Lyoubomira SOFTOVA PALAGACHEVA | MATHEMATICAL ANALYSIS IV

cod. 0512300011

MATHEMATICAL ANALYSIS IV

	0512300011
	DIPARTIMENTO DI MATEMATICA
	EQF6
	MATHEMATICS
	2018/2019

CURRICULUM MATEMATICA AD INDIRIZZO APPLICATIVO Cohort 2017/2018

	OBBLIGATORIO
	YEAR OF COURSE 2
	YEAR OF DIDACTIC SYSTEM 2016
	SECONDO SEMESTRE

TEACHING UNITS

	SSD	CFU	HOURS	ACTIVITY	TYPE OF ACTIVITY
	MAT/05	7	56	LESSONS	COMPULSORY SUBJECTS, CHARACTERISTIC OF THE CLASS

PROFESSORS

LYOUBOMIRA SOFTOVA PALAGACHEVA T Curriculum

	Objectives
	AWARENESS:IN THIS COURSE ARE INTRODUCED THE BASIC PORPERTIES OF MULTIPLE INTEGRALS. MAIN ATTENTION IS FOCUSED ON DIVERGENCE THEOREM AND GAUSS-GREEN FORMULA. DIFFERENTIAL FORMS, STOKES FORMULA AND OPTIMIZATION PROBLEMS USING LAGRANGE MULTIPLIERS ARE STUDIED. ABILITY TO APPLY AWARENESS: ONE OF THE MAIN PURPOSE OF THE COURSE IS TO ACHIEVE THE STUDENT TO SOLVE PROBLEMS USING THE TECHNICQUE ASSIMILATED. INDEPENDENCE IN JUDJEMENT:THE STUDENT IS GUIDED TO DEVELOP DISCRIMINANTING ABILITIES ABOUT THE SUBJECTS STUDIED. COMUNICATIVE ABILITIES: THE STUDENT WILL BE ABLE TO ARTICULATE THE STATEMENTS AND THE PROOF OF THE THEOREM DEALED IN THE COURSE. EDUCATIONAL SKILLS: THE STUDENT WILL ACQUIRE THE KNOWLEDGE OF MATEMATICAL TOOLS THAT ALLOW HIM TO HANDLE WITH MORE ADVANCED MATEMATOCAL TOPICS.

AWARENESS:IN THIS COURSE ARE INTRODUCED THE BASIC PORPERTIES OF MULTIPLE INTEGRALS. MAIN ATTENTION IS FOCUSED ON DIVERGENCE THEOREM AND GAUSS-GREEN FORMULA. DIFFERENTIAL FORMS, STOKES FORMULA AND OPTIMIZATION PROBLEMS USING LAGRANGE MULTIPLIERS ARE STUDIED.
ABILITY TO APPLY AWARENESS:
ONE OF THE MAIN PURPOSE OF THE COURSE IS TO ACHIEVE THE STUDENT TO SOLVE PROBLEMS USING THE TECHNICQUE
ASSIMILATED.
INDEPENDENCE IN JUDJEMENT:THE STUDENT IS GUIDED TO DEVELOP DISCRIMINANTING ABILITIES ABOUT THE SUBJECTS STUDIED.
COMUNICATIVE ABILITIES: THE STUDENT WILL BE ABLE TO ARTICULATE THE STATEMENTS AND THE PROOF OF THE THEOREM DEALED IN THE COURSE.
EDUCATIONAL SKILLS: THE STUDENT WILL ACQUIRE THE KNOWLEDGE OF MATEMATICAL TOOLS THAT ALLOW HIM TO HANDLE WITH MORE ADVANCED MATEMATOCAL TOPICS.

	Prerequisites
	BASIC PROPERTIES OF FUNCTIONS OF SEVERAL REAL VARIABLE: CONTINUITY, DIFFERENTIABILITY.

