SlideShare a Scribd company logo
𝐶
𝑑𝑧
𝑧 − 1
=
0
2𝜋
𝑖𝑒 𝑖𝜃
𝑑𝜃
𝑒 𝑖𝜃-1
= log 𝑒 𝑒 𝑖𝜃
− 1 0
2𝜋
= 発散
𝐶: 𝑧 = 1 ⇔ 𝑧 = 𝑒 𝑖𝜃 (0 ≤ 𝜃 < 2𝜋)
𝑑𝑧
𝑑𝜃
= 𝑖𝑒 𝑖𝜃
∴ 𝑑𝑧 = 𝑖𝑒 𝑖𝜃
𝑑𝜃
2015/04/29 Hanpen Robot 改訂版 𝑧 = 1 + 𝑒 𝑖𝜃
を𝑧 = 𝑒 𝑖𝜃
に修正して計算

More Related Content

Viewers also liked

anchorRTP_resume_Davis-B
anchorRTP_resume_Davis-BanchorRTP_resume_Davis-B
anchorRTP_resume_Davis-BBrandon Davis
 
Avaliação de software educativo
Avaliação de software educativoAvaliação de software educativo
Avaliação de software educativo
Fabiulacdill
 
Heidegger, martin la frase de nietzsche dios ha muerto
Heidegger, martin   la frase de nietzsche dios ha muertoHeidegger, martin   la frase de nietzsche dios ha muerto
Heidegger, martin la frase de nietzsche dios ha muertoanthrolopithecus
 
Gallery assistant perfomance appraisal 2
Gallery assistant perfomance appraisal 2Gallery assistant perfomance appraisal 2
Gallery assistant perfomance appraisal 2tonychoper2104
 
Hr admin assistant perfomance appraisal 2
Hr admin assistant perfomance appraisal 2Hr admin assistant perfomance appraisal 2
Hr admin assistant perfomance appraisal 2tonychoper2104
 
Glosario de comunicacion interactiva
Glosario de comunicacion interactivaGlosario de comunicacion interactiva
Glosario de comunicacion interactiva
nacho_col
 
Disliexia
DisliexiaDisliexia
Disliexia
mnnmd
 
Vinculación de la estrategia y de la estructura organizativa con los sistema ...
Vinculación de la estrategia y de la estructura organizativa con los sistema ...Vinculación de la estrategia y de la estructura organizativa con los sistema ...
Vinculación de la estrategia y de la estructura organizativa con los sistema ...
Jesús Rangel
 
Taller de alfabetización científica 11 de marzo 2015
Taller de alfabetización científica 11 de marzo 2015Taller de alfabetización científica 11 de marzo 2015
Taller de alfabetización científica 11 de marzo 2015Marcela Alejandra Lisowyj
 
April 28 (101A)
April 28 (101A)April 28 (101A)
April 28 (101A)
MelissaJLong
 
Gap sales associate perfomance appraisal 2
Gap sales associate perfomance appraisal 2Gap sales associate perfomance appraisal 2
Gap sales associate perfomance appraisal 2tonychoper2104
 
ICT Megatrend and Project based learning
ICT Megatrend and Project based learningICT Megatrend and Project based learning
ICT Megatrend and Project based learning
Barlin Kesuma
 
Pandya and vijaynagara
Pandya and vijaynagaraPandya and vijaynagara
Pandya and vijaynagara
Nalini Badola
 
Personal branding - CV van de Toekomst
Personal branding - CV van de ToekomstPersonal branding - CV van de Toekomst
Personal branding - CV van de Toekomst
Tom Scholte
 
An Incomplete Guide to Open Graph metatags for Facebook
An Incomplete Guide to Open Graph metatags for FacebookAn Incomplete Guide to Open Graph metatags for Facebook
An Incomplete Guide to Open Graph metatags for Facebook
Mat Morrison
 
Cybercriminals Are Lurking
Cybercriminals Are LurkingCybercriminals Are Lurking
Cybercriminals Are Lurking
Charlie Lewis M.S.
 

