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Complex Analysis III

Sunday, March 18, 2007. Examples of diff/cont at a point. Cont only at a point. F(z) = z if z irrational and - z if z is irrational. (Rotate usual function.). Note that if z 0 =/= 0 then lim {z- z 0}f(z) DNE. Given epsilon 0 consider f(z)-f(z 0) for z in B( epsilon,z 0). If z 0 irrat then z- z 0 along rational approximations gives f(z)-f(z 0) =2 z 0 epsilon -/- 0 as z- z 0. So f is not cts at z 0. As z- 0 f(z)-f(0) = z 0 - 0. So cts at 0. Diff only at a pt. Example in lectures: x I think. It includes fou...

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Complex Analysis III | complexanalysisiii.blogspot.com Reviews

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Sunday, March 18, 2007. Examples of diff/cont at a point. Cont only at a point. F(z) = z if z irrational and - z if z is irrational. (Rotate usual function.). Note that if z 0 =/= 0 then lim {z- z 0}f(z) DNE. Given epsilon 0 consider f(z)-f(z 0) for z in B( epsilon,z 0). If z 0 irrat then z- z 0 along rational approximations gives f(z)-f(z 0) =2 z 0 epsilon -/- 0 as z- z 0. So f is not cts at z 0. As z- 0 f(z)-f(0) = z 0 - 0. So cts at 0. Diff only at a pt. Example in lectures: x I think. It includes fou...

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2 more work necessary

3 posted by

4 pjmm

5 1 comment

6 a brief tutorial

7 overview

8 no comments

9 to investigate soon

10 subject heading s topology

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Complex Analysis III | complexanalysisiii.blogspot.com Reviews

https://complexanalysisiii.blogspot.com

Sunday, March 18, 2007. Examples of diff/cont at a point. Cont only at a point. F(z) = z if z irrational and - z if z is irrational. (Rotate usual function.). Note that if z 0 =/= 0 then lim {z- z 0}f(z) DNE. Given epsilon 0 consider f(z)-f(z 0) for z in B( epsilon,z 0). If z 0 irrat then z- z 0 along rational approximations gives f(z)-f(z 0) =2 z 0 epsilon -/- 0 as z- z 0. So f is not cts at z 0. As z- 0 f(z)-f(0) = z 0 - 0. So cts at 0. Diff only at a pt. Example in lectures: x I think. It includes fou...

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complexanalysisiii.blogspot.com

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Complex Analysis III: A Brief Tutorial

http://complexanalysisiii.blogspot.com/2007/02/brief-tutorial.html

Wednesday, February 21, 2007. Simply stated, Bombelli is just another computer programme for plotting complex functions. Nevertheless, it features many characteristics that are at least unusual amongst other applications at its level, namely:. It is gratuitous;. On account of having been written in JAVA, it is platform independent and avaiable through the Internet;. It offers a high degree of flexibility on defining new functions such as polymomial, trigonometric, exponential, Möbius Transformations, etc.

2

Complex Analysis III: Complex Analysis

http://complexanalysisiii.blogspot.com/2007/01/complex-analysis.html

Tuesday, January 30, 2007. A free textbook on Complex Analysis (useable? This is a textbook for an introductory course in complex analysis. It has been used for our undergraduate complex analysis course here at Georgia Tech and at a few other places that I know of. I am also grateful to Professor Pawel Hitczenko of Drexel University, who prepared the nice supplement to Chapter 10 on applications of the Residue Theorem to real integration. Subscribe to: Post Comments (Atom). Notes for Conformal Maps.

3

Complex Analysis III: February 2007

http://complexanalysisiii.blogspot.com/2007_02_01_archive.html

Wednesday, February 21, 2007. Simply stated, Bombelli is just another computer programme for plotting complex functions. Nevertheless, it features many characteristics that are at least unusual amongst other applications at its level, namely:. It is gratuitous;. On account of having been written in JAVA, it is platform independent and avaiable through the Internet;. It offers a high degree of flexibility on defining new functions such as polymomial, trigonometric, exponential, Möbius Transformations, etc.

4

Complex Analysis III: Notes for Conformal Maps

http://complexanalysisiii.blogspot.com/2007/01/notes-for-conformal-maps.html

Monday, January 29, 2007. Notes for Conformal Maps. Maple has a nice series of packages for viewing conformal maps: in particular, the "Maple Book" on p282 lists the Joukowski plot for airfoils. First they define a proc for JoukowskiP and then use it like. Display(JoukowskiP(1/10,1/10),scaling=constrained,thickness=2);. Subscribe to: Post Comments (Atom). Notes for Conformal Maps. View my complete profile.

5

Complex Analysis III: To investigate soon...

http://complexanalysisiii.blogspot.com/2007/02/to-investigate-soon.html

Wednesday, February 21, 2007. Chinn and Steenrod's popular-ish book, including discussion of winding number etc. Chinn, William G. Title: First concepts of topology : the geometry of mappings of segments, curves, circles, and disks / by W. G. Chinn and N. E. Steenrod. Published: [New York] : Random House, [1966]. Description: viii, 160 p. : illus ; 23 cm. Other Author(s): Steenrod, Norman Earl, 1910-1971, joint author. Series Title(s): New mathematical library, 18. Location: Barr Smith Main collection.

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complexanalysisiii.blogspot.com

Complex Analysis III

Sunday, March 18, 2007. Examples of diff/cont at a point. Cont only at a point. F(z) = z if z irrational and - z if z is irrational. (Rotate usual function.). Note that if z 0 =/= 0 then lim {z- z 0}f(z) DNE. Given epsilon 0 consider f(z)-f(z 0) for z in B( epsilon,z 0). If z 0 irrat then z- z 0 along rational approximations gives f(z)-f(z 0) =2 z 0 epsilon -/- 0 as z- z 0. So f is not cts at z 0. As z- 0 f(z)-f(0) = z 0 - 0. So cts at 0. Diff only at a pt. Example in lectures: x I think. It includes fou...

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