# MATH2230B - Complex Variables with Applications - 2018/19

Teacher:
Course Year:
2018/19
Term:
2

### Announcement

• The first midterm will be held on Jan. 31 in class
• The first midterm covers the first 6 sections in the lecture note
• The second midterm will be held on Mar. 21 in class
• The second midterm will cover all we have taught before and include Taylor/Laurent series
• The final exam is accumulative and will cover all in the lecture notes (updated version), except the Sect. 23.

### General Information

#### Lecturer

• YU, Yong
• Office: LSB 214
• Tel: 39438900
• Email:
• Office Hours: Any time/ by appointment

#### Teaching Assistant

• TAI, Ho Man
• Office: LSB 232
• Tel: 3943 5294
• Email:

#### Time and Venue

• Lecture: Mo 2:30PM - 4:15PM, LSB LT4; Th 3:30PM - 4:15PM, LSB LT3
• Tutorial: Th 9:30AM - 10:15AM, LSB C2; Th 2:30PM - 3:15PM, LSB LT3; Th 5:30PM - 6:15PM, LSB LT5

### Course Description

This course is to introduce the basic properties of complex functions and analytic functions and to illustrate the important use of these theories to other branches of mathematics and sciences. Topics include: complex numbers; limits, continuity and derivatives, Cauchy-Riemann equations, analytic functions; elementary functions; mapping by elementary functions; Contours integrals, Cauchy-Goursat theorem, Cauchy integral formula, Morera’s theorem, maximum moduli of functions, the fundamental theorem of algebra; Taylor series and Laurent’s series; residues and poles, evaluation of infinite real integrals. This course will start on Jan. 7, 2019 and end on Apr 18, 2019.

### Textbooks

• Complex Variables and Applications, Ninth Edition, by James Ward Brown/Ruel V. Churchill

### References

• Complex Analysis, Princeton lectures in analysis II, by Elias M. Stein/Rami Shakarchi
• Complex Analysis: An Introduction to the Theory of Analytic Functions of One Variable, by Lars Ahlfors

### Assessment Scheme

 Homework 10% Midterm 1 20% Midterm 2 20% Final 50%