## Syllabus

### Updated A.Y. 2016-2017

Mathematics 2

prof. Annalisa Fabretti

Academic year 2016-2017

Linear Algebra

- Matrices. Matrix algebra, Determinant, Trace, Rank, Inverse Matrix, Eigenvalues and eigenvectors.

- Linear Spaces. The algebra of vectors, Euclidean Spaces, Inner product, Linear independence.

- Systems of Linear equations. Cramer’s Theorem, Cramer’s rule, Rouche Capelli theorem.

Calculus

- Integral Calculus. Definite and indefinite integrals, Integral properties, The fundamental theorem of calculus, Integration by parts and integration by substitution, Improper integrals.

Optimization

- Calculus of several variables. Domain, Partial derivatives, gradient, hessian matrix. Stationary points. Countour curves.

- Unconstrained optimization. First and second order conditions

- Constrained optimization with Equality constraints. First and second order conditions