MATH2230B  Complex Variables with Applications  2014/15
Announcement
 The course will be evaluated as follows: 2 midterms (20% each); HW (10%); Attendance (5%); Tutorial (5%); Final (40%)
 There is no homework on first week
 Suggested solution to HW 1 is posted. If you find any mistakes in this or the future suggested solutions, please let us know and thanks in advance.
 About the last question of HW1, please read the definition of principal root again in page 27 of the text book.
 The first midterm will be on Oct. 14th in class. No calculator is allowed during the exam. Makeup exam will not be provided if there is no excuse on your absence.
 lecture note 09 is updated
 For HW5, please refer to the files on the website of MATH2230A.
 The second midterm will be held on Nov. 18 in class
General Information
Lecturer

Yong YU
 Office: LSB 214
 Tel: 39438900
 Email:
 Office Hours: By appointment
Teaching Assistant

Chen Guanheng
 Office: Room 505, AB1
 Tel: 3943 4298
 Email:

Tang Wen
 Office: Room 222B, LSB
 Tel: 3943 7963
 Email:
Time and Venue
 Lecture: M 10:3012:15, LSB LT2; Tu 16:3017:15, LSB LT5
 Tutorial: M 12:301:15, LSB C1; Tu 17:3018:15, MMW 705
Course Description
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
 Brown and Churchill: Complex variables and applications
References
 Lars Ahlfors: Complex Analysis
 T. Needham. Visual Complex Analysis. Oxford University Press.
 A. Beardon. Complex Analysis: the argument principle in analysis and topology. Wiley
Lecture Notes
 lecture note 1
 lecture note 2
 Graph in lecture 2
 lecture note 3
 lecture note 4
 lecture note 5
 lecture note 6
 lecture note 7
 lecture note 8
 lecture note 9
 lecture note 10
 lecture note 11
 lecture note 12
 lecture note 13
 lecture note 14
 lecture note 15
 lecture note 16
 lecture note 17
 Graph 1 in lecture note 17
 Graph 2 in lecture note 17
 lecture note 1819
 Graph in lecture note 1819
 lecture note 20
 lecture note 21
 Graph in lecture note 20
Assignments
 HW 1 (due on Sept. 19): Ch 1, Sect 3, No. 1, 5; Ch 1, Sect. 5, No. 5, 6, 8; Ch. 1, Sect. 6, No. 2, 13; Ch. 1, Sect. 11, No. 1, 2, 3.
 HW 2 (due on Sept. 26): Sect. 18, No. 5, 10, 11; Sect. 20, No. 8, 9; Sect. 24 No. 2
 HW 3 (due on Oct. 3): prove that any rational function can be written as a sum of partial fractions. as an example write the following function into sum of partial fractions: (z^4 + z^3  2 z^2 +1 )/(z^3 + 2 z^2 + z).
 HW 4 (due on Oct. 10): Sect. 98, No. 5, 9 ; Sect. 100, No. 2; Find a linear transformation which carries z = 1 and  z  1/4  = 1/4 into concentric circles. What is the ratio of the radii; Reflect imaginary axis, x = y and  z  = 1 into circle  z  2  = 1.
 HW 5 (due on Oct. 20): Sect. 33, No. 1, 2, 4, 5, 9; Sect. 36, No. 1; Sect. 108, No.8
 HW 6 (due on Oct. 31): Sect. 46, No. 1,2,3,4; Sect. 47, No. 1, 4; Sect. 49, No. 2; Sect. 53, No. 1
 HW 7 (due on Nov.07): Sect. 57, No. 1, 2, 3, 4, 7, 10; Sect. 59, No. 1, 4, 6
 HW 8 (due on Nov.14): Sect. 65, No. 9, 10, 11; Sect. 68, No. 1, 2, 4, 5, 6, 7
 HW 9 (due on Nov.21): Sect. 94, No. 1, 2
 HW 10 (due on Nov. 28): How many roots does the function in Problem No. 8 of Sect. 94 have on the righthalf plane
 HW 11 (NO NEED TO HAND IN): Sect. 86, No. 2, 4; Sect. 88, No. 4, 6; Sect. 2, 4; Sect. 92, No. 1, 2; Sect. 94, No. 6, 8
Quizzes and Exams
 Sample problems and preparation guide for midterm I
 Sample problems and preparation guide for midterm 2
 Sample problems and preparation guide for final
 Solution to Midterm 2
 Examples in preparation guide for final
Solutions
 Suggested Solution to HW1
 Suggested Solution to HW2
 Suggested Solution to HW3
 Suggested Solution to HW4
 Suggested Solution to HW5
 Suggested Solution to HW6
 Suggested Solution to HW7
 Suggested Solution to HW8
 Suggested Solution to HW9&10
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: July 27, 2015 16:07:20