Università degli Studi di Napoli "Parthenope"

Teaching schedule

Academic year: 
2020/2021
Belonging course: 
Course of Bachelor's Degree Programme on COMPUTER SCIENCE
Disciplinary sector: 
MATHEMATICAL ANALYSIS (MAT/05)
Language: 
Italian
Credits: 
9
Year of study: 
2
Teachers: 
Cycle: 
First Semester
Hours of front activity: 
72

Language

Italian

Course description

The purpose of the course is to provide the students with the necessary background of differential and integral calculus for functions of several variables, differential equations and some notions of probability theory. A further aim is to apply analytical techniques in other scientific disciplines.

Learning outcomes (declined compared with respect to 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.

Applying knowledge and understanding. The ability to understand the problems proposed during the course, the ability concerning a correct application of 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 behavior of series of functions.

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 logical-deductive and synthetic exposition. He must be able to explain (even to non-expert people) the power of some applications of the mathematical tools described in the course, in the field of Engineering.

Ability to learn.
Ability to develop, outline, summarize the contents from several sources, in order to achieve a broad overview of the problems connected to the topics discussed in the course. The student will also develop the skill of learning more advances techniques of Mathematical Analysis.

Prerequisites

It is necessary to acquire and assimilate the following knowledge provided by the course "Mathematical I": sequences of real numbers, differential and integral calculus for functions of one variable, linear systems.

Syllabus

Series and power series: Taylor expansions. Differential calculus for functions of several real variables. Differential equations of first and second order.
Line Integral and differential forms. Double and triple integrals. A glimpse to probability theory: combinatorial calculus, basic definitions of probability, conditional probability, the Bayes theorem, random variables.

Series and power series: Taylor expansions. Differential calculus for functions of several real variables. Differential equations of first and second order.
Line Integral and differential forms. Double and triple integrals. A glimpse to probability theory: combinatorial calculus, basic definitions of probability, conditional probability, the Bayes theorem, random variables.

Teaching Methods

Lectures, exercise sessions.

Textbooks

Robert A. Adams, Christopher Essex, Calculus: A Complete Course, Pearson Canada.

Learning assessment

The objective of the exam is to check the level of achievement of the above-mentioned training objectives. In particular, the students attending the courses will have the chance to be evaluated on two partial written exams, containing various exercises and theoretical questions. In case of a positive evaluation, the student will be given the chance either to accept the final score or to integrate it with an oral exam, based on the theoretical aspects of the course, focusing basically on the proofs of the main results shown during the course. In case the student will fail the partial tests, he/she will be given the possibility to attend a 3 hours written exam, based on 5 exercises and some theoretical question. The written test will have a positive evaluation if the student answers correctly at least 3 exercise and 2 theoretical questions. If the written exam has a positive evaluation, the student will be given the above-mentioned chance, that is to accept the vote or to integrate it with an oral examination: in the latter case, the final score will be the average of the two tests. In any case, the student will have a positive evaluation if he shows to have a sufficient mastery in the classical topics of multivariable calculus, power series, differential equations and the basics of probability theory.

More information

Lectures are in Italian. The professor is fluent in English and is available to interact with students in English, also during the examination. Time table: Friday from 10.00 to 12.00. I am also available on other days by appointment by e-mail.