Complex Analysis (MATH 425, Fall 2015)

Teacher: Alexandre Eremenko
OFFICE: Math 600

OFFICE HOURS: Mo 12-1, Th 1-2.
or by appointment. You can also ask questions by e-mail.

PHONE: (765) 494-1975

EMAIL: eremenko@math.purdue.edu

GENERAL INFORMATION

Syllabus

HW 1 (due September 1) p. 5: 9, 10, 22, 23; p. 13: 7(g,i,h), 17; p. 22: 7(a,h), 13; p. 31: 1(c), 3(c), p. 37: 5(f), 7(c), p. 42: 2, 3, 4.

HW 2 (due September 8) p. 37: 8, 9, 10, 11, 16, 17; p. 42: 15, 17, 20; p. 50: 2(ab), 5; p. 56: 5, 6, 12, 13, p. 63: 11(a-c).

HW 3 (due September 15) p. 71: 7(a-e) 11(a-h), 13(a-f), P. 77: 1(A-B), 6, 13.

HW 4 (due September 22) p. 84: 3(a-f), 10; p. 108: 3(a,b), 11(a); p. 115: 5(a-c), 17; p. 123: 1(a-d), 5(a-c), 12.

HW 5 (due September 29) p. 136: 1(abd),7, 10,15(a-d); p. 160: 3,8; p. 170: 3(ab),8,13, p. 178: 1(a-e),4. p. 200: 7,9a-f, 15, 18.

First exam: October 1, covers Ch. I-III and IV.1-3, except 2.7, 3.6.

No homework due October 6,13.
First exam solutions

HW 6 (due October 20) p. 212 1,3(abdf), 7; p. 219: 4,5,6,13.

HW 7 (due October 27) p. 239: 1(a,c,e), 11(a-d); p. 250: 5(a-c), 11, 13, p. 259: 3(a-c), 13a; p. 267: 3(a-c), 9; p. 276: 3(a-c), 4.

HW 8 (due November 3) p. 285: 1(a-h), 2, 3, , 5(a-e); p. 290: 1(a-e), 3, 6, 7.

HW 9 (due November 10) p. 313: 1(a-h), 3(a-d), p. 317: 1,3; p. 325: 1, 11; p. 336: 5,9; p. 344: 2,10; p. 354: 4,8.

HW 10 (due November 17) p. 327: 15 (a,b), 17 (a), 19; p. 344: 4,5; p. 364: 3, 7, 8, 10, 12a, 16.

Second midterm exam is on November 19. Covers all up to the end of Capter VI.

Second Exam solutions

HW 11 (due December 1) p. 382: 3, 13(a-d). p. 392: 1,2,8,9;

HW 12 (due December 8) p. 403: 3 (a-c),6,17; p. 430: 1,3,5,7.


Additional topics. Everything below this line is not a part of the homework and will not be asked on the exams. But it is recommended, and may help in understanding the subject.


Why complex numbers were invented

Problem 1. Express the primitive 5-th root of 1, that is (cos A+i sin A), where A=72 degrees = 1/5 of the circle, algebraically, that is without using trigonometric or exponential functions.