by yourself).
- (Due on 09 Dec) HW Set 11 (last): P264-265: 2, 4, 9; P273: 3, 5, 8, 12; P282: 1, 2; P287: 1, 2, 3, 4; P293-294: 1, 2, 6, 8.
Solutions
- HW1 (Solutions)
- HW2 (Solutions)
- HW3 (Solutions)
- HW3 (Comments and Common Mistakes)
- HW4 (Solutions)
- HW4 (Comments and Common Mistakes)
- HW5 (Solutions)
- HW5 (Comments and Common Mistakes)
- HW6 (Solutions with Facts on Cauchy Theorems )
- HW7 (Solutions with Facts on Taylor's Theorem)
- Midterm (Solutions)
- HW8 (Solutions with Facts on Power Series)
- HW9 (Solutions with Facts about Poles and Residues)
- HW9 (Comments and Student Samples on Q3b)
- HW10 (Solutions with Facts about the Conincidence Principle)
- HW11 (Solutions with Facts about Computing Definite Integrals/ Argument Principles)
Assessment Scheme
| Homework | 10% | |
| Midterm | 40% | |
| Final Exam | 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: December 10, 2020 00:03:42