Ateneo - UPO

Common to the two courses (Management and Economia): linear algebra, vectors, matrices, two variables functions, unconstrained optimization, constraint optimization of multiple variables functions, economic applications, enterprise problem, customer problem.

Economia course only: insights, multiple variables functions,

C. Mattalia, F. Privileggi, Matematica per le scienze economiche e sociali - algebra lineare, funzioni di più variabili e ottimizzazione statica, Maggioli editore

The aim of the course is to present the mathematical tools to be used in economic environments.

Knowledge required on: elementary calculus, polynomials and their operations, equations and inequalities, linear and quadratic, radical, rational, exponential, logarithmic, absolute-value. Analytic geometry. Solution of elementary linear systems. Elements of logic and set theory.

Face to face lectures with integrated exercises.

All the informations related to the course as well as supplementary resources
can be found on the course's page on the website www.dir.uniupo.it.

The exam consists of a written test.

Linear algebra: vectors, representation, operations, definitions. Matrices, operations, classifications, determinants, minors, rank, scaling, Gauss algorithm. Linear systems, Rouchè-Capelli theorem, Cramer theorem.
Functions of two variables: domain, level curves, gradient, Hessian matrix.
Uncontrined optimization: maxima, minima, inflexions, first order condition, second order condition.
Economic-financial applications.

Insights into linear algebra, quadratic forms, classification, associated matrices, principal minors. Functions of multiple variables. Extension of unconstrained optimization. Constrained optimization, equality constraints, inequality constraints, Lagrange method, Khun-Tucker method. Enterprise problem, consumer problem.

- knowing the techniques and the mathematical tools commonly used in the solution of problems of economic and financial nature;

- using such techniques and tools to formalize and solve problems;

- being able to communicate the results obtained using a clear and appropriate mathematical notation and language.