Financial mathematics - 3 - lezione (2008/2009)

Learning outcomes

This module of the course provides the mathematical tools to analyze the economic and financial models presented in the subsequent two year of Laurea magistrale. It is focused on some advanced topics in linear algebra and it provides a fairly wide overview on the main theoretical results and operative techniques in both unconstrained and constrained optimization. Students are encouraged to attend this course after having obtained a positive grade in Mathematics.

1. Functions of more than one variable
Metric and topology in R^n. Functions of more than one variable: domain, graphic, level sets, limits and continuity. Partial derivatives. Differentiability, continuity and tangent subspace. Calculus of derivatives. Directional derivatives and gradient. Vector valued functions. Jacobian matrix.

2. Linear algebra
Linearly dependent and independent vectors. Basis and dimension of a linear space. Orthogoonal vectors, orthogonal projections, orthonormal basis. Linear transformations and matrices. Kernel and rank of a linear transformation. Change of basis. Similar matrices. Decomposizione di un’applicazione lineare: autovettori e autovalori. Diagonalizzazione di una matrice.

The final examination consists of a written test and an oral test. The access to the oral test is conditional of a positive outcome on the written test.