Instructor: Shaoyun Yi

Time: Monday (10:10-11:50),  Wednesday (8:00-9:40)

Location: Room 206 at Teaching Building

Email: yishaoyun926@xmu.edu.cn

Office: 616

Office Hours: By appointment

Week No.	Topics	Homework	Due Date (Day)
1	Complex numbers and complex planes	HW 1   [Pages 14-16: Ex. 5, 8, 13, 15, 17-(3), (5), (7), (9)]	3/4 (M)
2	Holomorphic functions and the Cauchy-Riemann condition	HW 2   [Pages 38-39: Ex. 3-(3), (4), 5, 8, 9, 10]	3/11 (M)
3	Harmonic functions, Elementary functions and multi-valued functions I	HW 3   [Page 169: Ex. 2;   Pages 39-40: Ex. 7, 11, 16-(2), 19]	3/18 (M)
4	Elementary functions and multi-valued functions II	HW 4   [Page 40: Ex. 12, 13, 15, 17, 18]	3/25 (M)
5	Integral of a complex variable function	HW 5   [Pages 58-59: Ex. 1, 3, 5, 7, 9]	4/1 (M)
6	Cauchy's Theorem and Cauchy's formulas	HW 6   [Pages 59-60: Ex. 11-(2), (4), 13, 15, 16, 17]	4/8 (M)
7	Series of complex numbers	HW 7   [Page 87: Ex. 1, 2, 5-(1), (3), (4), (5)]	4/15 (M)
8	Taylor series	HW 8   [Page 88: Ex. 8, 9-(2), (4), (5), 10, 11]	4/29 (M)
9	Laurent series,   Midterm: 4/24 (W)
10	Isolated singularities,   No class: 5/1 (W)	HW 9   [Pages 88-89: Ex. 12-(1), (2), (3), (5), 13-(1), (3), (4), (5), 15, 16]	5/6 (M)
11	Holomorphic functions at infinity, Entire functions and meromorphic functions, Residues	HW 10   [Page 89: Ex. 14, 21;   Page 109: Ex. 1, 2, 3-(1), (2), 4, 5-(2), (3)]	5/13 (M)
12	Evaluation of definite integrals I	HW 11   [Pages 110-111: Ex. 8-(1), (2), (3), (4), (5), (10), (11), (12), 9]	5/20 (M)
13	Evaluation of definite integrals II, Argument principle and Rouche's theorem	HW 12   [Pages 110-111: Ex. 8-(6), (7), (9), (13), (15), (16), 10, 11, 12]	5/27 (M)
14	Univalent functions and conformal mappings, Fractional linear transformations	HW 13   [Pages 134-135: Ex. 1, 2, 3, 4, 5, 6, 7]	6/3 (M)
15	The maximum modulus principle and the Riemann mapping theorem	HW 14   [Pages 135-136: Ex. 8, 9, 11, 12, 13, 16, 19]	6/20 (R)
16	No class
17	Final Exam: 6/20 (R) 10:30-12:30, Room 204 at Teaching Building