Differential calculus 3

Back to differentiable functions: partial derivatives, differentiable function, differential of a function at a point, C1 class functions, Schwarz Theorem, Jacobian, solving partial differential equations with change of variable
Extrema: local extrema, global extrema, necessary condition for the existence of a local extremum on an open, Taylor's formula of order 2, Hessian matrix, link with the existence of a local extremum
Differential forms: differential form, exact differential form, closed differential forms (on an open, an exact differential form is closed), starry open, Poincaré's theorem, curvilinear integral.