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Консультация № 186093
18.05.2012, 19:38
102.44 руб.
0
13
2
Здравствуйте! Помогите пожалуйста
Буду очень благодарен, помогите пожалуйста.
Буду очень благодарен, помогите пожалуйста.
Обсуждение
18.05.2012, 19:52
общий
это ответ
Здравствуйте, Иван Васильевич Митяев!
1. a)
Внутри контура интегрирования функция голоморфна везде, кроме нуля. Поэтому интеграл равен
, умноженный на вычет в нуле. Вычет равен коэффициенту при (-1) степени в ряде Лорана в нуле.
.
Значит интеграл равен
.
1. a)
Внутри контура интегрирования функция голоморфна везде, кроме нуля. Поэтому интеграл равен
, умноженный на вычет в нуле. Вычет равен коэффициенту при (-1) степени в ряде Лорана в нуле..Значит интеграл равен
.
19.05.2012, 14:36
общий
это ответ
Здравствуйте, Иван Васильевич!
1б) Изобразим контур интегрирования на комплексной плоскости. Он является окружностью с центром z0 = 2 и радиусом 1 (рисунок).
Особые точки z1 = 0 и z2 = -2 внутрь контура интегрирования не попадают. Поэтому, согласно теореме Коши,
С уважением.
1б) Изобразим контур интегрирования на комплексной плоскости. Он является окружностью с центром z0 = 2 и радиусом 1 (рисунок).
Особые точки z1 = 0 и z2 = -2 внутрь контура интегрирования не попадают. Поэтому, согласно теореме Коши,
С уважением.
5
Об авторе:
Facta loquuntur.
Facta loquuntur.
Неизвестный
29.05.2012, 23:57
общий
Ну хотя бы какие формулы, просто преподавателя не устраивает ответ, требует больше расписать (
30.05.2012, 00:08
общий
Ну, есть такая теорема (Коши): если функция голоморфна в области, за исключением конечного числа изолированных особых точек, причём граница гладкая и особых точек не содержит, то интеграл по границе - 2 pi i * сумму вычетов в этих особых точках. Есть другая теорема: вычет в особой точке равен коэффициенту при (-1) степени в разложении в ряд Лорана. Вот мы и раскладываем функцию в ряд.
Неизвестный
30.05.2012, 00:13
общий
А вы можете раписать как вы получили ответ 
Тоесть действия расписать
Тоесть действия расписать
30.05.2012, 00:17
общий
Коэффициент при члене (-1) степени оказался 1/4. Это значение вычета. Интеграл - 2 pi i * сумму вычетов. Вычет тут один ои он равен 1/4. Вот и получается.
Неизвестный
30.05.2012, 00:31
общий
это спасибо, но все что мне нужно, это продлить решение вот этого:
просто к этому преподаватель придерается, говорит как получился ответ
просто к этому преподаватель придерается, говорит как получился ответ
.
Неизвестный
30.05.2012, 00:53
общий
Эх, если бы я понимал к чему =( Вроде все так и записано а все что то не нравится, ладно, спасибо огромное за помощь!!!)
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