2003/03/26 Chapter 6 1頁1頁 Chapter 6 : Residues & Their Use in Integration 6.1 Definition of the Residues.

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Presentation transcript:

2003/03/26 Chapter 6 1頁1頁 Chapter 6 : Residues & Their Use in Integration 6.1 Definition of the Residues

2003/03/26 Chapter 6 2頁2頁

2003/03/26 Chapter 6 3頁3頁

2003/03/26 Chapter 6 4頁4頁

2003/03/26 Chapter 6 5頁5頁 -

2003/03/26 Chapter 6 6頁6頁

2003/03/26 Chapter 6 7頁7頁

2003/03/26 Chapter 6 8頁8頁

2003/03/26 Chapter 6 9頁9頁

2003/03/26 Chapter 6 10 頁

2003/03/26 Chapter 6 11 頁 Proof Theorem 2:

2003/03/26 Chapter 6 12 頁 CvCv CLCL

2003/03/26 Chapter 6 13 頁 CnCn CnCn

2003/03/26 Chapter 6 14 頁

2003/03/26 Chapter 6 15 頁 6.2 Isolated Singularities

2003/03/26 Chapter 6 16 頁

2003/03/26 Chapter 6 17 頁

2003/03/26 Chapter 6 18 頁

2003/03/26 Chapter 6 19 頁

2003/03/26 Chapter 6 20 頁

2003/03/26 Chapter 6 21 頁

2003/03/26 Chapter 6 22 頁

2003/03/26 Chapter 6 23 頁 Z  Z0

2003/03/26 Chapter 6 24 頁

2003/03/26 Chapter 6 25 頁

2003/03/26 Chapter 6 26 頁

2003/03/26 Chapter 6 27 頁

2003/03/26 Chapter 6 28 頁

2003/03/26 Chapter 6 29 頁

2003/03/26 Chapter 6 30 頁

2003/03/26 Chapter 6 31 頁

2003/03/26 Chapter 6 32 頁

2003/03/26 Chapter 6 33 頁

2003/03/26 Chapter 6 34 頁 6.3 Finding the Residue

2003/03/26 Chapter 6 35 頁

2003/03/26 Chapter 6 36 頁

2003/03/26 Chapter 6 37 頁

2003/03/26 Chapter 6 38 頁

2003/03/26 Chapter 6 39 頁 z  z0

2003/03/26 Chapter 6 40 頁

2003/03/26 Chapter 6 41 頁

2003/03/26 Chapter 6 42 頁

2003/03/26 Chapter 6 43 頁

2003/03/26 Chapter 6 44 頁

2003/03/26 Chapter 6 45 頁

2003/03/26 Chapter 6 46 頁 z - 2

2003/03/26 Chapter 6 47 頁

2003/03/26 Chapter 6 48 頁

2003/03/26 Chapter 6 49 頁

2003/03/26 Chapter 6 50 頁

2003/03/26 Chapter 6 51 頁

2003/03/26 Chapter 6 52 頁 6.4 Evaluate Real Integral with Residue I

2003/03/26 Chapter 6 53 頁 = = -

2003/03/26 Chapter 6 54 頁

2003/03/26 Chapter 6 55 頁

2003/03/26 Chapter 6 56 頁

2003/03/26 Chapter 6 57 頁 6.5 Evaluate Real Integral with Residue II

2003/03/26 Chapter 6 58 頁

2003/03/26 Chapter 6 59 頁

2003/03/26 Chapter 6 60 頁

2003/03/26 Chapter 6 61 頁

2003/03/26 Chapter 6 62 頁

2003/03/26 Chapter 6 63 頁

2003/03/26 Chapter 6 64 頁 Proof Theorem 3:

2003/03/26 Chapter 6 65 頁

2003/03/26 Chapter 6 66 頁

2003/03/26 Chapter 6 67 頁

2003/03/26 Chapter 6 68 頁

2003/03/26 Chapter 6 69 頁

2003/03/26 Chapter 6 70 頁 6.6 Evaluate Real Integral with Residue III

2003/03/26 Chapter 6 71 頁

2003/03/26 Chapter 6 72 頁

2003/03/26 Chapter 6 73 頁

2003/03/26 Chapter 6 74 頁 C1 R 

2003/03/26 Chapter 6 75 頁 Proof Theorem 5:

2003/03/26 Chapter 6 76 頁

2003/03/26 Chapter 6 77 頁

2003/03/26 Chapter 6 78 頁

2003/03/26 Chapter 6 79 頁

2003/03/26 Chapter 6 80 頁

2003/03/26 Chapter 6 81 頁

2003/03/26 Chapter 6 82 頁 6.7 Integrals Involving Indented Contours

2003/03/26 Chapter 6 83 頁

2003/03/26 Chapter 6 84 頁 Proof Theorem 6:

2003/03/26 Chapter 6 85 頁

2003/03/26 Chapter 6 86 頁 Q. E. D.

2003/03/26 Chapter 6 87 頁

2003/03/26 Chapter 6 88 頁

2003/03/26 Chapter 6 89 頁

2003/03/26 Chapter 6 90 頁

2003/03/26 Chapter 6 91 頁

2003/03/26 Chapter 6 92 頁

2003/03/26 Chapter 6 93 頁

2003/03/26 Chapter 6 94 頁 6.8 Contour Integration with Branch Points & Cuts

2003/03/26 Chapter 6 95 頁

2003/03/26 Chapter 6 96 頁

2003/03/26 Chapter 6 97 頁

2003/03/26 Chapter 6 98 頁

2003/03/26 Chapter 6 99 頁

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