Prerequisites
Knowledge of Analisi Matematica AB
Course unit content
<p>Curves in two or three dimensions. <br />
Parametrisation and representation; tangent and normal vectors; tangent hyperplanes; length of a curve; integral of a function on a curve. <br />
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Functions in two variables <br />
Graph, sections, level sets; paraboloids, cones, spherical and elliptic surfaces. Functions depending on one variable and radial functions. <br />
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Continuity and differentiability of functions of two or three variables. <br />
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. <br />
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Ordinary differential equations. <br />
Linear differential equations of the first order, linear differential equations of higher order with constant coefficients; Cauchy problems. <br />
<br />
Integral calculus of functions of two or three variables. <br />
Multiple integrals over normal domains in two or three dimensions. Change of variables formula. Polar, spherical and cylindrical coordinates. <br />
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Vector fields. <br />
Central fields. Integration of fields; conservative and curl-free fields. <br />
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Bibliography
M. Belloni, L. Lorenzi: Calcolo differenziale ed integrale per funzioni di piu' variabili. Complementi ed esercizi. Pitagore Editrice, Bologna 2008
