MATH2230A - Complex Variables with Applications - 2014/15

Announcement

• This course will be evaluated as follows: 2 mid-terms (20% each), HW (10%), Final (50%)
• 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 held on Oct. 17 in class. The venue for the mid term is the same as the regular lecture. No calculator is allowed during the exam. Make-up exam will not be provided if you have no excuse for your absence.
• lecture note 09 is updated
• The second midterm will be held on Nov. 14 in class
• For midterm 2, please see the following file for details.

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General Information

Lecturer

• Yong YU
  • Office: LSB 214
  • Tel: 3943-8900
  • 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: We 8:30AM - 10:15AM LSB LT6; Fr 10:30AM - 11:15AM Y.C.Liang Hall 104
• Tutorial: We 12:30PM - 1:15PM LSB C1; We 6:30PM - 7:15PM LSB C1

Course Description

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

• R. V. Churchill and J. W. Brown. Complex Variables and Applications. 9 th edition. McGraw Hill.

References

• Complex Analysis, Third Edition by Lars V. Ahlfors
• 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 18-19
• Graph in lecture note 18-19
• lecture note 20
• Graph in lecture note 20
• lecture note 21

Tutorial Notes

• Tutorial Notes 9-10

Assignments

• HW 1 (due on Sept. 12): 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. 19): Sect. 18, No. 5, 10, 11; Sect. 20, No. 8, 9; Sect. 24 No. 2
• HW 3 (due on Sept. 26): 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. 3): 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. 10): Sect. 33, No. 4, 5, 9.
• HW 6 (due on Oct. 20): Sect. 33, No. 1, 2; Sect. 36, No. 1; Sect. 108, No. 8
• HW 7 (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 8 (due on Nov.07): Sect. 57, No. 1, 2, 3, 4, 7, 10; Sect. 59, No. 1, 4, 6
• HW 9 (due on Nov.14): Sect. 65, No. 9, 10, 11; Sect. 68, No. 1, 2, 4, 5, 6, 7
• HW 10 ( due on Nov.21): Sect. 94, No. 6, 7, 8
• HW 11 ( due on Nov.28): Sect. 94, No. 1, 2. The third problem is to find how many roots does the function in problem No. 8 of Sect. 94 have on the right-half plane.
• HW 12 (NO NEED TO HAND IN): Sect. 86, No. 2, 4; Sect. 88, No. 4, 6; Sect. 2, 4; Sect. 92, No. 1, 2

Quizzes and Exams

• Sample problems and preparation guide for midterm I
• Solution and Remarks to Midterm 1
• Sample problems and preparation guide for midterm 2
• Solution and Remarks to Midterm 2
• Sample problems and preparation guide for final
• 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
• Suggested Solution to HW10
• Suggested Solution to HW11

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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Last updated: December 01, 2014 15:17:44