	Contents
	RECTIFIABLE CURVES. CALCULATION OF CURVE LENGTH, NATURAL PARAMETER, REPARAMETERIZATION. CURVILINEAR INTEGRALS OF THE 1ST SPECIES. MULTIPLE INTEGRALS, DEFINITION OF DOUBLE INTEGRAL, PEANO JORDAN MEASURE, INTEGRALS ON SIMPLE DOMAINS, REDUCTION FORMULAS. INTEGRALS DEPENDENT ON A PARAMETER, LIMIT AND DERIVATION OF THE INTEGRAL WITH RESPECT TO A PARAMETER. CHANGE OF VARIABLES. TRIPLE INTEGRALS, REDUCTION FORMULAS, CHANGE OF VARIABLES. CENTER OF GRAVITY AND MOMENT OF INERTIA. EULER GAMMA AND BETA FUNCTIONS. VECTOR FIELDS, CURVILINEAR INTEGRALS OF THE 2ND SPECIES, WORK. THE KINETIC ENERGY THEOREM, CONSERVATIVE FIELDS AND IRROTATIONAL FIELDS. RECOGNITION THEOREMS OF CONSERVATIVE FIELDS, POTENTIAL FUNCTION. SOLENOID FIELDS AND VECTOR POTENTIAL. GAUSS-GREEN THEOREM IN THE PLANE. REGULAR SURFACES, SURFACE INTEGRALS. LOCAL COORDINATES AND CHANGE OF PARAMETERS. DINI THEOREM IN RN, LOCAL AND GLOBAL INVERSION THEOREM. DIFFERENTIAL EQUATIONS, QUALITATIVE STUDY OF SOLUTIONS.

Contents

RECTIFIABLE CURVES. CALCULATION OF CURVE LENGTH, NATURAL PARAMETER, REPARAMETERIZATION. CURVILINEAR INTEGRALS OF THE 1ST SPECIES. MULTIPLE INTEGRALS, DEFINITION OF DOUBLE INTEGRAL, PEANO JORDAN MEASURE, INTEGRALS ON SIMPLE DOMAINS, REDUCTION FORMULAS. INTEGRALS DEPENDENT ON A PARAMETER, LIMIT AND DERIVATION OF THE INTEGRAL WITH RESPECT TO A PARAMETER. CHANGE OF VARIABLES. TRIPLE INTEGRALS, REDUCTION FORMULAS, CHANGE OF VARIABLES. CENTER OF GRAVITY AND MOMENT OF INERTIA. EULER GAMMA AND BETA FUNCTIONS. VECTOR FIELDS, CURVILINEAR INTEGRALS OF THE 2ND SPECIES, WORK. THE KINETIC ENERGY THEOREM, CONSERVATIVE FIELDS AND IRROTATIONAL FIELDS. RECOGNITION THEOREMS OF CONSERVATIVE FIELDS, POTENTIAL FUNCTION. SOLENOID FIELDS AND VECTOR POTENTIAL. GAUSS-GREEN THEOREM IN THE PLANE. REGULAR SURFACES, SURFACE INTEGRALS. LOCAL COORDINATES AND CHANGE OF PARAMETERS. DINI THEOREM IN RN, LOCAL AND GLOBAL INVERSION THEOREM. DIFFERENTIAL EQUATIONS, QUALITATIVE STUDY OF SOLUTIONS.

	Teaching Methods
	FRONTAL LESSONS. PRACTICE LESSONS.

	Verification of learning
	THE STUDENT WILL TAKE THE FOLLOWING TESTS: WRITTEN AND ORAL EXAMINATION CONCERNING THE TOPICS COVERED IN THE COURSE.

	Texts
	C.PAGANI, S.SALSA, ANALISI MATEMATICA 1, ZANICHELLI C.PAGANI, S.SALSA, ANALISI MATEMATICA 2, ZANICHELLI M.BRAMANTI, C.PAGANI,S.SALSA, ANALISI MATEMATICA 2, , ZANICHELLI, 2009, BOLOGNA. M. AMAR, A.M. BERSANI, ESERCIZI DI ANALISI MATEMATICA, PROGETTO LEONARDO, BOLOGNA, 2004.

	More Information
	E-MAIL: LSOFTOVA@UNISA.IT

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Lyoubomira SOFTOVA PALAGACHEVA | MATHEMATICAL ANALYSIS IV