У нас вы можете посмотреть бесплатно Manifolds #6 - Tangent Space (Detail) или скачать в максимальном доступном качестве, которое было загружено на ютуб. Для скачивания выберите вариант из формы ниже:
Если кнопки скачивания не
загрузились
НАЖМИТЕ ЗДЕСЬ или обновите страницу
Если возникают проблемы со скачиванием, пожалуйста напишите в поддержку по адресу внизу
страницы.
Спасибо за использование сервиса ClipSaver.ru
Notes are on my GitHub! github.com/rorg314/WHYBmaths In this video I discuss the tangent space in a bit more detail. I introduce the concept of a differential operator known as the directional derivative, which acts on a function to give the tangent vector at a particular point. The algebraic structure generated by the set of all such possible directional derivatives forms a vector space (not proven although it is intuitively clear, derivatives act linearly on functions) and this vector space is identified as the tangent space at the point p. I then explain how we use the chart map to obtain an expression for the vector in terms of it's components, with respect to a particular 'coordinate basis'. I briefly allude to the notion of integral curves, which generate the vector (to be discussed in detail in future videos!) but for now we simply view these as specifying the direction along which the derivative should be taken (tangent to the corresponding curve).