4520.001,  Fall 2001
Functions of One Complex Variable
Conley

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INSTRUCTOR:   Charles Conley,  GAB 475,  (940) 565-3326

OFFICE HOURS:   Tuesday and Thursday, 1:30-3:30 and by appointment

CLASS MEETS:   TR 3:30-4:50, GAB 201

EXAMS, HOMEWORK, AND GRADING: There will be two 100 point midterms, on Tuesday, Oct. 9 and Tuesday, Nov. 13, and a comprehensive 180 point final, on Thursday, Dec. 13, 1:30-3:30.  There will also be twelve 10 point homeworks, due Thursdays at the beginning of class.  There will be no make-up exams except for emergencies, and late homework will be worth half-credit.

TEXT, PREREQUISITES, AND OTHER REFERENCES: The text is Complex Analysis for Mathematics and Engineering (fourth edition), by Mathews and Howell.  The prerequisites are Math 1710-20 and 2730, the calculus sequence.

TOPICS:   We will begin by going over multiplication of complex numbers in rectangular and polar coordinates.  Then we will study differentiability of functions of one complex variable, followed by Taylor and Laurent series and contour integration.  We will also discuss conformal maps and Julia and Mandelbrot sets if time permits.  We will give some rigorous proofs, but no prior exposure to proofs will be assumed.  Concrete examples and calculations will be emphasized.

Chapters 1-2:  Complex numbers and functions.

Chapters 3-5:  Analytic and harmonic functions, power series functions, and the elementary functions such as e^z.

Chapters 6-8:  Complex integration, contour integration, and Taylor and Laurent series.  These chapters contain many surprising and beautiful theorems, and comprise the centerpiece of the course.

It is the responsibility of students with certified disabilities to provide the instructor with appropriate documentation from the Dean of Students Office.

Since class was cancelled on Sept. 11, there will be only 11 problem sets.

FINAL EXAM:   Thursday, Dec. 13, 1:30-3:30

HOMEWORK  11,  Due Thursday, Dec. 6:

Section 7.3:   1 (only do this one way, not two), 3, 5, 8 (for |z|<1, not |z|>1), 12
Section 7.4:   1abdg, 2bcj, 3bfgh, 4*
Section 8.2:   1acdefghi*j, 2, 3abce, 4, 5

HOMEWORK  10,  Due Thursday, Nov. 29:

Section 6.6:   3, 5, 6 (part a should say n>1), 7, 10, 11
Section 7.2:   1c, 2acd, 3b, 4, 5, 7b, 8a (it should say powers of z, not z bar), 9*

HOMEWORK  9,  Due Tuesday, Nov. 20 (this is a short homework due to Thanksgiving):

Section 6.5:   1-6, 8-15.

EXAM 2:   Tuesday, Nov. 13

HOMEWORK  8,  Due Thursday, Nov. 9:

Section 6.3:   1, 2, 4, 5, 7, 10, 11, 12, 13
Section 6.4:   1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14

HOMEWORK  7,  Due Thursday, Nov. 1:

Section 5.4:   1, 2, 5ab, 6abc, 7ab, 8ab, 9, 10b
Section 6.1:   1abde, 2, 3
Section 6.2:   1, 2, 6a, 7, 10, 15

HOMEWORK  6, Due Thursday, Oct. 25:

Section 5.1:   3, 4, 6ef, 7bc, 8, 9a, 13bc, 18
Section 5.2:   1abc, 3bc, 6, 10, 12
Section 5.3:   1, 4

HOMEWORK  5, Due Thursday, Oct. 18:

Section 4.1:   1, 6
Section 4.3:   1, 2, 4, 5
Section 4.4:   3 (skip parts c and g), 4, 5, 6

EXAM 1:   Tuesday, Oct. 9.  I will be away the week of Oct. 8-12, and so Professor Douglass (GAB 413) will proctor the exam on Tuesday and begin Chapter 4 on Thursday, Oct. 11.  You may ask him questions any time between 10:00 and 2:00 on Monday (but please don't tax him too much!).  Thursday, Oct 4 will be a review day.  I will pass out a review sheet with a practice exam.

HOMEWORK  4,  Due Thursday, Oct. 4:

Section 3.1:   1bd, 3, 7bf, 8, 11, 14
Section 3.2:   1cd, 4, 7, 11b, 15b (10a is cancelled)
Section 3.3:   1b, 2, 5a, 6, 8, 10

HOMEWORK  3,  Due Thursday, Sept. 27 (note that the due date has been extended, and that Section 2.5 is included):

Section 2.3:  1, 2, 6, 7, 8, 9, 11b, 16a, 18
Section 2.4:  1bc, 2, 6b, 7, 16
Section 2.5:  1, 5

HOMEWORK  2,  Due Tuesday, Sept. 18 (note that the the due date has changed and the Section 2.3 problems have been dropped):

Section 1.5:  3 [there is a misprint in the solution, sin(3 theta) is 3sin(theta)cos^2(theta) - sin^3(theta) ]
Section 1.6:  1abc, 2a, 3a, 5a, 9ab for parts ii-vi
Section 2.1:  1b, 2b, 3b, 4b, 5b, 6, 9, 10d
Section 2.2:  1a, 2, 3a, 4, 7, 8

HOMEWORK  1,  Due Thursday, Sept. 6:

Section 1.2:  1abef, 2cfh, 3, 5
Section 1.3:  1, 2a, 3b, 5, 6ab, 9, 11, 12
Section 1.4:  1abdeh, 2b, 3abcd, 5fg
Section 1.5:  1, 4, 5