Metodi matematici II - 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





•    Language
Italian

•    Contents
First module: Finantial mathematics.

Second module: Linear algebra.

Third module:  Optimization.

•    Course Texts

M. D’Amico, G. Fusai e G. Longo, Dispense di Calcolo Finanziario, Algebra Lineare e Ottimizzazione, 2015, available on the the web page of the course.
F. Privileggi, Matematica per l’Economia. Gruppo editoriale Esselibri – Simone, 2008.
S. Margarita -  E. Salinelli, MultiMath: Matematica Multimediale per l’Università, Springer, 2004.
The above mentioned books are available in the library.
Additional reading materials, past exams and further informations can be found on the web page of the course at the URL:
https://eco.dir.unipmn.it/

•    Educational target
The course is aimed to give a basic knowledge of finacial calculus for making economic and financial decisions, of linear algebra for being able to analyze multidimensional problems and of optimization which is fundamental in many aspects of a company life as well as in theoretical models.


•    Prerequisites

Students have to pass Mathematical Methods 1. Also for giving the partial exams of these course.

•    Teaching methods

Lectures.

•    Other informations


•    Exam methods
Written exam as a test (mandatory) plus a second, optional, classic, written exam with theoretical questions and exercises, which can be accessed to only after getting a positive note on the first test. In case of positive result in the second written exam the student can give an (optional) oral exam. Further informations can be found on the web page of the course at the URL:
https://eco.dir.unipmn.it/

•    Extended programme
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.