Università degli Studi di Napoli "Parthenope"

Teaching schedule

Academic year: 
2017/2018
Belonging course: 
Course of Bachelor's Degree Programme on ECONOMICS AND BUSINESS
Disciplinary sector: 
MATHEMATICAL ANALYSIS (MAT/05)
Credits: 
6
Year of study: 
3
Teachers: 
Cycle: 
Second semester
Hours of front activity: 
48

Language

Italian

Course description

Expected learning outcomes
The course aims to provide basic knowledge concerning the theory of functions of several real variables (continuity, differentiability, integrability), unconstrained and constrained optimization problems, ordinary differential equations. The student will be able to use the studied methods for modeling and solving economic and environmental problems.

Prerequisites

Contents of the course of Introduction to Mathematics of the first year.

Syllabus

FUNCTIONS OF TWO OR SEVERAL VARIABLES (8 hours)
Graphs and domain of functions of two variables; limits and continuity; partial derivatives, directional derivatives.

QUADRATIC FORMS (8 hours)
Definiteness of a quadratic form. Principal minors and leading principal minors. Criterion for the definiteness of a quadratic form.

UNCONSTRAINED AND CONSTRAINED OPTIMIZATION (16 hours)
Local and Global Maxima and Minima. Concave and convex functions. Constrained maxima and minima with Laplace multipliers. Applications.

INTEGRATION (16 hours)
Definite and indefinite integrals. Double integrals.

CONTINUOUS MODELS (24 hours)
First and second order linear differential equations. Applications: population growth models; predator-prey systems, competition and cooperation; epidemic model; heat loss of a body; the oxygen debt; passage of a substance across a membrane; some applications in Physic.

Teaching Methods

Textbooks

P.Marcellini, C.Sbordone: Esercitazioni di Matematica 2, parte I e II, Liguori Editore, Napoli, 1991.

C.P. Simon - L.E. Blume, Mathematics for Economists

Learning assessment

More information