The purpose of the course is to provide the students with the necessary background of differential and integral calculus for functions of several variables, and of differential equations. A further aim is to apply analytical techniques in other scientific disciplines.
Learning outcomes (compared with the Dublin descriptors).
-Knowledge and understanding. Knowledge of the differential and integral calculus for functions of several variables. The student will be able to state and prove basic theorems of Mathematical Analysis.
- Skills of applying knowledge and understanding. The ability to understand the problems proposed during the course, the ability to correctly apply the theoretical knowledge. The student will be able to study functions, to solve integration problems, to solve differential equations of first and second order, to discuss the behaviof of some series of functions, with the aim of using such tools in the study of some enginnering problems
- Making judgments. Develop the ability to critically evaluate the problems and propose the most appropriate approach
- Communication skills. Ability to report and present the results with a ogical-deductive and synthetic exposition.
- Ability to learn. Ability to develop, outline, summarize the contents
The objective of the exam is to check the level of achievement of the above-mentioned training objectives. The exam is divided into two parts: - A written test that aims to evaluate the ability to correctly use the theoretical knowledge acquired during the course to solve mathematical problems. The student who does not show sufficient mastery of the arguments is not admitted to the next test. The expected time is 2 hours. - an oral test in which the ability to link and compare different aspects of the course will be evaluated. The final vote takes into account the evaluation of both tests.
It is mandatory for the student to achieve a sufficient knowledge of the main topics provided by the courses of Calculus pt.1 and the course of Linear Algebra, namely: sequence and series of real numbers, differential calculus for functions of one variable, integral calculus for functions of one variable, linear systems.
Functions of several real variables: continuity, gradient, differentiability. Maxima and minima. Double and triple integrals. Curves, surfaces. Line and surface integrals of a function. Vector fields in 2-D and 3-D: rotation and divergence; line integral of a vector field; potential function and conservative fields; Gauss' and Stokes' theorems. Ordinary differential equations: initial value problems; solutions of first-order equations, of higher-order linear equations. Power series.
N.FUSCO - P.MARCELLINI - C.SBORDONE, Elementi di Analisi Matematica due, Liguori Ed.
P.MARCELLINI - C.SBORDONE, Esercitazioni di Matematica (II vol.), Liguori ed.
M. Bramanti, C.D. Pagani, S. Salsa, Analisi Matematica II, Zanichelli Ed.
The aim of the exam consists in verifying the level of the objectives previously explained. The exam is divided in two parts:
-a written exam, which aims to test the skill about the application of the theoretical knowledge achieved in the course for the resolution of some mathematical problems. A student who does not show a sufficient mastery of the main topics fails the exam and is not admitted to the second stage. This part of the exam lasts 2 hours.
-an oral exam, in which the skill of the student of linking and comparing various parts of the course is evaluated. The final score takes into account of the results of both parts of the exam.