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.

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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, 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 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. P4-5, 1, 4, 11; P7, 1; P13, 3, 4, 5, 6; P16, 1, 2, 7, 9, 13, 14; P34-35, 1, 2, 3, 4, 5.
• Homework Set 2 (Due on Jan. 29). P30, 1, 2; P44, 8; P54, 1, 5; P61-62, 8, 9.
• Homework Set 3. P70-71, 1, 2, 3, 4, 7; P76-77, 1, 5; P85, 4, 5.
• Homework Set 4. P89-90, 1, 3, 4, 10; P95-97, 1, 2, 5, 10; P99, 2; P103, 1, 2, 3, 6; P107-108, 3, 4, 8, 9, 14; P112, 16-17; P114, 1-3.
• Homework Set 5. P119, 2-4; P124, 2, 6.
• Homework Set 6. P132-135, 1-13; P138-139, 1-6; P147, 1-3, 5
• Homework Set 7 (Due on Mar. 12). P159-161, 2-6; P170, 1-4; P172, 10; P177-178, 4, 6.
• Homework Set 8. P195-197, 1-3, 7-11; P205-207, 1-2, 5-9; P219-221, 4-11.
• Homework Set 9: P237-238, 1-7; P242, 1-4; P246-247, 1-7;P253-254, 1, 3, 5, 6, 7;
• Homework Set 10: P264-265, 2, 4, 9; P273, 3, 5, 8, 12;
• Homework Set 11 (Due on Apr. 23). P282-283, 1-4; P287, 1-4; P293-294, 6-9.

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.

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Assessment Policy

Last updated: April 19, 2018 15:56:43