Student guide Faculty of Economics A.Y. 2007/08

Mathematics for Economics and Finance 2
Aim of the course
The first part of the course covers material which completes and expands upon the differential calculus studied in Mathematics for Economics and Finance 1. Particular attention is given to linear algebra and to functions of many real variables. The presentation of the theory is backed up by examples of applications to economic and management problems.
Picking up on the fundamental ideas of financial calculus introduced in Mathematics for Economics and Finance 1, the second part of the course then covers the mathematical tools necessary for constructing and valuing certain financial contracts which frequently recur in business management.
The first part of the course focuses mainly on the theory and methods, while the second part deals more directly with the professional applications.
1.  Linear algebra. Vectors and matrices. Vector operations, linear combinations, linear dependence. Subspace, basis and dimension. Operations between matrices, determinant, inverse matrix, rank. Linear systems and linear functions. Discussion and resolution of a linear system: Rouché-Capelli theorem, Cramer's theorem. Homogeneous systems and structure of solutions. Linear functions, representation theorem. Leontiev model.
2.  Functions in many variables: differential calculus, constrained and unconstrained extrema; typical business applications in finance, marketing, and logistics.
Second part
1.  Financial calculus: compounding, discounting, different regimes and types of rates, financial laws in one and two variables.
2.  Discounted cash-flow: net present value of a financial transaction and internal rate of return.
3.  Business applications: depreciation, valuing of investments, fixed income securities,  average financial duration, leasing and instalment credit.
The course will be assessed by a written examination.
Reading list
·         L. Peccati,  S. Salsa,  A. Squellati - Matematica per l’economia e l’azienda. Milano, Egea 2004.
·         E.Castagnoli, L.Peccati - Matematica in azienda: 1.Calcolo finanziario con applicazioni. III edizione - Milano, Egea 2005
·         E.Castagnoli, M. Cigola, L.Peccati - Matematica in azienda: 2. Complementi di analisi. III edizione – Milano, Egea 2005