Messages - Page 2
In today's lecture: I finished chapter 3 by completing parts 3.3 and 3.5.
In the next lecture: I will start complex integration by defining contours and contour integrals (chapter 4.1 and 4.2).
The oblig has now been corrected, and can be found in the usual place on the 7th floor. You can also see if you have passed in the devilry system, https://devilry.ifi.uio.no/
For those who did not pass, the deadline to hand in a second and final version is October 6th, 14:30. -SR
In today's lecture: i defined the logarithm as a complex valued function and showed analyticity of the principal branch of the Logarithm on a sub-domain of the complex plane. Most of the material was from chapter 3.3.
In the next lecture: i will introduce the notion of branches of a complex function and illustrate their domains of analyticity. I will also cover powers of a complex function and introduce inverse trigonometric functions (chapter 3.5).
In today's lecture: i covered chapter 2.5, 3.1 and 3.2.
In the next lecture: i will cover chapter 3.3 and 3.5
VIKTIG:: NO LECTURES next week.
There will be no problem session on September 20. in order to give you more time to work on the obligatory exercise set. -SR
In today's lecture, i finished part 2.4 of the book (analytic functions) and start part 2.5 (harmonic functions). I also derived the heat equation and the Laplace's equation from first principles.
In the next lecture, i will finish chapter 2 and start chapter 3 of the book.
In today's lecture: i introduced the concept of derivative of a complex function and defined analyticity. The Cauchy-Riemann equations for ensuring differentiability were also introduced.
In the next lecture: I will prove sufficient conditions for checking analyticity. Harmonic functions (solutions of the Laplace equation) will be introduced and related to analytic functions.
Next lecture in B1036, NHA.
IMPORTANT: FIRST OBLIGATORY EXERCISE SET CAN BE DOWNLOADED FROM OBLIG1
DUE DATE FOR OBLIG 1: 22-09-2011
In today's lecture: i introduced the concepts of limits and continuity of functions of complex variables -- chap 2.1 and 2.2 of the book.
In Friday's lecture: i will cover the concept of differentiability of functions of complex variable and introduce the notion of analytic functions.
In last friday's lecture: i finished chapter 1 of the book by covering stereographic projection.
Tomorrow's lecture: will be on chapter 2 -- functions of complex variables. I will introduce limits of complex functions and notion of continuous complex functions.
IMPORTANT: Tomorrow's lecture will be held at B1036, NHA.
Problems for the problem session next week are now published - see link to the left. Problems will be published each Tuesday on that page.
In today's lecture: i covered parts 1.4, 1.5 and 1.6 of the book: complex exponential, roots of complex numbers and concepts of open sets, boundary points, closed sets and connected sets of complex numbers.
Lecture on friday will be on stereographic projection and if time permits, on elementary properties of functions of complex numbers.
VIKTIG !!!! Lecture tomorrow will be held at B1036, Nils Henrik Abels (NHA) hus.
Text book for the course: Fundamental of complex analysis (with applications to engineering and science), Third edition, by E. B. Saff and A. D. Snider, Prentice hall, 2003.
In today's lecture, I introduced the contents and context for complex analysis and covered 1.1, 1.2, 1.3 and 1.4 of Saff and Snider's book.
For next lecture (Tuesday 30th): i will do properties of the complex exponential, complex roots, sets of complex numbers and start stereographic projection -- 1.5, 1.6 and 1.7 of the book.
For next exercise session (Tuesday 30th): Prepare problems 1.1 (1,5,7,15), 1.2( 3, 4, 7(a,b,d,g,i,j), 17), 1.3(7(a,b,c,f,g), 15, 16) and 1.4 (1,3,11,17).
NO LECTURE ON FRIDAY 26th
CHECK THIS PAGE ON MONDAY 29th for where the next lecture will be held