Mathematics for the Environment (I MOD)
Expected learning outcomes
The course aims to provide basic knowledge concerning the theory of functions of several real variables (continuity, differentiability, integrability) and unconstrained and constrained optimization problems. The student will be able to use the studied methods for modeling and solving economic and environmental problems.
Expected learning outcomes
Knowledge and understanding
The student will demonstrate that he has acquired the tools of mathematical analysis and has to be able to apply them to model and solve real problems.
Applying Knowledge and understanding
The student should be able to apply the acquired mathematical techniques to real problems, especially of environmental nature and, in particular, he has to be be able to solve optimization problems.
The student will demonstrate that he is able to translate into mathematical terms a problem that describes a real phenomenon.
The student will demonstrate his ability to expose, with a certain rigor, the knowledge acquired, answering in a exhaustive way to the questions of the oral examination.
Lifelong learning skills
The student should be able to show a good learning ability of the acquired methodologies and he should know how to use mathematical tools to solve application problems.
Contents of the course of Introduction to Mathematics of the first year.
UNCTIONS 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.
The course includes frontal lessons, during which the themes of the program are discussed, and exercises in attendance.
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
The assessment is based on written examination (duration 90 minutes) and an oral interview.
The written test is composed of exercises in order to assess the achievement by the student of the learning objectives. The oral exam focuses on the theoretical topics dealt with during the course and it is designed to evaluate the student's ability to express and formalize mathematical concepts. The vote of the examination is expressed in scale from 0 to 30, and it is results of written and oral examination.
During the examination, the use of notes, books and informatics devices (smartphone, tablet, pc, ecc.) is not allowed.