Math 421 -- Fall 2008
Schedule of lectures and assignments
 
Date
Section in Saff and Snider and assigned problems

What's due/ other remarks
Tuesday  9/2
Historical introduction. Historical quotes.
Definition and algebraic properties of complex numbers.
Sections 1.1 and 1.2.
Page 5: Problems 7, 8, 14, 15, 16, 20, 22
Page 12: Problems 4, 5, 7, 8, 16

Thursday 9/4
Section 1.3  Polar form of complex numbers
Page 22: Problems 5, 6, 7, 9, 13, 25, 26, 28


Tuesday 9/9
Section 1.4: Complex exponential.
Section 1.5: Powers and Roots
Page 31: Problems 1, 2a, 3b,c, 4b, 10, 12, 17a,b, 18a
Page 37: Problems 4, 5, 6, 7, 9, 10 ,15
Page 5: Problems  816
Page 12: Problems 8, 16
Page 22: Problems  5c,  7g,  26
Solutions
Thursday 9/11 Sections 1.6 and 1.7.
Page 42: Problems 2 - 8, 12
Page 50: Problems 1, 2, 5
Quiz #1: Sections 1.1, 1.2, and 1.3
Solutions
Tuesday 9/16
Section 2.1
Page 56: Problems 1, 4, 6, 9, 10, 13

Page 31: Problems 2a, 3c, 12, 18a
Page 37: Problems 4b, 5b,d, 6c, 10
Page 42: Problems 2, 3, 5.
Solutions
Thursday 9/18
Section 2.2
Page 63:  Problems 7, 11, 21


Quiz #2: Sections 1.4, 1.5, and 1.6
Solutions

Tuesday 9/23
Section 2.3
Page 70: Problems 6, 7, 10
Page 56: Problems 1 c,d,f ;  6,  13
Page 63:  Problems 7 e,f;  11 a,d ; 21 d
Solutions
Thursday 9/25 Sections 2.4 and 2.5
Page 77: Problems 1c, 2, 4, 5, 8, 11
Page 84: Problems  2, 3, 8, 14

Quiz #3: Sections 2.1 and 2.2
Solutions
Tuesday 9/30

Section 2.5
Page 84:  Problems 5, 6, 11, 18, 22

Page 70: Problems 6, 7 c,d.
Page 77: Problems 1c, 4, 11
Page 84: Problems  2, 3d, 8
Solutions
Thursday 10/2 Sections 3.2 and beginning of 3.3
Page 115: Problems 5, 6, 9, 11, 13a, 16, 20, 23
Page 123: Problems 1, 3, 5, 6.

Quiz #4: Sections 2.3, 2.4 and 2.5

Solutions
Tuesday 10/7 Cauchy-Riemann Equations in polar coordinates.
Complex powers.
Review:  Wednesday 10/8, 6 pm., LGRT 202

Page 84:  Problems 11, 18, 22
Page 115: Problems 9c, 13a, 16, 20
Page 123: Problems 1, 5
Solutions
Thursday 10/9 Hour Exam # 1.  In class.  Solutions
It will cover all the material discussed
in class through Thursday 10/2.

Tuesday 10/14 No Class -  Monday Schedule


Thursday 10/16

Complex powers.  Inverse trigonometric functions.
Integration of complex valued functions of one real variable.
Page 123: Problems 11, 12, 13, 14, 16.
Page 136: Problems 1, 3, 5, 6, 7, 8, 9, 11

Tuesday 10/21

Contours and Integration.
Page 160: Problems 3, 7, 8, 10, 11
Page 170: Problems 3, 5, 6, 8, 11

Thursday 10/23

Integration.  Primitives (antiderivatives).
Page 170: Problem 14
Page 178: Problems 1, 11, 12
Quiz #5: Sections 3.3, 3.5
Solutions
Tuesday 10/28

Cauchy's Integral Theorem
Page 199: Problems 7, 10, 13, 15
Page 136: Problems 1d,  3b, 7, 11
Page 160: Problems 3, 7, 11
Page 170: Problems 3b, 6, 11b, 14b
Page 178: Problems 1 c,g,h, 12.
Solutions
Thursday 10/30

Cauchy' Integral Formula. 
Page 212: Problems 1, 2, 3, 6, 7, 16
Quiz #6: Sections 4.1, 4.2, 4.3.
Solutions

Tuesday 11/4

Section 4.6: Liouville's Theorem, Fundamental Theorem
of Algebra, Mean value property.
Page 219: Problems 3, 5, 6, 7.
Page 199: Problems 7, 10cd, 13, 15
Page 212: Problems 3 b,c,d, 7.
Solutions
Thursday 11/6

Series of complex numbers. Power series.
Page 239: Problems 1, 2, 5, 6, 7, 11, 14.
Page 259: Problems 3, 4, 5.
Quiz #7: Sections 4.4, 4.5
Solutions
Tuesday 11/11

No Class - Holiday

Wednesday 11/12
Tuesday Class Schedule!
Power series.  Taylor and Laurent Series.
Page 249:  Problems 1, 3, 5, 11, 13, 14, 18a
Page 259:  Problems 6, 8, 13.
Page 219: Problems  5, 7.
Page 239: Problems 1d, 2c,  6, 11b, 14b.
Page 259: Problems 3 c, d,   5 a, b, d.
Solutions
Thursday 11/13

Laurent Series.
Page 276:  Problems 1, 3, 4, 5, 6, 7
Quiz #8: Sections 4.6, 5.1, 5.3.
Solutions

Tuesday 11/18

Zeroes and singularities.
Page 285: Problems 1, 3, 5, 6, 10, 12, 15.
Page 249:  Problems 1c, 3c, 5b,e, 11b, 18a
Page 259:  Problem 8
Page 276:  Problems 1 b,c,  3 b,  4,  7 b
Solutions
Wed. 11/19

Review: 6 pm, LGRT 123.

Thursday 11/20

Hour Exam # 2.  In class.  Solutions
It will cover all the material discussed
in class from Tuesday 10/7 to Thursday 11/13.

Tuesday 11/25

The Residue Theorem.
Page 313: Problems 1, 2, 3, 4, 5, 6

Thursday 11/27

No Class -  Thanksgiving.

Tuesday 12/2

Trigonometric integrals.
Improper integrals of rational functions.
Page 317: Problems 2, 4, 6
Page 325: Problems 2, 4, 6, 8
Page 285: Problems 1 b,d,e,  6,  12.
Page 313: Problems 1 g, h, 3 c, d, f, 4, 5
Solutions
Thursday 12/4

Improper integrals of rational and
trigonometric functions.
Page 336: Problems 1, 2, 3, 5.
Quiz #9: Sections 5.6, 6.1.
Solutions
Tuesday 12/9

Indented contours.
Page 344: Problems 1, 2, 4, 5.
Some residue integrals
Thursday 12/11


Using residues to find the sum of some series.
Last Class.
Quiz #10: Sections 6.2, 6.3, 6.4.
Solutions

Monday 12/15

Final Exam -- 4 pm
LGRT 101
Solutions


Thursday 1/1/09

Happy New Year!