# Matematica | MATHEMATICAL ANALYSIS IV

## Matematica MATHEMATICAL ANALYSIS IV

 0512300011 DIPARTIMENTO DI MATEMATICA EQF6 MATHEMATICS 2022/2023

 OBBLIGATORIO YEAR OF COURSE 2 YEAR OF DIDACTIC SYSTEM 2018 SPRING SEMESTER
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
 CRISTIAN TACELLI T
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.
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
More Information
Email: ctacelli@unisa.it
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