I Section (4 credits):
Complex numbers: trigonometric form, natural and rational powers, roots. Exponential in the complex field. Linear algebra: vectors, matrices, vectorial spaces, bases, change of ba¬sis. Rank and determinant. The inverse for a non singular matrix. Inner product. Orthonormal bases. Linear applications and linear systems: Kernel and Image. Sylvester, Cramer and Rouchè-Capelli theorems. Eigenvalues and eigenvectors, characteristic polynomial. Eigenvalues and eigenvectors properties. Simmetric matrices and their properties. Similarity. Reduction to triangular and diagonal form, diagonalizable matrices.
II Section (4 credits):
Functions of vectorial variables: limits, continuity, differential calculus: differentiable functions and differentiability, partial and diretional derivatives, total differentials. Taylor’s polynomial. The chain rule. Implicit functions, Dini’s theorem. Maximization and minimization without constraints. Maximization and minimization with equality constrains. Lagrange multipliers. First and second order conditions, quadratic forms. Maximization with inequality constrains: Kuhn-Tucker’s conditions.