OFFICE: Math 600 OFFICE HOURS: Tuesday and Thursday, 1:30-2:30, or by appointment PHONE: (765) 494-1975 EMAIL: eremenko@math.purdue.edu

Brightspace: Fall 2022 MA 425/52500

Homework 1 (due August 30) p. 5: 7, 16, 20 bd, 22, 23; p. 12: 7 cef, 13; p. 22: 11, 13; p. 31: 4-10.

Additional material (NOT required reading, NOT a part of HW):

How complex numbers were discovered?

Is there anything else like the
complex numbers?

Can you find the mistake?

HW2 (due September 6) p. 37: 5d, 7a, 10; p. 42: 2-8, 11, 15, 17; p. 56: 1, 3; p. 63: 7.

HW3 (due September 13) p. 56: 6(a-c), 13(a-c), p. 63: 11(a-c), p. 71: 7(a-e), 13(a-f).

HW4 (due September 20) p. 77: 1(a-b), 6, 13; 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.

Green formula and Cauchy theorem

Poisson formula

Uniqueness of solution of Dirichlet problem

HW5 (due September 27) p. 130: 3,4; p. 136: 1(abd),15(a); p. 160: 3,8; p. 170: 3(ab),8,13, p. 178: 1(a-e),4.

The book gives two alternative approaches to Cauchy's theorem: sections 4.4a and 4.4b. I mostly follow the second approach, based on the Green formula (section 4.4b). So 4.4a is an optional reading. See also the handout "Green formula and Cauchy theorem" above.

HW6 (due October 4) p. 200: 7,9a-f; p. 212 1,3(abdf), 7; p. 219: 4,5,6,13.

Midterm exam is scheduled on October 6, in class. Covers Chapters I-III, 4.1-4.4.

Additional material: Infinite series I

Infinite series II

Infinite series III. Abel's theorem

Infinite series IV. Bernoulli numbers

Infinite series V. Burmann-Lagrange formula

HW 7 (due October 18) p. 225: 4,6,7,14(a-e); p. 239: 1(a,c,e), 11(a-d); p. 250: 1(a,b), 5(a-g).

Examples of Laurent expansions

HW 8 (due October 25) p. 259: 3(a-f), 13a; p. 267: 3(a-f), 9; p. 276: 3(a-c), 4.

HW 9 (due November 1)
p. 285: 1(a-g), 5(a-e); p. 290: 1(a-e);
p. 313: 1(a-i), 3(a-f).

Since I did not cover p. 313 1(a-i), 3(a-f) in class,
it will not be graded. So it will make no difference for
the grade whether you sumbit it or not. But I strongly recommend
to solve these problems for yourself.

HW 10 (due Noverber 8) p. 317: 1,3; p 325: 1, 11, 15ab, 19; p. 336: 5,9; p. 344: 2,10; p. 354: 4,8. Read sections 6.1-6.6.

HW 11 (due November 15) p. 364: 3, 7, 8, 10; p. 375: 2; p. 382: 3, 13(a-d).

Problem 3, p. 382 will not be graded. The statement of this problem in the book is not accurate.

Final exam, Fall 2021

More problems for preparation to the final

What to expect on the final exam

HW 12 (due November 22) p. 392: 1,2,8,9; p. 403: 3(a-c), 6,17;

HW 13 (due December 29) p. 416: 4,8; p. 430: 1,3,5, 7; p. 440: 3,5.

Why airplanes fly and ships sail and propellers pull, etc.