Metodi matematici 2 - ENG

Mathematical Methods 2

Course A – Prof. Gianluca Fusai
Course B – Prof. Giovanni Longo

Course Code: E0362
SSD code: SECS – S/06
6 CFU – 48 hours
Location: Novara


Educational aims

The purpose of this course is to complete the mathematical education acquired previously. This aim is achieved  trough the introduction to three main areas such as financial calculus, linear algebra and optimization.  



Content of the course
First module: Financial Calculus. Present and final value. Amortization, leasing and fixed and floating rate mortgages. The term structure of interest rates. Pricing of discount and coupon bond. How to price defaultable bonds. Financial choices: the net present value rule and its improvements. Case Studies in economics and finance.
Second module: Linear Algebra. Vectors and Matrices and their operations (sum, product, trans position, inner product, inversion). Linear independence. Ranl. Elementary operations and the solution of linear system (Gaussian pivoting). The Rouché-Capelli Theorme. Case Studies in economics and finance.
Third module:  Optimization. Multivariable functions and their representations (graphs and contour levels). Maximum and minimum points (local and global) and how to find them. Weierstrass Theorem. Differential calculus, gradient and Hessian and necessary and sufficient conditions for a non linear programming. Constrained optimization. Linear programming. Case Studies in economics and finance.

Prerequisites
Mathematical Methods 1.

Course Texts

M. D’Amico, G. Fusai e G. Longo, Calcolo Finanziario, available on the the web page of the course.
E. Castagnoli - L. Peccati, La matematica in azienda vol. II; Modelli lineari, Egea, 1996  (In Italian). The book is available in the library

F. Privileggi, Matematica per l’Economia. Gruppo editoriale Esselibri – Simone, 2008. S. Margarita The book is available in the library

E. Salinelli, MultiMath: Matematica Multimediale per l’Università, Springer, 2004. The book is available in the library
The above mentioned books are available in the library.
Additional reading materials, past exams and further informations can be found in the web page of the course at the URL:
https://eco.dir.unipmn.it/


Teaching methods

Lectures.


Examination

Written exam. Further informations can be found in the web page of the course at the URL:
https://eco.dir.unipmn.it/