Week

Date

Context

Homework

Week1 
08/31 
Ch1. Complex numbers 
HW1 (duedate: 09/07 Tuesday): Sec1.1. 14, 16, 20,
24; Sec1.2. 4, 14, 16; 

09/02 
Polar forms; Powers 
HW1 (duedate: 09/07 Tuesday): Sec1.3. 8, 10, 18; Sec1.4.
2, 4, 7, 10, 12, 23. 
Week2 
09/07 
Roots; Riemann sphere and Stereographic projection 
HW2 (duedate: 09/14 Tuesday): Sec1.5. 4, 6, 8; Sec1.6.
2, 4, 6, 8, 16; Sec1.7. 1, 2, 5 

09/09 
Ch.2 Fundtions of a complex variable 
HW2 (duedate: 09/14 Tuesday): Sec2.1. 4, 8, 9, 10 
Week3 
09/14 
Differentiability and Analyticity 
HW3 (duedate: 09/21 Tuesday): Sec2.2. 3, 4, 11,
14, 21; Sec2.3. 3, 4, 7, 10. 

09/16 
The CauchyRiemann Equations; Harmonic fuctions 
HW3 (duedate: 09/21 Tuesday): Sec2.3. 11(a); Sec2.4.
1, 2, 4, 6, 8, 11; Sec2.5. 1, 3, 6. 
Week4 
09/21 
Ch.3 Elementary functions 
HW4 (duedate: 09/28 Tuesday): Sec2.5. 8, 9, 10, 14 

09/23 
Complex polynomials, rational, and excponential functions 
HW4 (duedate: 09/28 Tuesday): Sec3.1. 3, 5, 11,
13, 15 
Week5 
09/28 
Complex trigonometric functions 
HW5 (duedate: 10/05 Tuesday): Sec3.2. 4,
5(a)(b)(c)(d), 6, 9(a)(b)(c)(d), 14(a)(b). 

09/30 
Complex logarithmic fucntions 
HW5 (duedate: 10/05 Tuesday): Sec3.2.17; Sec3.3.
1, 3, 5. 
Week6 
10/05 
Ch4. Complex integration 
HW6 (duedate: 10/14 Thursday): Sec3.3. 9, 13, 16; Sec3.5.
3, 7, 11, 15(b); Sec4.1. 1(a)(c), 11. 

10/07 
Cauchy's integral formula 
HW6 (duedate: 10/14 Thursday): Sec4.2. 5, 11,
14(a); Sec4.3. 1(b)(c)(g), 5; Sec4.4. 10(a)(c)(d). 
Week7 
10/12 
No class 
N/A 

10/14 
Cauchy's integral formula 
HW7 (duedate: 10/19 Tuesday): Sec4.4. 13, 15, 16,
17; Sec4.5. 2, 3(a)(b)(c)(f), 4 
Week8 
10/19 
Bounds for analytic functions 
HW8 (duedate: 10/28 Thursday): Sec4.5. 3(d)(e), 5,
6, 7. 

10/21 
Maximum modulus Principle 
HW8 (duedate: 10/28 Thursday): Sec4.6. 5, 7, 8,
10, 11, 15. 
Week9 
10/26 
Midterm 
N/A 

10/28 
Ch5. Series representations for analytic functions 
N/A 
Week10 
11/02 
Taylor series 
HW9 (duedate: 11/09 Tuesday): Sec5.1. 1, 2, 6, 11,
15; Sec5.2. 1(a)(b), 2(a)(f). 

11/04 
Power series 
HW9 (duedate: 11/09 Tuesday): Sec5.2. 4, 5, 7,
11(a)(c), 14, 15; Sec5.3. 1, 2, 3(a)(b), 4. 
Week11 
11/09 
Laurent Series 
HW10 (duedate: 11/16 Tuesday): Sec5.3. 5, 13(b);
Sec5.5. 1, 2, 6, 9, 13. 

11/11 
Ch6. Residue Theory 
HW10 (duedate: 11/16 Tuesday): Sec5.6. 1, 5, 13;
Sec5.7. 1. 
Week12 
11/16 
Trigonometric integrals 
HW11 (duedate: 11/23 Tuesday): Sec6.1. 3, 6;
Sec6.2. 1, 5. 

11/18 
Improper integrals 
HW11 (duedate: 11/23 Tuesday): Sec6.3. 5, 10, 11;
Sec6.4. 1, 5, 6, 9; Sec6.5. 2, 7, 10. 
Week13 
11/23 
The argument principle and Rouche's theorem 
HW12 (duedate: 11/30 Tuesday): Sec6.7. 1, 7, 8 (Hint:
Show that the polynomial has all six zeros inside the disk of radius 2, it
has no zero inside the disk of radies 1, and it has no zero on the circle
of radius 1.), 10, 18. 

11/25 
Thanksgiving 
N/A 
Week14 
11/30 
Ch7. Conformal mapping 
HW13 (no need to submit) Sec7.2. 10;
Sec7.3. 3. 

12/02 
Mobius Transformation 
HW13 (no need to submit) Sec7.4. 1, 3, 6, 7, 9,
20. 