( english version )
Mathematical Analisys C ( 5 CFU )
Prof. Luca Lorenzi
     Tel. 0521.032207 - Fax. 0521.032350           E-mail. luca.lorenzi@unipr.it


Programma
Curves in two or three dimensions.
Parametrisation and representation; tangent and normal vectors; tangent hyperplanes; length of a curve; integral of a function on a curve.

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

Continuity and differentiability of functions of two or three variables.
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.

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

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





 
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