Viewers also liked (18)

anchorRTP_resume_Davis-B
anchorRTP_resume_Davis-BanchorRTP_resume_Davis-B
anchorRTP_resume_Davis-B
 
Avaliação de software educativo
Avaliação de software educativoAvaliação de software educativo
Avaliação de software educativo
 
Heidegger, martin la frase de nietzsche dios ha muerto
Heidegger, martin   la frase de nietzsche dios ha muertoHeidegger, martin   la frase de nietzsche dios ha muerto
Heidegger, martin la frase de nietzsche dios ha muerto
 
Gallery assistant perfomance appraisal 2
Gallery assistant perfomance appraisal 2Gallery assistant perfomance appraisal 2
Gallery assistant perfomance appraisal 2
 
Famous
FamousFamous
Famous
 
Hr admin assistant perfomance appraisal 2
Hr admin assistant perfomance appraisal 2Hr admin assistant perfomance appraisal 2
Hr admin assistant perfomance appraisal 2
 
Glosario de comunicacion interactiva
Glosario de comunicacion interactivaGlosario de comunicacion interactiva
Glosario de comunicacion interactiva
 
Disliexia
DisliexiaDisliexia
Disliexia
 
Vinculación de la estrategia y de la estructura organizativa con los sistema ...
Vinculación de la estrategia y de la estructura organizativa con los sistema ...Vinculación de la estrategia y de la estructura organizativa con los sistema ...
Vinculación de la estrategia y de la estructura organizativa con los sistema ...
 
Taller de alfabetización científica 11 de marzo 2015
Taller de alfabetización científica 11 de marzo 2015Taller de alfabetización científica 11 de marzo 2015
Taller de alfabetización científica 11 de marzo 2015
 
April 28 (101A)
April 28 (101A)April 28 (101A)
April 28 (101A)
 
Gap sales associate perfomance appraisal 2
Gap sales associate perfomance appraisal 2Gap sales associate perfomance appraisal 2
Gap sales associate perfomance appraisal 2
 
ICT Megatrend and Project based learning
ICT Megatrend and Project based learningICT Megatrend and Project based learning
ICT Megatrend and Project based learning
 
Pandya and vijaynagara
Pandya and vijaynagaraPandya and vijaynagara
Pandya and vijaynagara
 
Personal branding - CV van de Toekomst
Personal branding - CV van de ToekomstPersonal branding - CV van de Toekomst
Personal branding - CV van de Toekomst
 
An Incomplete Guide to Open Graph metatags for Facebook
An Incomplete Guide to Open Graph metatags for FacebookAn Incomplete Guide to Open Graph metatags for Facebook
An Incomplete Guide to Open Graph metatags for Facebook
 
Cybercriminals Are Lurking
Cybercriminals Are LurkingCybercriminals Are Lurking
Cybercriminals Are Lurking
 
Iiq clase 4
Iiq clase 4Iiq clase 4
Iiq clase 4
 

More from HanpenRobot

fermat's little theorem and …
fermat's little theorem and …fermat's little theorem and …
fermat's little theorem and …
HanpenRobot
 
Campbell hasudorff formula
Campbell hasudorff formulaCampbell hasudorff formula
Campbell hasudorff formula
HanpenRobot
 
構造定数が随伴表現になることの証明
構造定数が随伴表現になることの証明構造定数が随伴表現になることの証明
構造定数が随伴表現になることの証明
HanpenRobot
 
Log complex
Log complexLog complex
Log complex
HanpenRobot
 
代数幾何memo_2020March30_1337
代数幾何memo_2020March30_1337代数幾何memo_2020March30_1337
代数幾何memo_2020March30_1337
HanpenRobot
 
金利スワップのメモ
金利スワップのメモ金利スワップのメモ
金利スワップのメモ
HanpenRobot
 
Conditional expectation projection 2018 feb 18
Conditional expectation projection 2018 feb 18 Conditional expectation projection 2018 feb 18
Conditional expectation projection 2018 feb 18
HanpenRobot
 
集合の上極限,下極限
集合の上極限,下極限集合の上極限,下極限
集合の上極限,下極限
HanpenRobot
 
確率微分方程式の基礎
確率微分方程式の基礎 確率微分方程式の基礎
確率微分方程式の基礎
HanpenRobot
 
Noether環上の有限生成加群の有限表示
Noether環上の有限生成加群の有限表示Noether環上の有限生成加群の有限表示
Noether環上の有限生成加群の有限表示
HanpenRobot
 
微分演算子と多項式の剰余環の関係 2016 october 12
微分演算子と多項式の剰余環の関係 2016 october 12微分演算子と多項式の剰余環の関係 2016 october 12
微分演算子と多項式の剰余環の関係 2016 october 12
HanpenRobot
 
位相空間の開集合の成す圏 2016 august 30
位相空間の開集合の成す圏 2016 august 30位相空間の開集合の成す圏 2016 august 30
位相空間の開集合の成す圏 2016 august 30
HanpenRobot
 
Fourier transform on real-valued function over symmetric group
Fourier transform on real-valued function over symmetric groupFourier transform on real-valued function over symmetric group
Fourier transform on real-valued function over symmetric group
HanpenRobot
 
