1

Aug 23 (Pretest), 25

1.1-1.3

(Schaum p. 9-32)

Complex numbers. Polar form.

section 1.1: #7,9,11,13-16,20,22-24; section 1.2: #4,7(except (f)), 9,10; section 1.3: #2,5,7,9,10,12,13

2

Aug 30, Sep 1 (Q 1 & HW 1 on 1.1-1.3)

1.4, 1.5

home reading: 1.6

Complex exponential. Roots. Planar sets.

section 1.4: #1,2,4,5,7-11,16,17; section 1.5: #4-8; section 1.6: #2-8

3

Sep 6, 8 (Q 2 & HW 2 on 1.4, 1.5, 1.6)

Drop with no grade: Sep 9

2.1, 2.2

(Schaum p. 62-67)

Functions of complex variables. Limits and continuity.

section 2.1: #1-5,6(a,b),7-9,11,13; section 2.2: #7,11,19-21,25

4

Sep 13, 15 (Q 3 & HW 3 on 2.1, 2.2)

2.3, 2.4,

home reading: 3.1

(Schaum p. 85-96)

Analytic functions. Cauchy-Riemann equations. Polynomials and rational functions.

section 2.3: #4,7,11,13,15; section 2.4: #1,3,5,7,8,10,11,13 (apply 10,12), 15; section 3.1: #1,3(a,b),7,11,13 (using (21) is not required)

5

Sep 20, 22 (Q 4 on 2.3, 2.4, 3.1)

2.5, 3.2, 3.3

Harmonic functions. Exponential, trigonometric, and logarithmic functions.

section 2.5: #1-4,7,16,18; section 3.2: #1,2,4,5(a,b,c,d),7,9(a,b,c,d),10,11,15,17-20; section 3.3: #1-6,9-15

6

Sep 27, 29 (Exam 1 on 1.1-3.3; HW 4 on 2.3-2.5, 3.1-3.3)

3.4

Application: boundary value problems.

section 3.4: #1*-6 (*there is a typo in the book answer)

7

Oct 4, 6

3.5, 4.1-4.3

Complex powers & inverse trigonometric functions. Complex integration.

section 3.5: #1-9*,11 (*instead of deriving (11), may derive -i(z^2-1)^(-1/2)); section 4.1: #1-5,7,8,10,11; section 4.2: #3,5-14; section 4.3: #1,2,4,5,7

8

Oct 11 (HW 5 on 3.4, 3.5, 4.1-4.3)

4.4

Cauchy's integral theorem.

section 4.4: #1,3,9-13,15-17

9

Oct 18, 20 (Q 5 on 3.4, 3.5, 4.1-4.3)

4.5, 4.6,

home reading: 5.1

(Schaum p. 184-186)

Cauchy's integral formula. Bounds for analytic functions. Review of series.

section 4.5: #1,3,4,5,7,8,11,14; section 4.6: #4,5,6,8,10,11,13,14; section 5.1: # 1(a,b,c),2(b,c),7,11,14(b,c),21

10

Oct 25, 27 (Q 6 & HW 6 on 4.4-4.6, 5.1)

5.2, 5.3, 5.5

(Schaum p. 188-190)

Power, Taylor, and Laurent Series.

section 5.2: #5(a,b,c,d,g),7,8,13,14; section 5.3: #4,5(a,b,c),6; section 5.5: #1-6,9

11

Nov 1, 3 (Exam 2 on 3.4-5.5; HW 7 on 5.2, 5.3, 5.5)

5.6

home reading: 5.7

Laurent Series. Classification of singularities.

section 5.6: #1(a,b,c,d,g),3,5; section 5.7: #1,3(b,c)

12

Nov 8, 10 (HW 8 on 5.6, 5.7)

Withdrawal deadline: Nov 11

6.7, 7.1, 7.2, 7.3

Argument principle and Rouche's theorem. Conformal mappings and their applications.

section 6.7: #1,3(see Theorem 3),6-9,13,18; section 7.1: #1; section 7.2: #3,5,10,11(a,c,d,e)

13

Nov 15, 17 (Q 7 on 5.6, 6.7, 7.1, 7.2; HW 9 on 6.7, 7.1, 7.2)

7.3, 7.4, 7.6

Möbius transformations and boundary value problems.

section 7.3: #2-9; section 7.4: #2,6,9; section 7.6: #1,2,3,6

14

Nov 22 (HW 10 on 7.3, 7.4, 7.6)

6.1, 6.2

(Schaum p. 214-226)

Residue theorem and its applications. Trigonometric integrals.

section 6.1: #3,7; section 6.2: #1,2&3(see Example 2),4,5

15

Nov 29, Dec 1 (Q 8 on 7.3, 7.4, 7.6, 6.1, 6.2)

6.3, 6.4, 6.5

Improper integrals. Indented contours.

section 6.3: #1,2,3(use Example 2 in 6.1),4-7; section 6.4: #4-9; section 6.5: #2-7

16

Dec 6 (HW 11 on 6.1-6.5), 8

6.6

Integrals involving multiple-valued functions. Review.

section 6.6: #1-4

17

Dec 13 (Tuesday), 12:30-2:30 p.m.: Final Exam