asp net display barcode FUNCTIONS OF A COMPLEX VARIABLE in Visual Studio .NET

Maker Denso QR Bar Code in Visual Studio .NET FUNCTIONS OF A COMPLEX VARIABLE

FUNCTIONS OF A COMPLEX VARIABLE
QR Code 2d Barcode Scanner In .NET
Using Barcode Control SDK for .NET Control to generate, create, read, scan barcode image in VS .NET applications.
Painting Denso QR Bar Code In Visual Studio .NET
Using Barcode creator for VS .NET Control to generate, create QR image in .NET framework applications.
[CHAP. 16
Decoding QR Code ISO/IEC18004 In .NET Framework
Using Barcode reader for VS .NET Control to read, scan read, scan image in .NET applications.
Barcode Encoder In .NET Framework
Using Barcode creator for .NET Control to generate, create bar code image in Visual Studio .NET applications.
(b) Since jzj 10 encloses both poles z 1 and z 3 the required integral 2i e 5e 3 16 16 ! i e 5e 3 8
Read Barcode In .NET Framework
Using Barcode recognizer for Visual Studio .NET Control to read, scan read, scan image in Visual Studio .NET applications.
Print QR Code 2d Barcode In C#
Using Barcode encoder for Visual Studio .NET Control to generate, create QR Code 2d barcode image in VS .NET applications.
EVALUATION OF DEFINITE INTEGRALS 16.27. If j f z j @ M for z Rei , where k > 1 and M are constants, prove that lim R!1 Rk where is the semicircular arc of radius R shown in Fig. 16-9.
Painting QR Code 2d Barcode In .NET Framework
Using Barcode printer for ASP.NET Control to generate, create QR Code 2d barcode image in ASP.NET applications.
Drawing QR-Code In VB.NET
Using Barcode generation for .NET Control to generate, create Denso QR Bar Code image in .NET framework applications.
By the result (4), Page 394, we have     M M  f z dz @ j f z jjdzj @ k R k 1   R R
Generating ANSI/AIM Code 128 In .NET
Using Barcode generator for Visual Studio .NET Control to generate, create Code 128 Code Set B image in Visual Studio .NET applications.
EAN / UCC - 13 Maker In .NET Framework
Using Barcode maker for .NET Control to generate, create EAN13 image in .NET framework applications.
f z dz 0
EAN128 Creation In .NET Framework
Using Barcode generation for .NET Control to generate, create GS1-128 image in .NET applications.
Generate USS 93 In .NET
Using Barcode generation for .NET Control to generate, create Code 9/3 image in .NET applications.
since the length of arc L R. Then     and so lim lim  f z dz 0 f z dz 0  
Paint Universal Product Code Version A In Objective-C
Using Barcode maker for iPhone Control to generate, create UPC-A image in iPhone applications.
USS Code 128 Reader In VB.NET
Using Barcode reader for Visual Studio .NET Control to read, scan read, scan image in .NET applications.
R!1 R!1
Draw Bar Code In .NET
Using Barcode encoder for Reporting Service Control to generate, create bar code image in Reporting Service applications.
Recognizing Code-39 In Visual Studio .NET
Using Barcode decoder for .NET Control to read, scan read, scan image in .NET framework applications.
Fig. 16-9
Painting USS Code 39 In Java
Using Barcode creator for Java Control to generate, create Code 3/9 image in Java applications.
UCC - 12 Reader In .NET Framework
Using Barcode scanner for VS .NET Control to read, scan read, scan image in .NET framework applications.
16.28. Show that for 1 f z . 1 z4
Create USS Code 128 In Java
Using Barcode creator for Android Control to generate, create Code 128B image in Android applications.
DataMatrix Printer In Objective-C
Using Barcode drawer for iPad Control to generate, create Data Matrix ECC200 image in iPad applications.
z Re ,
M j f z j @ k ; k > 1 R
  1 1 1 2 @ @ 4 if R is large enough (say R > 2, for 4 e4i  1 R jR4 e4i j 1 R4 1 R example) so that M 2; k 4. Note that we have made use of the inequality jz1 z2 j A jz1 j jz2 j with z1 R4 e4i and z2 1.
  If z Rei , j f z j  
1 16.29. Evaluate
dz , where C is the closed contour of Problem 16.27 consisting of the line from R to R z4 1 and the semicircle , traversed in the positive (counterclockwise) sense. Since z4 1 0 when z ei=4 ; e3i=4 ; e5i=4 ; e7i=4 , these are simple poles of 1= z4 1 . Only the poles ei=4 and e3i=4 lie within C. Then using L Hospital s rule, & ' 1 Residue at ei=4 lim z ei=4 4 z 1 z!ei=4 1 1 3i=4 e lim 3 4 z!ei=4 4z & ' 1 3i=4 Residue at e lim z e3i=4 4 z 1 z!e3i=4 1 1 9i=4 e lim 3 4 z!e3i=4 4z Consider
dx . x4 1
Thus p  2 dz 2i 1 e 3i=4 1 e 9i=4 4 4 4 2 Cz 1 1
CHAP. 16]
FUNCTIONS OF A COMPLEX VARIABLE
i.e., R dx 4 R x 1 p dz  2 4 2 z 1 2
Taking the limit of both sides of (2) as R ! 1 and using the results of Problem 16.28, we have p R 1 dx dx  2 lim 4 R!1 R x4 1 2 1 x 1 1 Since dx 2 4 1 x 1 1
p dx  2 : ; the required integral has the value 4 x4 1
1 16.30. Show that
x2 dx 7 : 2 50 1 x 1 x 2x 2
z2 enclosed by the contour C of Problem 16.27 are z i of order 2 and 1 z2 2z 2 z 1 i of order 1. ( ) d z2 9i 12 2 z i : Residue at z i is lim z!i dz 100 z i 2 z i 2 z2 2z 2 The poles of z2
Residue at z 1 i is Then R or
z! 1 i
lim z 1 i
z2 3 4i 25 1 z 1 i z 1 i
& ' z2 dz 9i 12 3 4i 7 2i 2 2 100 25 50 C z 1 z 2z 2
x2 dx 2 1 2 x2 2x 2 R x
z2 dz 7 1 z2 2z 2 50
Taking the limit as R ! 1 and noting that the second integral approaches zero by Problem 16.27, we obtain the required result.
2 16.31. Evaluate
d . 5 3 sin 
Then sin  ei e i z z 1 , dz iei d iz d so that 2i 2i 2 d dz=iz 2 dz ! 2 0 5 3 sin  C C 3z 10iz 3 z z 1 5 3 2i
Let z ei .
where C is the circle of unit radius with center at the origin, as shown in Fig. 16-10 below. 2 The poles of 2 are the simple poles 3z 10iz 3 p 10i 100 36 z 6 10i 8i 6 3i; i=3: Only i=3 lies inside C. Fig. 16-10
FUNCTIONS OF A COMPLEX VARIABLE
[CHAP. 16
Residue at i=3 lim
   i 2 2 1 z lim by L Hospital s rule. z! i=2 z! i=2 6z 10i 3 3z2 10iz 3 4i   2 dz 1  2i Then , the required value. 2 10iz 3 4i 2 C 3z
2 16.32. Show that
cos 3  d . 5 4 cos  12
z z 1 e3i e 3i z3 z 3 ; cos 3 ; dz iz d. 2 2 2 2 cos 3 z3 z 3 =2 dz ! d 5 4 cos  0 C z z 1 iz 5 4 2 1 z6 1 dz 3 2i C z 2z 1 z 2
Copyright © OnBarcode.com . All rights reserved.