# Unit MATHEMATICAL ANALYSIS IIND

Course
Physics
Study-unit Code
GP005444
Location
PERUGIA
Curriculum
In all curricula
Teacher
Enzo Vitillaro
Teachers
• Enzo Vitillaro
Hours
• 84 ore - Enzo Vitillaro
CFU
12
Course Regulation
Coorte 2022
Offered
2022/23
Learning activities
Base
Area
Discipline matematiche e informatiche
MAT/05
Type of study-unit
Obbligatorio (Required)
Type of learning activities
Attività formativa monodisciplinare
Language of instruction
Italian
Contents

Functions sequences and series. Differential and integral calculus in several variables, potentials, ordinary differential equations.
Reference texts
Lecture Notes by the teacher. The following texbooks (in italian) are also usefull: Theory E. Giusti. Analisi Matematica II, Terza Ed. Bollati Boringhieri 2003 G. Gilardi Analisi Due. Mc Graw Hill 1996 G. Prodi Analisi Matematica II Ed. Bollati Boringhieri 2011 Fusco, Marcellini, Sbordone Analisi Matematica Due Liguori 1996 Bramanti Pagani Salsa Analisi Matematica 2. Zanichelli 2009. Ahmad Ambrosetti A textbook on Ordinary Differential Equations Springer Italia Unitext vol. 73 2014. Exercises Marcellini, Sbordone Esercitazioni di Matematica Vol.II parti 1 e 2, 1995 Acerbi, Modica, Spagnolo- Problemi scelti di Analisi Matematica II , Liguori ed., 1986 Salsa- Squellati Esercitazioni di Analisi Matematica 2 Zanichelli 1993 E. Giusti. Esercizi e complementi di Analisi Matematica II, Bollati Boringhieri, 2000. Textbooks of Analisi I G. Gilardi Analisi Uno. Mc Graw Hill C. Vinti Lezioni di Analisi Matematica Vol. 1 Marcellini, Sbordone Esercitazioni di Matematica Vol.I parte 1 e 2.
Educational objectives

The main aim of the Course is to give the main tools of Calculus and some elements of approximation theory. The main knowledge acquired will be the one listed in the program. The main competence acquired will be: to be able to make calculations in complex numebrs, to calculate partial derivatives, multiple integrals, curve and surface integrals, to approximate functions of one real variable with polynomia and trigonometric polinomia, to analyze ordinary differential equations, solving them when possible.
Prerequisites

In order to be able to understand and apply the majority of the techniques described within the Course, you mush have successfully passed the ANALISI MATEMATICA I and GEOMETRIA exams.
Teaching methods

Face to face.
Other information
The course will include an assisted study activity, scheduled depending on the students needs.
Learning verification modality

Written exam, taking 3 hours, divided in two parts: 1) practical exam, taking 2 hours, to understand the ability of the student to solve practical problems related to the arguments of the course. The exam will consists in solving the maximum possible among 5 exercises proposed; 2) teorical exam, taking 1 hour, to understand how the student understood the theory. It ocnsists in doing one or more dissertations among 3 proposed, concering the arguments done in the Course. On demand the student can also face an oral exam, to integrate the evaluation of the wrtitten exam.
Extended program

Functions sequences and series. Differential and integral calculus in several variables, potentials, ordinary differential equations. Differential calculus in several variables and applications. Peano Jordan measure and Riemann integral in several variables. Implicit functions, curves, surfaces and manifolds. Line and surface integrals, divergence and Stokes theorems. Scalar and vector potentials, differential forms. Ordinary differential equations, general theory, solution methods, linear equations and systems.
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