Download presentation

Presentation is loading. Please wait.

Published byRowan Bronson Modified over 4 years ago

1
Chapter 20 Complex variables

4
20.2 Cauchy-Riemann relation A function f(z)=u(x,y)+iv(x,y) is differentiable and analytic, there must be particular connection between u(x,y) and v(x,y)

5
Chapter 20 Complex variables

7
20.3 Power series in a complex variable

8
Chapter 20 Complex variables 20.4 Some elementary functions

9
Chapter 20 Complex variables

11
20.5 Multivalued functions and branch cuts A logarithmic function, a complex power and a complex root are all multivalued. Is the properties of analytic function still applied? (A) (B) (A) (B)

12
Chapter 20 Complex variables Branch point: z remains unchanged while z traverse a closed contour C about some point. But a function f(z) changes after one complete circuit. Branch cut: It is a line (or curve) in the complex plane that we must cross, so the function remains single-valued.

13
Chapter 20 Complex variables

14
(A) (B)

15
Chapter 20 Complex variables 20.6 Singularities and zeros of complex function

16
Chapter 20 Complex variables

20
20.10 Complex integral

21
Chapter 20 Complex variables

25
20.11 Cauchy theorem

26
Chapter 20 Complex variables

28
20.12 Cauchys integral formula

29
Chapter 20 Complex variables

31
20.13 Taylor and Laurent series Taylors theorem:

32
Chapter 20 Complex variables

35
How to obtain the residue ?

36
Chapter 20 Complex variables

37
20.14 Residue theorem

38
Chapter 20 Complex variables Residue theorem:

39
Chapter 20 Complex variables

40
20.16 Integrals of sinusoidal functions

41
Chapter 20 Complex variables

42
20.17 Some infinite integrals

43
Chapter 20 Complex variables

44
For poles on the real axis:

45
Chapter 20 Complex variables Jordans lemma

46
Chapter 20 Complex variables

47
20.18 Integral of multivalued functions

48
Chapter 20 Complex variables

Similar presentations

OK

DIVIDING INTEGERS 1. IF THE SIGNS ARE THE SAME THE ANSWER IS POSITIVE 2. IF THE SIGNS ARE DIFFERENT THE ANSWER IS NEGATIVE.

DIVIDING INTEGERS 1. IF THE SIGNS ARE THE SAME THE ANSWER IS POSITIVE 2. IF THE SIGNS ARE DIFFERENT THE ANSWER IS NEGATIVE.

© 2018 SlidePlayer.com Inc.

All rights reserved.

To ensure the functioning of the site, we use **cookies**. We share information about your activities on the site with our partners and Google partners: social networks and companies engaged in advertising and web analytics. For more information, see the Privacy Policy and Google Privacy & Terms.
Your consent to our cookies if you continue to use this website.

Ads by Google

Ppt on cloud computing in ieee format Download ppt on development class 10 economics Ppt on eid Ppt on polynomials of 98 Ppt on accounting standards 11 Ppt on combination of resistances eve Ppt on grooming and etiquettes Ppt on group development phases Ppt on cells and organelles Ppt on cross border merger and acquisition