Elliptic Curves: Singular Points and Group Law

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

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

Covers the topology of Riemann surfaces, focusing on orientation and orientability.

Covers differential calculus applications and reminders, emphasizing the importance of differentiability in mathematical analysis.

Explains partial and directional derivatives, and functions' derivability.

Explores canonical transformations, the Hamilton-Jacobi equation, symplectic groups, and differential equations in physics.

Explores the Cayley-Bacharach theorem in incidence geometry and introduces elliptic curves with a commutative law.

Explores partial derivatives and functions in multivariable calculus, emphasizing their importance and practical applications.

Explains partial derivatives, Hessienne matrix, and their properties.

Explores functions of class C^p, emphasizing continuity and differentiability properties.

Covers derivatives, differentiability, and tangent planes for functions of one and two variables.

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Explores partial derivatives and derivability of functions, emphasizing geometric interpretations and avoiding common pitfalls.

Covers differentiability of functions in two variables and the conditions for a function to be differentiable.

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

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