Università Roma Tre

1- Symmetric bilinear forms. Lengths, angles, orthogonality. Orthogonal and orthonormal bases. Gram-Schmidt algorithm.
2- Quadratic forms. Spectral Theorem. Diagonalization and classification of quadratic forms in a Euclidean space. Sylvester bases and Sylvester canonical form. Vectorial product in a euclidean space of dimension three.
3- Analytic geometry in the plane and in space. Cartesian and parametric equations of linear spaces. Proper and improper sheaves of lines and planes.
Determination of recyprocal position of linear varieties from their equations.
4- Parametrised curves. Regular curves. Rectifiability and length. Curvilinear parameter. Orthonormal mobile basis. Curvatere, torsion, curvature ray and obsculating plane. Frenet formulas.
5- Functions of several real variables and their graphs. Elements of the topology of R^n. Continuity, partial derivatives, differentiability. Gradient and directional derivatives.
6- Higher order derivatives and Schwarz Theorem, Hessian matrix and its interpretation.
7-Vector valued functions of several real variables..
8-Differential equations.

F. Flamini; A. Verra: "Matrici e vettori -Corso di base di geometria e algebra lineare" Carocci ed.
Notes from the lectures