The course aims to provide basic knowledge concerning the theory of the functions of several variables (continuity, differentiability) and unconstrained and constrained optimization problems and the mathematical tools suitable for solving problems related to optimal management and planning.
Contents of the course of Introduction to Mathematics of the first year.
PART I (24 hours)
Functions of two or several variables. Graphs. Level curves. Production function. Utility function. Limits and continuity. Weirstrass theorem.
Partial derivatives. Higher Order Derivatives. Hessian matrix. Schwarz theorem. Differentiability and continuity. Sufficient condition for the differentiability.
Regular curve. Tangent vector. Directional derivatives.
Local and Global Maxima and Minima. Constrained maxima and minima. Economic applications.
Parte II (24 hours)
Nonlinear programming. Method of Lagrange multipliers. Economic interpretation of the Lagrange multiplier. Necessary conditions. Quadratic forms. Sufficient conditions.
Economic applications: utility and demand, profit and cost.
The course includes frontal lessons, during which the themes of the program are discussed, and exercises in attendance.
C.P. Simon - L.E. Blume, Mathematics for Economists.
The assessment is based on written examination (duration 90 minutes) and an oral interview.
The vote of the examination is results of written and oral examination.
The oral exam is allowed only to students who have passed the written test with minimum 18/30.
During the examination, the use of notes, books and informatics devices (smartphone, tablet, pc, ecc.) is not allowed.