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Консультация № 176887
24.02.2010, 01:46
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Помогите пожалуйста. Можете объяснить(как человеку с интелектом=школьному) мне тему по дифференциальным уравнения. Название темы "Виды положения равновесия на плоскости".
Мне нужно понять на основе системы x'=ax+by y'=cx+dy почему она имеет: устойчивый узел, неустойчивый узел, центр, седло, устойчивый фокус, неустойчивый фокус. Т.е. мне нужно будет рассказать что такое устойчивый узел, центр, ... и показать, почему система x'=ax+by y'=cx+dy имеет все эти виды положения.
П.с. если можно, хотелось бы поподробней с объяснением на графиках.
Мне нужно понять на основе системы x'=ax+by y'=cx+dy почему она имеет: устойчивый узел, неустойчивый узел, центр, седло, устойчивый фокус, неустойчивый фокус. Т.е. мне нужно будет рассказать что такое устойчивый узел, центр, ... и показать, почему система x'=ax+by y'=cx+dy имеет все эти виды положения.
П.с. если можно, хотелось бы поподробней с объяснением на графиках.
Обсуждение
24.02.2010, 11:41
общий
Azarov88:
Чтобы понять тему "Дифференциальные уравнения", нужно вначале изучить математический анализ и линейную алгебру. Школьных знаний явно недостаточно.
Чтобы понять тему "Дифференциальные уравнения", нужно вначале изучить математический анализ и линейную алгебру. Школьных знаний явно недостаточно.
Неизвестный
24.02.2010, 19:15
общий
Присоединяюсь к словам Гаряки Асмик. Для изучения могу посоветовать книгу Е.П. Попов Теория нелинейных систем автоматического регулирования.
Книга посвящена, главным образом, техническим вопросам теории управления. Однако прочитайте хотя бы первую главу. Потом, может быть сформулируете свои вопросы более корректно. Удачи.
Книга посвящена, главным образом, техническим вопросам теории управления. Однако прочитайте хотя бы первую главу. Потом, может быть сформулируете свои вопросы более корректно. Удачи.
24.02.2010, 22:09
общий
Azarov88:
Можно дать 1(один) ответик: система x'=ax+by y'=cx+dy "имеет все эти виды положения", потому что это просто общий вид линейной системы 2-го порядка. Вернее сказать, что она может иметь это всё -- при соответствующих значениях коэфиициентов.
А в остальном то, что вы написали -- не задача, на которую можно дать решение. Тут надо разговаривать.
Можно дать 1(один) ответик: система x'=ax+by y'=cx+dy "имеет все эти виды положения", потому что это просто общий вид линейной системы 2-го порядка. Вернее сказать, что она может иметь это всё -- при соответствующих значениях коэфиициентов.
А в остальном то, что вы написали -- не задача, на которую можно дать решение. Тут надо разговаривать.
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