Course Details for A.Y. 2014/2015

The information on this page refer to the academic year 2014/2015. Therefore, several links are not available and data may be incomplete. To read the current information on the course, if it is still available, go to the university course catalogue . To read information relating other academic years, use the list at the bottom of this page.

A. Year:

2014/2015

Name:

Analisi Matematica II / Mathematical Analysis II

Type:

Course

Basic information

Code:

I0201

Sector:

MAT/05

Credits:

: Laurea in Ingegneria dell'Informazione 9 CFU (a)

Term:

2^nd semester

Degree(s):

Laurea in Ingegneria dell'Informazione 1^st anno curriculum Comune Compulsory

Language:

Italian

Teacher(s):

Rosella Colomba Sampalmieri

Propaedeutics:

Mathematical Analysis I
Geometry

Course Objectives

TO ACQUIRE AND BE ABLE TO APPLY, IN THE VARIOUS FIELDS OF ENGINEERING, THE CONCEPTS AND THE COMPUTATIONAL TECHNIQUES OF THE NOTIONS INTRODUCED IN THE COURSE. IN PARTICULAR TO HAVE KNOWLEDGE AND UNDERSTANDING OF THE CONCEPT OF SOLUTION (EXISTENCE AND UNIQUENESS) OF AN ORDINARY DIFFERENTIAL EQUATION, OF CONSERVATIVE VECTOR FIELDS, OF CONVERGENCE OF A SEQUENCE OR OF A SERIES OF FUNCTIONS

Course Content

Taylor approximation of functions of several variables. Implicit functions. Dini's theorem. Implicit function theorem in more than two variables. Non-linear systems of m equations in n unknowns. Taylor approximation to the function defined implicitly.
Elements of vector analysis . Reminders on scalar and vector product and their properties. Curves in space. Main definitions . Physical examples . Plane curves . Regular curves. Rectifiable curves . Length of a curve . Curvilinear abscissa . Normal and binormal vectors . Curvilinear integrals . Surfaces in space . Main definitions . Smooth surfaces . Examples from elementary geometry . Edge of a surface. Normal vector . Tangent plane. Orientation . Area of ??a surface . Surface integrals . Vector fields . Definition of the vector field . Irrotational and conservative vector fields . Potential. Simply connected domains . Flow of a vector field . Divergence and curl operators . Stokes' theorem in space. The Gauss' thorem in space. Intrinsic definition of the rotor and divergence. Multiple integrals . The theorems of Stokes , Gauss and Gauss-Green in IR^2.
Opimization
Complex numbers. Modulus, argument, conjugate. Algebraic, trigonometric, exponential form. N-th roots of a complex number. Fundamental Theorem of Algebra: real and complex case.
Cauchy problem. General equations of the 1st order. 1st order differential equations with separable variables. Linear differential equations of the 1st order. General structure of the integral of a linear differential equation of order n. Linear differential equations of higher order with constant coefficients. Outline of boundary value problems for ordinary differential equations.
Sequences and series of functions. Pointwise and uniform convergence of a sequence. Pointwise convergence, absolute, uniform and total for a series of function. Power series. Fourier series. Complete orthonormal systems in Hilbert spaces. Space of square-integrable functions. Trigonometric polynomials. Fourier series. Main convergence results.

Learning Outcomes (Dublin Descriptors)

On successful completion of this course, the student should

HAVE KNOWLEDGE AND UNDERSTANDING OF THE CONCEPT OF SOLUTION (EXISTENCE AND UNIQUENESS) OF AN ORDINARY DIFFERENTIAL EQUATION, OF CONSERVATIVE VECTOR FIELDS, OF OPTIMIZATION, OF CONVERGENCE OF A SEQUENCE OR OF A SERIES OF FUNCTIONS AND TO INCREASE THE BACKGROUND OF MATHEMATICAL TOOLS NECESARY TO DEAL WITH PROBLEMS FROM THE APPLIED SCIENCES
TO ACQUIRE AND BE ABLE TO APPLY, IN THE VARIOUS FIELDS OF ENGINEERING, THE CONCEPTS AND THE COMPUTATIONAL TECHNIQUES OF THE NOTIONS INTRODUCED IN THE COURSE
SHOULD DEMOSTRATE SKILL IN MATHEMATICAL REASONING AND ABILITY TO CONCEIVE AN AUTONOUMUS SOLUTION OF A PROBLEM
TO BE ABLE TO PRESENT THE SOLUTION OF A TECHNICAL PROBLEM BY MEANS OF CORRECT MATHEMATICAL LANGUAGE AND NOTATIONS
STUDENT SHOULD BE ABLE TO TO READ AND UNDERSTAND TECHNICAL BOOKS WHICH USE AN ADVANCED MATHEMATICAL LANGUAGE

Prerequisites and Learning Activities

ALL THE NOTIONS AND TECHNIQUES OF THE FIRST COURSE IN MATHEMATICAL ANALYSIS AND MANY BASIC CONCEPTS FROM GEOMETRY, SUCH AS VECTOR FIELDS, MATRICES, ETC.

Assessment Methods and Criteria

WRITTEN AND ORAL EXAMINATION

Textbooks

C. Lattanzio, B. Rubino, Analisi Matematica III: appunti per gli studenti della Facoltà di Ingegneria 2005. http://www.mathmods.eu/resources/downloads/viewcategory/17-appunti
B. Rubino, Equazioni differenziali, teoria ed esercizi, versione preliminare 2004 2004. http://www.mathmods.eu/resources/downloads/viewcategory/17-appunti
C.D. PAGANI-S.SALSA, ANALISI MATEMATICA 2 , ZANICHELLI. (vol. secondo) 1995.
P. Marcellini-C.Sbordone, Esercitazioni di matematica , Liguori. (vol. secondo, parte prima e seconda) 1994.
S.Salsa-A.Squellati, Esercizi di Analisi Matematica 2 , Zanichelli. (vol. 1, 2, 3) 1994.

Notes

OFFICE HOURS: Please check the office hour time-table on the web page: http://www.ing.univaq.it/personale/scheda_personale.php?codice=255

Internet Resources

Homepage:

http://www.ing.univaq.it/cdl/scheda_corso.php?codice=I0201_I3N

Course page updates

This course page is available (with possible updates) also for the following academic years:

To read the current information on this course, if it is still available, go to the university course catalogue .

Course information last updated on: 29 maggio 2014, 23:41