MATH2230B  Complex Variables with Applications  2017/18
Announcement
 The first midterm will be on Feb. 8 in class. Teaching from week 1 to week 3 will be covered.
 The second midterm will be on Mar. 19 in class. It will cover the topics before and include Taylor series/Laurent series expansions. The uniqueness part will not be covered.
 The final exam is an accumulative exam.
General Information
Lecturer

YU, YONG
 Office: LSB 214
 Tel: 39438900
 Email:
 Office Hours: Anytime when available
Teaching Assistant

CHEN, YUAN
 Office: LSB 232
 Tel: 39435294
 Email:

TAI, HO MAN
 Office: LSB 232
 Tel: 39435294
 Email:
Time and Venue
 Lecture: Th 3:30PM  4:15PM, LT3; Mo 2:30PM  4:15PM LT4
 Tutorial: Th 9:30AM  10:15AM, LSB C2; Th 2:30PM  3:15PM, LSB LT3; Th 5:30PM  6:15PM, LSB LT5
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, CauchyRiemann equations, analytic functions; elementary functions; mapping by elementary functions; Contours integrals, CauchyGoursat 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 Variable, by Lars Ahlfors
Lecture Notes
 lecture 1
 lecture 2
 lecture 3
 lecture 4
 lecture 5
 lecture 6
 lecture 7 and 8
 lecture 9 and 10
 lecture 9 and 10 (appendix)
 lecture 11
 lecture 12 and 13
 lecture 14 and 15
 lecture 16 and 17
 lecture 18 and 19
 lecture 20 and 21
 lecture 22 and 23
Tutorial Notes
 Tutorial 1
 Tutorial 2
 Tutorial 3
 Tutorial 4
 Tutorial 5
 Tutorial 6
 Tutorial 7
 Tutorial 8
 Tutorial 9
 Tutorial 10
 Tutorial 11
 Some worked examples about integration using residue
Assignments
 Homework Set 1. P45, 1, 4, 11; P7, 1; P13, 3, 4, 5, 6; P16, 1, 2, 7, 9, 13, 14; P3435, 1, 2, 3, 4, 5.
 Homework Set 2 (Due on Jan. 29). P30, 1, 2; P44, 8; P54, 1, 5; P6162, 8, 9.
 Homework Set 3. P7071, 1, 2, 3, 4, 7; P7677, 1, 5; P85, 4, 5.
 Homework Set 4. P8990, 1, 3, 4, 10; P9597, 1, 2, 5, 10; P99, 2; P103, 1, 2, 3, 6; P107108, 3, 4, 8, 9, 14; P112, 1617; P114, 13.
 Homework Set 5. P119, 24; P124, 2, 6.
 Homework Set 6. P132135, 113; P138139, 16; P147, 13, 5
 Homework Set 7 (Due on Mar. 12). P159161, 26; P170, 14; P172, 10; P177178, 4, 6.
 Homework Set 8. P195197, 13, 711; P205207, 12, 59; P219221, 411.
 Homework Set 9: P237238, 17; P242, 14; P246247, 17;P253254, 1, 3, 5, 6, 7;
 Homework Set 10: P264265, 2, 4, 9; P273, 3, 5, 8, 12;
 Homework Set 11 (Due on Apr. 23). P282283, 14; P287, 14; P293294, 69.
Assessment Scheme
Midterm 1  5%  
Midterm 2  35%  
Homework  10%  
Final  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.
Assessment Policy Last updated: April 19, 2018 15:56:43