Week |
Important Dates |
Sections |
Topics |
Homework |
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 |