( english version )

Mathematical analysis C ( 5 CFU ) Tel. 0521.906954 - Fax. 0521.906950 E-mail. marino.belloni@unipr.it Home page. http://www2.unipr.it/~belmar68/

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.

Central fields. Integration of fields; conservative and curl-free fields.