Demidovich for Highschool
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Б . П . Демидович СБОРНИК ЗАДАЧ И УПРАЖНЕНИЙ ПО МАТЕМАТИЧЕСКОМУ АНАЛИЗУ В сборник (11-е изд. — 1995 г.) включено свыше 4000 задач и упражнений по важнейшим разделам математического анализа: введение в анализ: дифференциальное исчисление функций одной переменной; неопределенный и определенный интегралы; ряды; дифференциальное исчисление функций нескольких переменных; интегралы, зависящие от параметра; кратные и криволинейные интегралы. Почти ко всем задачам даны ответы. В приложении помешены таблицы. Для студентов физических и механико-математических специальностей высших учебных заведений. ЧАСТЬ ПЕРВАЯ. ФУНКЦИИ ОДНОЙ НЕЗАВИСИМОЙ ПЕРЕМЕННОЙ Отдел I. Введение в анализ 7 1. Вещественные числа 7 2. Теория последовательностей 12 3. Понятие функции 26 4. Графическое изображение функции 35 5. Предел функции 47 6. O-символика 72 7. Непрерывность функции 77 8. Обратная функция. Функции, заданные параметрически 87 9. Равномерная непрерывность функции 90 10. Функциональные уравнения 94 Отдел II. Дифференциальное исчисление функций одной переменной 96 1. Производная явной функции 96 2. Производная обратной функции . Производная функции, заданной параметрически. Производная функции, заданной в неявном виде 114 3. Геометрический смысл производной 117 4. Дифференциал функции 120 5. Производные и дифференциалы высших порядков 124 6. Теоремы Ролля, Лагранжа и Коши 134 7. Возрастание и убывание функции. Неравенства 140 8. Направление вогнутости. Точки перегиба 144 9. Раскрытие неопределенностей 147 10. Формула Тейлора 151
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