Matematica | MATHEMATICAL ANALYSIS IV

cod. 0512300011

MATHEMATICAL ANALYSIS IV

	0512300011
	DIPARTIMENTO DI MATEMATICA
	EQF6
	MATHEMATICS
	2022/2023

PERCORSO SHARED STUDY PATHWAY

	OBBLIGATORIO
	YEAR OF COURSE 2
	YEAR OF DIDACTIC SYSTEM 2018
	SPRING SEMESTER

TEACHING UNITS

SSD	CFU	HOURS	ACTIVITY	TYPE OF ACTIVITY
MAT/05	5	40	LESSONS	COMPULSORY SUBJECTS, CHARACTERISTIC OF THE CLASS
MAT/05	3	36	EXERCISES	COMPULSORY SUBJECTS, CHARACTERISTIC OF THE CLASS

	Objectives
	MAKE STUDENTS ACQUIRE A GOOD UNDERSTANDING OF THE THEORY AND APPLICATIONS OF THE INTEGRAL CALCULUS FOR FUNCTIONS OF MULTIPLE VARIABLES, DIFFERENTIAL FORMS AND CURVILINEAR INTEGRALS.

	Prerequisites
	KNOWLEDGE OF THE THEORY AND APPLICATIONS OF INTEGRAL AND DIFFERENTIAL CALCULUS FOR FUNCTIONS OF ONE VARIABLE.

	Contents
	CURVES AND CURVILINEAR INTEGRALS. LINEAR DIFFERENTIAL FORMS. VECTOR FIELDS. CONSERVATION FIELDS. CURVILINEAR INTEGRAL OF A LINEAR DIFFERENTIAL FORM. MULTIPLE INTEGRALS. DOUBLE INTEGRALS ON NORMAL DOMAINS. REDUCTION FORMULAS. GAUSS-GREEN FORMULAS. DIVERGENCE THEOREM. STOKES FORMULA. CHANGE OF VARIABLES IN INTEGRALS DOUBLE. TRIPLE INTEGRALS. SURFACE SURFACES AND INTEGRALS. REGULAR SURFACES. LOCAL COORDINATES AND CHANGE OF PARAMETERS. TANGENT PLANE AND NORMAL VERSOR. AREA OF A SURFACE. SURFACES WITH EDGE. SURFACE INTEGRALS. STOKES FORMULA. DIVERGENCE THEOREM. IMPLIED FUNCTIONS. THE THEOREMS OF DINI. LAGRANGE MULTIPLIERS.

CURVES AND CURVILINEAR INTEGRALS.
LINEAR DIFFERENTIAL FORMS. VECTOR FIELDS. CONSERVATION FIELDS.
CURVILINEAR INTEGRAL OF A LINEAR DIFFERENTIAL FORM. MULTIPLE INTEGRALS. DOUBLE INTEGRALS ON NORMAL DOMAINS. REDUCTION FORMULAS. GAUSS-GREEN FORMULAS.
DIVERGENCE THEOREM. STOKES FORMULA. CHANGE OF VARIABLES IN INTEGRALS
DOUBLE. TRIPLE INTEGRALS.
SURFACE SURFACES AND INTEGRALS. REGULAR SURFACES. LOCAL COORDINATES AND CHANGE OF
PARAMETERS.
TANGENT PLANE AND NORMAL VERSOR. AREA OF A SURFACE. SURFACES WITH EDGE.
SURFACE INTEGRALS. STOKES FORMULA. DIVERGENCE THEOREM.
IMPLIED FUNCTIONS. THE THEOREMS OF DINI. LAGRANGE MULTIPLIERS.

	Teaching Methods
	LECTURES AND EXERCISES.

	Verification of learning
	WRITTEN AND ORAL EXAM.

	Texts
	ANALISI MATEMATICA 2, C. PAGANI - S. SALSA, ZANICHELLI, 2016 ESERCIZI DI ANALISI MATEMATICA 2, S. SALSA-A. SQUELLATI, ZANICHELLI, 2011 ESERCITAZIONI DI ANALISI MATEMATICA 2, P. MARCELLINI - C. SBORDONE, ZANICHELLI, 2017 ESERCITAZIONI DI ANALISI MATEMATICA 2, M. BRAMANTI, PROGETTO LEONARDO, BOLOGNA, 2012 ESERCIZI DI ANALISI MATEMATICA, M. AMAR - A.M. BERSANI, PROGETTO LEONARDO, BOLOGNA, 2004