Mathematic Methods HW Solutions 65

Mathematic Methods HW Solutions 65 - , | z | < 1 2.37...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
Chapter 14 1.1 u = x 3 - 3 xy 2 , v = 3 x 2 y - y 3 1.2 u = x , v = y 1.3 u = x , v = - y 1.4 u = ( x 2 + y 2 ) 1 / 2 , v = 0 1.5 u = x , v = 0 1.6 u = e x cos y , v = e x sin y 1.7 u = cos y cosh x , v = sin y sinh x 1.8 u = sin x cosh y , v = cos x sinh y 1.9 u = x/ ( x 2 + y 2 ), v = - y/ ( x 2 + y 2 ) 1.10 u = (2 x 2 + 2 y 2 + 7 x + 6) / [( x + 2) 2 + y 2 ], v = y/ [( x + 2) 2 + y 2 ] 1.11 u = 3 x/ [ x 2 + ( y - 2) 2 ], v = ( - 2 x 2 - 2 y 2 + 5 y - 2) / [ x 2 + ( y - 2) 2 ] 1.12 u = x ( x 2 + y 2 + 1) / [( x 2 - y 2 + 1) 2 + 4 x 2 y 2 ], v = y (1 - x 2 - y 2 ) / [( x 2 - y 2 + 1) 2 + 4 x 2 y 2 ] 1.13 u = ln( x 2 + y 2 ) 1 / 2 , v = 0 1.14 u = x ( x 2 + y 2 ), v = y ( x 2 + y 2 ) 1.15 u = e x cos y , v = - e x sin y 1.16 u = 0, v = 4 xy 1.17 u = cos x cosh y , v = sin x sinh y 1.18 u = ± 2 - 1 / 2 [( x 2 + y 2 ) 1 / 2 + x ] 1 / 2 , v = ± 2 - 1 / 2 [( x 2 + y 2 ) 1 / 2 - x ] 1 / 2 , where the ± signs are chosen so that uv has the sign of y . 1.19 u = ln( x 2 + y 2 ) 1 / 2 , v = arc tan( y/x ) [angle is in the quadrant of the point ( x,y )]. 1.20 u = x 2 - y 2 - 4 xy - x - y + 3, v = 2 x 2 - 2 y 2 + 2 xy + x - y 1.21 u = e - y cos x , v = e - y sin x In 2.1 to 2.24, A = analytic, N = not analytic 2.1 A 2.2 A 2.3 N 2.4 N 2.5 N 2.6 A 2.7 A 2.8 A 2.9 A, z n = 0 2.10 A, z n = - 2 2.11 A, z n = 2 i 2.12 A, z n = ± i 2.13 N 2.14 N 2.15 N 2.16 N 2.17 N 2.18 A, z n = 0 2.19 A, z n = 0 2.20 A 2.21 A 2.22 N 2.23 A, z n = 0 2.24 N 2.34 - z - 1 2 z 2 - 1 3 z 3 ··· , | z | < 1 2.35 1 - ( z 2 / 2!) + ( z 4 / 4!) ··· , all z 2.36 1 + 1 2 z 2 - 1 8 z 4 ···
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: , | z | < 1 2.37 z-1 3 z 3 + 2 15 z 5 , | z | < / 2 2.38-1 2 i + 1 4 z + 1 8 iz 2-1 16 z 3 , | z | < 2 2.39 ( z/ 9)-( z 3 / 9 2 ) + ( z 5 / 9 3 ) , | z | < 3 2.40 1 + z + z 2 + z 3 , | z | < 1 2.41 1 + iz-z 2 / 2-iz 3 / 3! + z 4 / 4! , all z 2.42 z + z 3 / 3! + z 5 / 5! , all z 2.48 Yes, z n = 0 2.49 No 2.50 Yes, z n = 0 2.51 Yes 2.52 No 2.53 Yes, z n = 0 2.54-iz 2.55-iz 3 2.56-iz 2 / 2 2.57 (1-i ) z 2.58 cos z 2.59 e z 2.60 2 ln z 2.61 1 /z 2.62-ie iz 2.63-i/ (1-z ) 65...
View Full Document

This note was uploaded on 02/29/2012 for the course MHF 2312 taught by Professor Dr.chet during the Fall '11 term at UNF.

Ask a homework question - tutors are online