ml note math fggfdgdfgf

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Calculus/ˈkælkjələs/ (n) the type of mathematics that deals with rates of change, for example in the slope of a curve or the speed of a falling object Phép tính Derivative/dɪˈrɪvətɪv/ (n) a word or thing that has been developed or produced from another word or thing Đạo hàm Total Derivative Tg = Đối/Kề or detal Y / detal X Partial Derivative Why we need it: When a function depends one or more variables (For previous total derivative, a function only depends on one variable) How we calculate it: Consider other variables as constants, like fix the surface and make it come back to the function which depends one one variable only df/dx Scalar/ˈskeɪlər/a quantity that has size but no direction Đại lượng vô hướng Tensor/ˈtensɔːr/ One answer: In a given basis, a rank zero tensor is a scalar, one number A rank one tensor is a vector, n numbers (in n dimensions.) A rank tensor is an nxn matrix of numbers A rank tensor would be a cube of numbers, and so on Another view: a rank tensor is an object that takes two vectors as input and outputs a number, and which is linear in each input Einstein used the Riemann tensor which takes vectors as inputs and outputs a number Roughly speaking, that one says, “If in curved space I carry a vector and go in direction v1, and then direction v2, and then I come back with -v1 and then -v2, what is the component in the v3 direction of the change in the vector v4?” The technical definition is that a tensor is a set of numbers that “transforms as a tensor” under a coordinate transformation In short, tensors are linear transformations, the objects we study in linear algebra
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