置換族の一様分布
置換族の一様分布置換族の一様分布
置換族の一様分布
HanpenRobot
 
Duality of laplace transform
Duality of laplace transformDuality of laplace transform
Duality of laplace transform
HanpenRobot
 
Fourier analysis on symmetric group
Fourier analysis on symmetric groupFourier analysis on symmetric group
Fourier analysis on symmetric group
HanpenRobot
 
Conjugate cyclic permutation
Conjugate cyclic permutationConjugate cyclic permutation
Conjugate cyclic permutation
HanpenRobot
 
ベイズ識別 一般化逆行列
ベイズ識別 一般化逆行列ベイズ識別 一般化逆行列
ベイズ識別 一般化逆行列
HanpenRobot
 
電子光波Memo
電子光波Memo電子光波Memo
電子光波Memo
HanpenRobot
 
Minimize quadratic form
Minimize quadratic formMinimize quadratic form
Minimize quadratic form
HanpenRobot
 

More from HanpenRobot (20)

fermat's little theorem and …
fermat's little theorem and …fermat's little theorem and …
fermat's little theorem and …
 
Campbell hasudorff formula
Campbell hasudorff formulaCampbell hasudorff formula
Campbell hasudorff formula
 
構造定数が随伴表現になることの証明
構造定数が随伴表現になることの証明構造定数が随伴表現になることの証明
構造定数が随伴表現になることの証明
 
Log complex
Log complexLog complex
Log complex
 
代数幾何memo_2020March30_1337
代数幾何memo_2020March30_1337代数幾何memo_2020March30_1337
代数幾何memo_2020March30_1337
 
金利スワップのメモ
金利スワップのメモ金利スワップのメモ
金利スワップのメモ
 
Conditional expectation projection 2018 feb 18
Conditional expectation projection 2018 feb 18 Conditional expectation projection 2018 feb 18
Conditional expectation projection 2018 feb 18
 
集合の上極限,下極限
集合の上極限,下極限集合の上極限,下極限
集合の上極限,下極限
 
確率微分方程式の基礎
確率微分方程式の基礎 確率微分方程式の基礎
確率微分方程式の基礎
 
Noether環上の有限生成加群の有限表示
Noether環上の有限生成加群の有限表示Noether環上の有限生成加群の有限表示
Noether環上の有限生成加群の有限表示
 
微分演算子と多項式の剰余環の関係 2016 october 12
微分演算子と多項式の剰余環の関係 2016 october 12微分演算子と多項式の剰余環の関係 2016 october 12
微分演算子と多項式の剰余環の関係 2016 october 12
 
位相空間の開集合の成す圏 2016 august 30
位相空間の開集合の成す圏 2016 august 30位相空間の開集合の成す圏 2016 august 30
位相空間の開集合の成す圏 2016 august 30
 
Fourier transform on real-valued function over symmetric group
Fourier transform on real-valued function over symmetric groupFourier transform on real-valued function over symmetric group
Fourier transform on real-valued function over symmetric group
 
置換族の一様分布
置換族の一様分布置換族の一様分布
置換族の一様分布
 
Duality of laplace transform
Duality of laplace transformDuality of laplace transform
Duality of laplace transform
 
Fourier analysis on symmetric group
Fourier analysis on symmetric groupFourier analysis on symmetric group
Fourier analysis on symmetric group
 
Conjugate cyclic permutation
Conjugate cyclic permutationConjugate cyclic permutation
Conjugate cyclic permutation
 
ベイズ識別 一般化逆行列
ベイズ識別 一般化逆行列ベイズ識別 一般化逆行列
ベイズ識別 一般化逆行列
 
電子光波Memo
電子光波Memo電子光波Memo
電子光波Memo
 
Minimize quadratic form
Minimize quadratic formMinimize quadratic form
Minimize quadratic form
 

Complex line integral (fixed)

  • 1. 𝐶 𝑑𝑧 𝑧 − 1 = 0 2𝜋 𝑖𝑒 𝑖𝜃 𝑑𝜃 𝑒 𝑖𝜃-1 = log 𝑒 𝑒 𝑖𝜃 − 1 0 2𝜋 = 発散 𝐶: 𝑧 = 1 ⇔ 𝑧 = 𝑒 𝑖𝜃 (0 ≤ 𝜃 < 2𝜋) 𝑑𝑧 𝑑𝜃 = 𝑖𝑒 𝑖𝜃 ∴ 𝑑𝑧 = 𝑖𝑒 𝑖𝜃 𝑑𝜃 2015/04/29 Hanpen Robot 改訂版 𝑧 = 1 + 𝑒 𝑖𝜃 を𝑧 = 𝑒 𝑖𝜃 に修正して計算