פונקציות מרוכבות חוברת קורס 2010
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<p>9002.01.81-9002.01.03</p>
<p>" 11 9002.11.31</p>
<p> 2</p>
<p>9002.11.1-9002.11.31</p>
<p>4-3</p>
<p> 3</p>
<p>9002.11.51-9002.11.72</p>
<p>6-5</p>
<p>" 20 9002.21.11</p>
<p> 3,4</p>
<p>9002.11.92-9002.21.11) (</p>
<p>8-7</p>
<p>" 30 9002.21.52</p>
<p> 4,5</p>
<p>9002.21.31-9002.21.52)- (</p>
<p>01-9</p>
<p> 5</p>
<p>9002.21.72-0102.1.8</p>
<p>21-11</p>
<p>" 21 0102.1.22</p>
<p> 6</p>
<p>0102.1.01-0102.1.22</p>
<p>41-31</p>
<p>) 0102(</p>
<p> 6,7</p>
<p>0102.1.42-0102.2.5</p>
<p>61-51</p>
<p>" 31 0102.2.91</p>
<p> 7</p>
<p>0102.2.7-0102.2.91</p>
<p>81-71</p>
<p>* " ". . .</p>
<p> - " " )( )"( * 8 02-91</p>
<p>0102.2.12-0102.3.5)- ( ) 0102(</p>
<p>" 41 0102.3.21</p>
<p> 8,9</p>
<p>0102.3.7-0102.3.91</p>
<p>22-12</p>
<p>" 40 0102.3.62</p>
<p> 9</p>
<p>0102.3.12-0102.4.2) ( )- (</p>
<p>42-32</p>
<p>" 51 0102.4.61</p>
<p> 9,01</p>
<p>0102.4.4-0102.4.61)- ( ) (</p>
<p>62-52</p>
<p> 01,11</p>
<p>0102.4.81-0102.4.03) , (</p>
<p>82-72</p>
<p>" 61 0102.5.41</p>
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<p> 21</p>
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<p>23-13</p>
<p>" 71 0102.6.4</p>
<p> 21</p>
<p>0102.5.03-0102.6.11</p>
<p>43-33</p>
<p>" 81 0102.6.81</p>
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<p>3</p>
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<p>3 2</p>
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<p>11</p>
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<p> 3 4 . 5 . 1. 2.</p>
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<p> zdz = zdz6</p>
<p>1. 2.</p>
<p>1 2 . </p>
<p> 6 .</p>
<p> f ( z ) dz </p>
<p> ) f ( z f ( z ) dz</p>
<p>1. 2.</p>
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<p>1= z</p>
<p>8 = z 1 dz</p>
<p> 7 1. , L . 1dz = L</p>
<p>2. C 1 = z- ) z = 1 + i 1 (, . Im zdz Re zdz = 2 + iC C</p>
<p>21</p>
<p> 8 1. ) F ( z z C . F ( z ) = z< 1 ) f ( z 1 f } 1 < D = { z : z 2</p>
<p>2.</p>
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<p> 9 . lim1 z 2 + 10 z 0 = dz )1 + R ( z 2)( z 3 + z z =R</p>
<p>1.</p>
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<p> Im z 1 z + z dz 1= z</p>
<p>2.</p>
<p> 01 C - z = i - , z = iC</p>
<p>= z dz</p>
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<p>02</p>
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<p> 11 C 0 , 1 , i , 1 + i ,</p>
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<p> ) 3 , f ( x + iy ) = ( x3 3 xy 2 ) + i (3 x 2 y y t + i sin t</p>
<p>= f ( z ) dz i</p>
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<p> 2 </p>
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<p> 41 C 1 2 y = x )1 ,0( )0,1( , Log zdz -C</p>
<p>2</p>
<p>1 i</p>
<p>. .</p>
<p>2i2 ln</p>
<p>. . ) (. "" .</p>
