Università Roma Tre

Differential equations with separable variables. Linear differential equations of first order, homogeneous and non homogeneous. Linear equations of any order with constant coefficients, homogeneous and non-homogeneous. Method of indefinite parameters. Wronskian matrix and method of constants' variation. Special cases of linear differential equations with variable coefficients: Euler equation, lowering order.

Summaries of analytical geometry, in the plane and in the space. Implicit, explicit and parametric equations. Straight lines in the plane. Bundle. Conic sections. Planes in space. Ruled surfaces. Cones and cylinders. Rotation surfaces. Quadrics.

Notes on Peano-Jordan measurement theory. Integral of functions of several variables on compact sets. Normal domains of the plane. Reducing formula for double integers. Normal domains in Space. Reducing formula for triple integrals. Changes of variables. Integrals' applications: mass, center of gravity, moment of inertia.
Regular curves. Length of a curve arc. Abscissa on a curve. Line integral of a scalar function and applications. Line integral of a vector field. Conservative fields. Necessary and sufficient conditions for conservativity. Green's theorem in the plane.
Regular surfaces. Area of ​​a regular surface. Surface integral of a scalar function and applications. Surface integrale of a vector field. Rotor of a vector field. Stokes' theorem. Divergence of a vector field. Green's theorem in the space.

B. Palumbo: Integrali di funzioni di più variabili (II edition). Accademica, Roma, 2009.
Notes by the teacher (distributed on web).