Кратные и Криволинейные интегралы Соболев (549100), страница 6
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М.: Дрофа, 2003.4. Мельников Д.А., Неклюдов А.В., Титов К.В. Криволинейные иповерхностные интегралы. Методические указания к выполнениютипового расчета. МГТУ, 2002.5. Соболев С. К., Ильичев А. Т. Исследование и построение плоскихкривых, заданных параметрически и в полярных координатах. – М.:Изд-во МГТУ им.
Н.Э. Баумана, 2004. – 80 с.С.К.Соболев. Криволинейные интегралы31СодержаниеВведение··················································································································21. Криволинейный интеграл первого рода·············· ······································31.1. Определение криволинейного интеграла первого рода·······························31.2. Свойства криволинейного интеграла первого рода······································41.3. Вычисление криволинейного интеграла первого рода·································51.4. Геометрические приложения криволинейного интеграла первого рода····61.5. Физические приложения криволинейного интеграла первого рода············71.6.
Криволинейный интеграл первого рода от векторной функции·················91.7. Примеры на вычисление и приложения криволинейного интегралапервого рода·····································································································92. Криволинейный интеграл второго рода (работа векторного полявдоль ориентированного пути). ··································································112.1 Определение криволинейного интеграла второго рода·······························112.2. Свойства криволинейного интеграла второго рода····································132.3.
Вычисление криволинейного интеграла второго рода·······························143. Формула Грина································································································163.1. Предварительные определения·····································································163.2.
Теорема Грина································································································173.3. Приложения формулы Грина·······································································184. Потенциальные и безвихревые поля на плоскости· ································214.1. Основные определения··················································································214.2. Свойства плоских потенциальных и безвихревых полей···························234.3. Нахождение потенциала и вычисление работы плоскогопотенциального поля······················································································244.4. Вычисление циркуляции плоского безвихревого поляв многосвязной области················································································27Ответы к упражнениям ····················································································29Контрольные вопросы ·······················································································29Литература ··········································································································30Содержание ··········································································································31.
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