Elliptic Curves: Singular Points and Group Law

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Introduces gradient, Laplacian, Taylor formula, polynomial approximations, extrema, and Taylor series expansions in multiple variables.

Covers derivatives and continuity in multivariable functions, emphasizing the importance of partial derivatives.

Explores differentiability in analysis, discussing conditions for functions to be differentiable and continuous.

Covers derivable functions, partial derivatives, Jacobian matrix, and rule of composition.

Covers the calculation of partial derivatives of order 3 and the concept of differentiability in functions.

Presents the solution to finding the second-order Taylor polynomial of a function.

Explains partial derivatives, generalization, and second order derivatives with examples and mathematical notations.

Introduces the gradient concept and the Theorem of Mean Value for functions in several variables.

Covers partial derivatives, differentiability, differential equations, sets properties, and local extrema verification.

Covers differentiability, composition of functions, partial derivatives, Jacobian matrix, and polar coordinates.