# Università degli Studi di Napoli "Parthenope"  ## Teaching schedule

2017/2018
Partition:
Cognomi M-Z
Teaching:
Belonging course:
Course of Bachelor's Degree Programme on MANAGEMENT ENGINEERING
Location:
Napoli
Disciplinary sector:
MATHEMATICAL ANALYSIS (MAT/05)
Credits:
9
Year of study:
1
Teachers:
Cycle:
Second semester

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, and of differential equations. A further aim is to apply analytical techniques in other scientific disciplines.

Learning outcomes (declined 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.

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 integration problems, to solve differential equations of first and second order, to discuss the nature 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 ogical-deductive and synthetic exposition.

Ability to learn.
Ability to develop, outline, summarize the contents

### Prerequisites

It is necessary to acquire and assimilate the following knowledge provided by the course "Mathematical Analysis I" and "Algebra and Geometry": Sequences of real numbers and Series., Differential and integral calculus for functions of one variable, Linear Systems.

### Syllabus

Differential Calculaus for Functions of several real variables (3 CFUs - 24 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.
Ordinary Differential Equations (1.5 CFU-12 Hours) Cauchy Problem; existence and uniqueness results. Linear differential equations of first and second order. Linear equations with constant coefficients. The Lagrange method. Some non linear first order equation.
Line Integral and vector fields in 2-D and 3-D (1.5 CFU-12 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 (1 CFU-8 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 (1 CFU-8 hours) Regular surfaces, Rotation surfaces. Area of ​​a surface. The divergence theorem and the Stokes formula.
Power Series (1 CFU-8 Hours) Power Series in Real Field and Complex Field. Convergence set. Taylor's series .

Differential Calculaus for Functions of several real variables (3 CFUs - 24 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.
Ordinary Differential Equations (1.5 CFU-12 Hours) Cauchy Problem; existence and uniqueness results. Linear differential equations of first and second order. Linear equations with constant coefficients. The Lagrange method. Some non linear first order equation.
Line Integral and vector fields in 2-D and 3-D (1.5 CFU-12 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 (1 CFU-8 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 (1 CFU-8 hours) Regular surfaces, Rotation surfaces. Area of ​​a surface. The divergence theorem and the Stokes formula.
Power Series (1 CFU-8 Hours) Power Series in Real Field and Complex Field. Convergence set. Taylor's series .

### Textbooks

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.

### 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.
The final vote takes into account the evaluation of both tests.