Day

Date

Announcement

Lecture Description

Homework

Week 1

Mon

June 9

First Class; Introductions

§1.1 Introduction to Complex Numbers

Tue

June 10

§1.2 Properties of Complex Numbers

Wed

June 11

§1.3 Elementary Functions

Thur

June 12

§1.4 Continuous Functions (Review of Math 3220)

Week 2

Mon

June 16

§1.5 Basic Properties of Analytic Functions

HW 1.1---1.4 Due

Tue

June 17

§1.6 Differentiability of the Elementary Functions

Wed

June 18

§2.1 Contour Integrals

Thur

June 19

§2.2 Cauchy's Theorem---A First Look

Week 3

Mon

June 23

§2.3 A Closer Look at Cauchy

HW 1.5---2.2 Due

Tue

June 24

§2.4 Cauchy's Integral Formula

Wed

June 25

§2.5 Maximum Modulus Theorem and Harmonic Functions

Thur

June 26

§3.1 Convergent Series of Analytic Functions

Week 4

Mon

June 30

§3.2 Power Series and Taylor's Theorem

HW 2.3---2.5 Due

Tue

July 1

§3.3 Laurent Series and Classification of Singularities

Wed

July 2

Review

Thur

July 3

Exam 1: Covers Chapters 1 and 2

Week 5

Mon

July 7

§4.1 Calculation of Residues

HW 3.1---3.3 Due

Tue

July 8

§4.2 Residue Theorem

Wed

July 9

§4.3 Evaluation of Definite Integrals

Thur

July 10

§4.4 Evaluation of Infinite Series and Partial-Fraction Expansions

Week 6

Mon

July 14

§5.1 Basic Theory of Conformal Mappings

HW 4.1---4.4 Due

Tue

July 15

§5.2 Fractional Linear Transformations (no Schwarz-Christoffel)

Wed

July 16

Review

Thur

July 17

Exam 2: Covers Chapters 3 and 4

Week 7

Mon

July 21

§5.3 Applications of Conformal Mappings to PDEs

HW 5.1---5.2 Due

Tue

July 22

§6.1 Analytic Continuation and Elementary Riemann Surfaces

Wed

July 23

§7.1 Infinite Products and the Gamma Function

Thur

July 24

NO CLASS

Week 8

Mon

July 28

§8.1 Basic Properties of Laplace Transforms

HW 5.3---7.1 Due

Tue

July 29

§8.2 Complex Inversion Formula

Wed

July 30

§8.3 Applications of Laplace Transforms to ODEs

Thur

July 31

Final Exam (7:30 – 9:30 am): Covers Chapters 1 through 6.1, plus 8.1

HW 8.1---8.3 Due