Sep. 8

9

First day assignment for late registrants

12

Click here
Annotated solutions: p1,p2

13 notes

Through the end of 2.2: Holomorphic functions

15 notes

1.2.3 Power series

16

Ch. 1 Exercises 1, 3, 8, 10, 11, 13

19

Ch. 1 Exercise 12
Solutions 9/16-9/19

20 notes

1.3: Integration along curves

22 notes

1.3: Integration along curves
2.1 Goursat's theorem

23

Ch. 1 Exercises 9, 16(a-c), 18, 19 (can use Ex. 14), 24

26

Ch. 1 Exercise 17
Solution

27 notes

2.2 Cauchy's theorem on a disc

29 notes

2.3 Toy contour integrals
2.4 Cauchy's integral formulas

30

Ch. 1 Exercises 7a, 7b, 20, 23, 26

Oct. 3

Ch. 1 Exercise 25
Solutions

4 notes

2.4 Cauchy's integral formulas (consequences)

6 notes

2.5 Applications

7

Ch. 2 Exercises 1, 2, 5, 6

10

Holiday

11 notes

2.5 Schwarz reflection & Runge approximation

13 notes

2.5 Runge approximation

14

Ch. 2 Exercises 3, 7, 9, 12a

17

Ch. 2 Problem 1a

18 notes

3.1 Zeros & poles
3.2 Residue formula

20 notes

3.3 Singularities, application of residues to integrals

21

Ch 2. Exercises 10, 13, 14, 15

24

Optional Corrigendum

25 notes

3.3 Residue applications cont.

27

- Exam 1 -

28

No homework

31

Nov. 1 notes

3.3 Singularities; Riemann sphere

3 notes

Zeta function and prime numbers

4

Ch. 3 Exercises 1, 3, 6, additional problem

7

Optional Corrigendum

8 notes

3.3 Essential singularities & 3.4 Argument principle

10 notes

3.5 General Cauchy's theorem

11

Ch. 3 Problem 3, additional problem

14

Optional Corrigendum

15 notes

3.6 Complex logarithm
8.1 Conformal equivalence

16

17 notes

Linear fractional transformations

18

Ch. 2 Problem 4, additional problem

21

Optional Corrigendum

22 notes

8.1 Conformal equivalence: more examples; Riemann surfaces.

23

24

Happy Thanksgiving!
Something cool

25

28

Optional Corrigendum

29 notes

8.2 Automorphisms of the disc

Dec. 1 notes

8.2 Automorphisms of the upper half plane

2

No homework

6 notes

Riemann mapping theorem, conformal invariance

8

- Exam 2 -

14

- Final Project Due -