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Консультация № 187125
22.01.2013, 14:10
155.61 руб.
22.01.2013, 18:52
0
4
2
Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос:
1. Вычислить контурный интеграл от функции комплексной переменной с помощью вычетов:
,
С:|z|=2.
2. Найти частное решение дифференциального уравнения с заданными начальными условиями операторным методом
х'+2x=f(t); x(0)=0; функция f(t) задана графиком
.
1. Вычислить контурный интеграл от функции комплексной переменной с помощью вычетов:
С:|z|=2.
2. Найти частное решение дифференциального уравнения с заданными начальными условиями операторным методом
х'+2x=f(t); x(0)=0; функция f(t) задана графиком
Обсуждение
22.01.2013, 18:26
общий
Запишите, пожалуйста, выражение для функции из первого задания. На рисунке плохо видно.
Об авторе:
Facta loquuntur.
Facta loquuntur.
22.01.2013, 18:49
общий
22.01.2013, 18:53
Адресаты:
Я подправил изображения 
Об авторе:
"Если вы заметили, что вы на стороне большинства, —
это верный признак того, что пора меняться." Марк Твен
"Если вы заметили, что вы на стороне большинства, —
это верный признак того, что пора меняться." Марк Твен
22.01.2013, 20:43
общий
это ответ
Здравствуйте, Посетитель - 395932!
1.
Замкнутый контур С представляет собой окружность радиуса R=2 с центром в точке z=0.
Подынтегральная функция
имеет полюсы z=i и z=-i.
Эти точки находятся внутри контура С. Подсчитаем вычеты функции f(z) в указанных точках.
z=-i - простой полюс, поэтому вычет функции f(z) в этой точке
z=i - полюс третьего порядка, поэтому вычет функции f(z) в этой точке
Вычисляем интеграл:
1.
Замкнутый контур С представляет собой окружность радиуса R=2 с центром в точке z=0.
Подынтегральная функция
имеет полюсы z=i и z=-i.Эти точки находятся внутри контура С. Подсчитаем вычеты функции f(z) в указанных точках.
z=-i - простой полюс, поэтому вычет функции f(z) в этой точке
z=i - полюс третьего порядка, поэтому вычет функции f(z) в этой точке
Вычисляем интеграл:
22.01.2013, 22:49
общий
это ответ
Здравствуйте, Посетитель - 395932!
2. Пусть
Тогда 
Найдём изображение функции
с помощью теоремы запаздывания оригинала. Запишем функцию в виде
(Здесь
- единичная функция Хевисайда.) Тогда
Запишем теперь операторное уравнение:
откуда найдём
С уважением.
2. Пусть
Тогда Найдём изображение функции
с помощью теоремы запаздывания оригинала. Запишем функцию в виде(Здесь
- единичная функция Хевисайда.) ТогдаЗапишем теперь операторное уравнение:
откуда найдём
С уважением.
Об авторе:
Facta loquuntur.
Facta loquuntur.
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