<p> 51 lim - 0 rza =r</p>
<p>f ( z ) dz ) f ( z , z = a za</p>
<p>0</p>
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<p>)f (a) 2 if ( a</p>
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<p>1. 2.</p>
<p> z z a dz z =r</p>
<p>3</p>
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<p>2 ( u ( rei ) ) d</p>
<p>) ) ( v( rei 0</p>
<p>2</p>
<p>d</p>
<p> )0( u (0) = v</p>
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<p>51</p>
<p> 5 )01 ( f f ( z ) e z . z C</p>
<p> 6 )51 ( g , f M - ) ) Re ( f ( z ) ) M Re ( g ( z</p>
<p> . z C . b , a - f ( z ) = ag ( z ) + b . z C . M1 M - ) ) Re ( f ( z ) ) M 1 Re ( g ( z . z C : g , f .</p>
<p> 7 )51 ( ) f ( z 1 < . z1 ) f ( z 1 z</p>
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<p> an z n 0= n</p>
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<p>. . . .</p>
<p>z 21 z 2z2z 2 )1 + ( z</p>
<p>= ), f ( z</p>
<p>) 2 , f ( z ) = sin(2 z z</p>
<p> 2 )01 ( :</p>
<p> an z n 0=n</p>
<p>1 = 0 3an + 4an 1 an 2 = 0 , a1 = 1 , a 2 . n . : , .</p>
<p> 3 )01 ( 1 = z: = ). f ( z1 011 + z 2 + z 4 + z 6 + z 8 + z</p>
<p>: .</p>
<p>71</p>
<p> 4 )02 ( z 0, z 1 . f ( z) = ez 0=1 , z </p>
<p>. ) f ( z 0 = . z ? . )0( ) ) Bn = f ( n Bn Bernoulli , (. 2 n- 0 = 1+ B2 n n. n 1 n</p>
<p> Bk k =0 k </p>
<p> 0 =</p>
<p> = ) g ( z 0 = z .</p>
<p>0 z cot z , z 0=1 ,z</p>
<p>.</p>
<p>: ) g ( z- ) . f ( z</p>
<p>. tan z 0 = . z ? 5 )51 ( ) f ( z D 0, ei . 2</p>
<p>)1,0[ - )</p>
<p> f - . D 6 )01 ( g , f 0 , z 0 zn z - f f = g g } . { zn c - ) f ( z ) = cg ( z z . 7 )51 ( : . f D , f - . D . 0 = z:1 1 , 0 = f + f n. n n 0 = )0( f (0) = f</p>
<p> f 0 = z: 3 = , f 3 = f n. n 1+ n 1+ n n 1 n 1 n</p>
<p>.</p>
<p>81</p>
<p> )"( 4134202 : : 7 1.8, 2.8 8 3 : : 7 1/0102 :</p>
<p> : 0102.3.21</p>
<p> : " "</p>
<p> 1 )51 ( . .= )f ( z 1 cos z 2 z 3 + iz</p>
<p>.</p>
<p>f ( z) = e</p>
<p>cot z</p>
<p>.</p>
<p>= )f ( z</p>
<p>1 + ei z 2 )1 4 ( z</p>
<p>.</p>
<p> 2 )01 ( , , . 1= . z f ( z ) = sin z 1 z</p>
<p>. . .</p>
<p> 0 = . z 1 = . z</p>
<p>f ( z ) = Log z f ( z ) = tan 1 1 z</p>
<p> 3 )51 ( 0 ? z )f ( z 1 z</p>
<p> f }0{ \ C</p>
<p>91</p>
<p> 4 )02 ( f 1 = z- 3 = z f1</p>
<p> . f</p>
<p> an ( z 2)n = n</p>
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<p> 5 )01 ( f , 0 < z < R 0 > M 0 < r < R . r f ( rei ) d < M0 2</p>
<p> 0 = z . f</p>
<p> 6 )51 ( f . : 1 = ) f ( z ), ( 0 , z = ei f .</p>
<p>> . z: z . z</p>
<p>{</p>
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<p> }</p>
<p> 7 )51 (. ) f ( z</p>
<p>)f ( z 1 ) f ( z 1 = z 3z</p>
<p> f ( z ) z 1 . z3 ' 1 > 0 z - 0 f ( z0 ) = z 3 f ( z ) = z</p>
<p>3</p>
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<p>12</p>
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<p> 4 :. 61e . 21e</p>
<p>{z: z</p>
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