3 семестр ЭКТ / Учебники и методички / Криволинейные интегралы - МГТУ им. Н. Э. Баумана

С.К.Соболев. Криволинейные интегралы

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Содержание

Введение··················································································································2

1.Криволинейный интеграл первого рода·············· ······································3

1.1.Определение криволинейного интеграла первого рода·······························3

1.2.Свойства криволинейного интеграла первого рода······································4

1.3.Вычисление криволинейного интеграла первого рода·································5

1.4.Геометрические приложения криволинейного интеграла первого рода····6

1.5.Физические приложения криволинейного интеграла первого рода············7

1.6.Криволинейный интеграл первого рода от векторной функции·················9

1.7.Примеры на вычисление и приложения криволинейного интеграла первого рода·····································································································9

2.Криволинейный интеграл второго рода (работа векторного поля вдоль ориентированного пути). ··································································11

2.1 Определение криволинейного интеграла второго рода·······························11

2.2.Свойства криволинейного интеграла второго рода····································13

2.3.Вычисление криволинейного интеграла второго рода·······························14 3. Формула Грина································································································16

3.1.Предварительные определения·····································································16

3.2.Теорема Грина································································································17

3.3.Приложения формулы Грина·······································································18

4. Потенциальные и безвихревые поля на плоскости· ································21

4.1.Основные определения··················································································21

4.2.Свойства плоских потенциальных и безвихревых полей···························23

4.3.Нахождение потенциала и вычисление работы плоского потенциального поля······················································································24

4.4.Вычисление циркуляции плоского безвихревого поля

вмногосвязной области················································································27 Ответы к упражнениям ····················································································29 Контрольные вопросы ·······················································································29 Литература ··········································································································30 Содержание ··········································································································31