Advanced Mathematics

Course description in Osiris

In this course we will use the book of Serge Lang, Complex Analysis, fourth edition, Springer Graduate Text in Mathematics 103 and some lecture notes by W.W.L Chen.

Lectures are given by Johan van de Leur and João Mestre Fernandes da Silva in Newton room E.
There are no office hours, but you can always e-mail J.W.vandeLeur"AT"uu.nl or call 030-2533833 and we can agree to meet at UCU or in room 509 of the Math Building.

Wednesday February 2: Chapter 4 (not 4.3) of W.W.L Chen's Fundamentals of Analysis. See

http://rutherglen.science.mq.edu.au/wchen/lnfafolder/fa04.pdf

Friday February 4: Short lecture on section 4.3 of W.W.L Chen's Fundamentals of Analysis.

Exercises:

a Prove by using the definition that x² is continuous for every x.
b Prove by using the definition that xⁿ (n=1,2,3,4,...) is continuous in x=0.
c Prove a and b by using Theorem 4F.
d Prove that every polynomial is continuous.
Exercises 1, 2, 4 of Chapter 4 of W.W.L Chen's Fundamentals of Analysis.

Hand in exercise: Exercise 5 of Chapter 4 of W.W.L Chen's Fundamentals of Analysis.

Wednesday February 9: Chapter 1 pages 1-4 of W.W.L Chen's Multivariable and Vector Analysis. See

http://rutherglen.science.mq.edu.au/wchen/lnmvafolder/mva01.pdf

Friday February 11: Rest of Chapter 1 of W.W.L Chen's Multivariable and Vector Analysis.
Exercises: 1a, 2 of Chapter 1 of W.W.L Chen's Multivariable and Vector Analysis.

Wednesday February 16: Exercises: 3, 5b, 6, 7 and 9 of Chapter 1 of W.W.L Chen's Multivariable and Vector Analysis.

Hand in exercise: Exercise 4 of Chapter 1 of W.W.L Chen's Multivariable and Vector Analysis (hand in on February 23).

Friday February 18: No class

Wednesday February 23: Exercises: Ch 1.1: 2a,c, 7, 8a, 9, 10a,c,f,h, Ch 1.2: 1,b,d,h, 2a,c, 4, 5, 7, 13,

Hand in exercise: Exercises 11 and 12 of section 1.2 of Lang's Complex Analysis.

Friday February 25: Ch 1.3 and Ch 1.4 until Compact Sets

Wednesday March 2: Exercises: Ch 1.3: 1, 2, 4, Ch 1.4: 1, 2, 3

Hand in exercise: Exercise 6 of section 1.4

Friday March 4: Rest of Section 1.4 on Compact sets

Wednesday March 9: Exercises:Ch 1.2: 8, 9, Ch 1.4: 4, 5, 7 test exercises

Hand in exercise: Exercise 10 of section 1.2

Friday March 11: Rest of Ch 1 (section 1.7 not so important).

Wednesday March 16: test exercises

Friday March 18: MIDTERM EXAM material: two handouts + Chapter 1 book by Lang.

Wednesday March 30: Lecture starting with section 1 of Chapter II (No exercises today)
Some time to see the midterm test

Friday April 1: Lecture part of section 2 of Chapter II

Wednesday April 6: Exercises: Ch II.1: 1b, d, e, g, 3, 4, 5

Hand in exercise: Exercise 6 of section II.1

Friday April 8: Exercises: Ch II.2: 3, 4a, b, c, d, 5a, c, 7, 10

Wednesday April 13: Lecture: section 4 and section 5 of Chapter II

Friday April 15: Lecture: section 6 and maybe a part of section 7 of Chapter II

Wednesday April 20: Exercises: Ch II.4: 2, Ch II.5: 2, 5, 6, Ch II.6: 2, 4
Hand in exercise (due May 4): Exercise 6 of Ch II.6 solve this problem for the explicit example that k=2, a_0(z)=1, a_1(z)=0 and a_2(z)=-z.

Wednesday April 27: No new exercises, try to catch up.

Friday April 29: Lecture: section 7 of chapter II and beginning of section 1 of chapter III.

Wednesday May 4: Lecture: section 1 and part of 2 of chapter III.

Friday May 6: Lecture: Cauchy's theorem, notes last lecture

Wednesday May 11: Exercises 5 , 6 of section II.2, 1c of II.7, 19, 20 and 25 of section VI.1 (forget the remark about the residue)

Friday May 13:

Wednesday May 18:

Friday May 20: FINAL EXAM material: Chapter I and II and sections 1 and 2 from Chapter 3 from Lang + Cauchy's theorem (see notes last lecture)