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Mathematical Analisys C ( 5 CFU ) Programma

Parametrisation and representation; tangent and normal vectors; tangent hyperplanes; length of a curve; integral of a function on a curve.

Graph, sections, level sets; paraboloids, cones, spherical and elliptic surfaces. Functions depending on one variable and radial functions.

Elements of topology; limits, continuity, Weierstrass theorem. Differentiability and partial derivatives, directional derivatives, gradient vector, steepest ascent, estremal points; extremal points on a curve; constrained extrema. Vector valued functions and Jacobian matrix.

Linear differential equations of the first order, linear differential equations of higher order with constant coefficients; Cauchy problems.

Multiple integrals over normal domains in two or three dimensions. Change of variables formula. Polar, spherical and cylindrical coordinates.