Beatrice PATERNOSTER | NUMERICAL ANALYSIS

cod. 0522200003

NUMERICAL ANALYSIS

	0522200003
	DIPARTIMENTO DI MATEMATICA
	EQF7
	MATHEMATICS
	2018/2019

PERCORSO COMUNE Cohort 2017/2018

	YEAR OF COURSE 2
	YEAR OF DIDACTIC SYSTEM 2016
	PRIMO SEMESTRE

TEACHING UNITS

	SSD	CFU	HOURS	ACTIVITY	TYPE OF ACTIVITY
	MAT/08	6	48	LESSONS	SUPPLEMENTARY COMPULSORY SUBJECTS

PROFESSORS

	BEATRICE PATERNOSTER T Curriculum
	ANGELAMARIA CARDONE Curriculum

	Objectives
	1.KNOWLEDGE AND UNDERSTANDING THE AIM OF THE COURSE IS TO ACQUIRE KNOWLEDGE TO ANALYZE CRITICAL THEORY AND NUMERICAL METHODS RELATING TO THE NUMERICAL TREATMENT OF MAIN PROBLEMS MODELED BY EVOLUTIONARY EQUATIONS, IN PARTICULAR PARTIAL DIFFERENTIAL EQUATIONS. 2.APPLIED KNOWLEDGE AND UNDERSTANDING BY MEANS OF THE PRACTICE IN THE LABORATORY, THE STUDENTS WILL BE ABLE TO EXPERIMENT SOME NUMERICAL METHODS, TO ESTIMATE THE RELIABILITY OF THE OBTAINED RESULTS, TO DEVELOP ELEMENTS OF MATHEMATICAL SOFTWARE, TO USE PACKAGES OF NUMERICAL ANALYSIS AND TO EVALUATE PERFORMANCES.

1.KNOWLEDGE AND UNDERSTANDING
THE AIM OF THE COURSE IS TO ACQUIRE KNOWLEDGE TO ANALYZE CRITICAL THEORY AND NUMERICAL METHODS RELATING TO THE NUMERICAL TREATMENT OF MAIN PROBLEMS MODELED BY EVOLUTIONARY EQUATIONS, IN PARTICULAR PARTIAL DIFFERENTIAL EQUATIONS.
2.APPLIED KNOWLEDGE AND UNDERSTANDING
BY MEANS OF THE PRACTICE IN THE LABORATORY, THE STUDENTS WILL BE ABLE TO EXPERIMENT SOME NUMERICAL METHODS, TO ESTIMATE THE RELIABILITY OF THE OBTAINED RESULTS, TO DEVELOP ELEMENTS OF MATHEMATICAL SOFTWARE, TO USE PACKAGES OF NUMERICAL ANALYSIS AND TO EVALUATE PERFORMANCES.

	Prerequisites
	THEORY OF ORDINARY DIFFERENTIAL EQUATIONS. PROGRAMMING PRINCIPLES. BASIC NOTIONS OF PROGRAMMING LANGUAGES C AND MATLAB.

	Contents
	NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS: BASIC NOTIONS OF THEORY. GENERAL INFORMATION ON NUMERICAL TREATMENT OF SECOND ORDER LINEAR PARTIAL DIFFERENTIAL EQUATIONS. FINITE DIFFERENCE METHODS FOR ELLIPTIC, PARABOLIC AND HYPERBOLIC EQUATIONS. METHODS OF LINES. WEAK FORM OF A DIFFERENTIAL PROBLEM. POLYNOMIAL APPROXIMATION. GALERKIN AND COLLOCATION METHODS. FINITE ELEMENT METHOD FOR ELLIPTIC EQUATIONS. NUMERICAL LINEAR ALGEBRA: NON-STATIONARY METHODS FOR THE SOLUTION OF LARGE DIMENSIONE LINEAR SYSTEMS, SINGULAR VALUE DECOMPOSITION AND APPLICATION TO RECOMMENDATION SYSTEMS. INTRODUCTION TO THE NUMERICAL SOLUTION OF STOCHASTIC DIFFERENTIAL EQUATIONS. WEAK AND STRON CONVERGENCE. EULERO-MARUYAMA METHOD. PHYTON ELEMENTS FOR LINEAR ALGEBRA ALGORITHMS.

Contents

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS: BASIC NOTIONS OF THEORY. GENERAL INFORMATION ON NUMERICAL TREATMENT OF SECOND ORDER LINEAR PARTIAL DIFFERENTIAL EQUATIONS. FINITE DIFFERENCE METHODS FOR ELLIPTIC, PARABOLIC AND HYPERBOLIC EQUATIONS. METHODS OF LINES. WEAK FORM OF A DIFFERENTIAL PROBLEM. POLYNOMIAL APPROXIMATION. GALERKIN AND COLLOCATION METHODS. FINITE ELEMENT METHOD FOR ELLIPTIC EQUATIONS.
NUMERICAL LINEAR ALGEBRA: NON-STATIONARY METHODS FOR THE SOLUTION OF LARGE DIMENSIONE LINEAR SYSTEMS, SINGULAR VALUE DECOMPOSITION AND APPLICATION TO RECOMMENDATION SYSTEMS.
INTRODUCTION TO THE NUMERICAL SOLUTION OF STOCHASTIC DIFFERENTIAL EQUATIONS. WEAK AND STRON CONVERGENCE. EULERO-MARUYAMA METHOD. PHYTON ELEMENTS FOR LINEAR ALGEBRA ALGORITHMS.

	Teaching Methods
	LECTURES, EXERCISES, LABORATORY

	Verification of learning
	THE FINAL EXAM CONSISTS IN THE DISCUSSION ON THE THEORETICAL ISSUES OF THE COURSE, IN ORDER TO CHECK THE ABILITY TO ANALYZE AND PRESENT THE PROPERTIES OF THE NUMERICAL METHODS PRESENTED DURING THE COURSE, AND ON THE NUMERICAL PROJECT DEVELOPED DURING THE COURSE

	Texts
	ISAACSON, H.KELLER- ANALYSIS OF NUMERICAL METHODS - J. WILEY SONS. ALFIO QUARTERONI – MODELLISTICA NUMERICA PER PROBLEMI DIFFERENZIALI, SPRINGER

	More Information
	BEAPAT@UNISA.IT; ANCARDONE@UNISA.IT PIATTAFORMA MTOUCH {MATHEMATICS ORIENTED VIRTUAL CLASSROOM HYPERSPACE} SU HTTPS://WWW.ELEARNING.DIPMAT.UNISA.IT/

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Beatrice PATERNOSTER | NUMERICAL ANALYSIS