Università degli Studi di Napoli "Parthenope"

Teaching schedule

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Dott. FEO Filomena
First Semester
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Course description

The purpose of the course is to provide the students with the necessary background in differential and integral calculus for functions of several variables, series and Laplace and Fourier transforms. 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 differential and integral calculus for functions of several variables and properties of Laplace and Fourier Transforms. 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 discuss the behaviour of a series of functions and to apply the properties of Laplace and Fourier transforms.

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.


It is necessary to acquire and assimilate the following knowledge provided by the course "Mathematical I": complex filed, sequences of real numbers, differential and integral calculus for functions of one variable, Ordinary differential equation, Linear Systems


Differential Calculus for Functions of several real variables (20 Hours): Topology in R2; continuous functions; partial derivatives; differentiability and relative theorem; directional derivatives and gradient; higher order derivatives and Schwarz's theorem; Maxima and minima.
Line Integral and vector fields in 2-D and 3-D (16 hours) Regular curves; length of curve; line integral of a function; vector fields in 2-D and 3-D and its line integral; potential and conservative field; irrotational field; integrability criteria.
Double and triple integrals (12 hours) Double integrals on normal domains; integrability of continuous functions; reduction formulas ; change of variables ; Gauss-Green formulas, divergence theorem, Stokes formula; triple integrals.
Regular surfaces (10 hours) Regular surfaces, Rotation surfaces. Area of a surface. The divergence theorem and the Stokes formula.
Power Series (14) Power Series in Real Field and Complex Field. Convergence set. Taylor's series .
Laplace and Fourier Trasform (8+8 h): definition and properties.

Differential calculus for functions of several real variables.
Line Integral and differential forms. Double and triple integrals. Regular surfaces. Series. Complex functions of real variable.
Laplace transform.
Fourier transform.

Teaching Methods

Lectures, exercise sessions


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

Teams and
as well.

Learning assessment

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.

More information

Lectures are in Italian. The professor is available to interact with students in English, also during the examination.

Time table: ???. I am also available on other days by appointment by e-mail.