Beatrice PATERNOSTER | NUMERICAL CALCULUS II

cod. 0512300033

NUMERICAL CALCULUS II

	0512300033
	DIPARTIMENTO DI MATEMATICA

	MATHEMATICS
	2015/2016

CURRICULUM MATEMATICA AD INDIRIZZO APPLICATIVO

	YEAR OF COURSE 3
	YEAR OF DIDACTIC SYSTEM 2010
	PRIMO SEMESTRE

TEACHING UNITS

	SSD	CFU	HOURS	ACTIVITY	TYPE OF ACTIVITY
	MAT/08	6	48	LESSONS	COMPULSORY SUBJECTS, CHARACTERISTIC OF THE CLASS

PROFESSORS

	BEATRICE PATERNOSTER T Curriculum
	RAFFAELE D'AMBROSIO Curriculum

	Objectives
	KNOWLEDGE AND UNDERSTANDING: THE AIM OF THE COURSE IS THE THEORETICAL KNOWLEDGE AND CRITICAL ANALYSIS OF THE MAIN NUMERICAL METHODS FOR THE SOLUTION OF PROBLEMS MODELED BY ORDINARY DIFFERENTIAL EQUATIONS, TOGETHER WITH THE DEVELOPMENT OF THE CORRESPONDING MATHEMATICAL SOFTWARE. PART OF THE COURSE WILL DEAL WITH THE STUDY OF ELEMENTS OF PARALLEL CALCULUS FOR LINEAR ALGEBRA. APPLYING KNOWLEDGE AND UNDERSTANDING: THE AIM OF THE COURSE IS TO MAKE THE STUDENT CAPABLE TO SOLVE PROBLEMS OF SCIENTIFIC COMPUTING MODELED BY ORDINARY DIFFERENTIAL EQUATIONS BY DEVELOPING AND USING MATHEMATICAL SOFTWARE AND SUITABLE CALCULUS ENVIRONMENTS, TEACHING HIM TO CHOOSE THE MORE APPROPRIATE NUMERICAL METHOD TO SOLVE THE PROBLEM UNDER EXAMINATION. EXAMPLES WHOSE RESOLUTION REQUIRES THE USAGE OF THE DESCRIBED METHODS WILL BE FURNISHED. COMMUNICATION SKILLS THROUGH THE LABORATORY ACTIVITIES, THE COURSE WILL DEVELOP IN THE STUDENT THE CAPACITY TO MOTIVATE AND DEFEND HIS CHOICES IN THE SOLUTION OF THE CALCULUS PROBLEM, AND WILL SUPPORT THE DEVELOPMENT OF THE CAPACITY TO WORK IN A TEAM. MAKING JUDGEMENTS: THE STUDENTS WILL BE GUIDED TO LEARN IN CRITICAL AND RESPONSIBLE WAY EVERYTHING THAT IS EXPLAINED IN THE CLASSROOM, AND TO ENRICH THEIR JUDGMENT CAPACITIES THROUGH THE STUDY OF THE DIDACTIC MATERIAL INDICATED BY THE TEACHER. THE EVALUATION OF THE DEVELOPED OR USED MATHEMATICAL SOFTWARE, TOGETHER WITH THE COMPARISON OF THE SEVERAL USED ALGORITHMS, AIM TO DEVELOP MATURITY OF JUDGMENT AND CRITICAL SENSE. LEARNING SKILLS: THE STUDENTS WILL DEVELOP THE SKILLS THEY NEED IN ORDER TO CONTINUE THE STUDIES WITH HIGH DEGREE OF AUTONOMY.

KNOWLEDGE AND UNDERSTANDING:
THE AIM OF THE COURSE IS THE THEORETICAL KNOWLEDGE AND CRITICAL ANALYSIS OF THE MAIN NUMERICAL METHODS FOR THE SOLUTION OF PROBLEMS MODELED BY ORDINARY DIFFERENTIAL EQUATIONS, TOGETHER WITH THE DEVELOPMENT OF THE CORRESPONDING MATHEMATICAL SOFTWARE.
PART OF THE COURSE WILL DEAL WITH THE STUDY OF ELEMENTS OF PARALLEL CALCULUS FOR LINEAR ALGEBRA.

APPLYING KNOWLEDGE AND UNDERSTANDING:
THE AIM OF THE COURSE IS TO MAKE THE STUDENT CAPABLE TO SOLVE PROBLEMS OF SCIENTIFIC COMPUTING MODELED BY ORDINARY DIFFERENTIAL EQUATIONS BY DEVELOPING AND USING MATHEMATICAL SOFTWARE AND SUITABLE CALCULUS ENVIRONMENTS, TEACHING HIM TO CHOOSE THE MORE APPROPRIATE NUMERICAL METHOD TO SOLVE THE PROBLEM UNDER EXAMINATION. EXAMPLES WHOSE RESOLUTION REQUIRES THE USAGE OF THE DESCRIBED METHODS WILL BE FURNISHED.

COMMUNICATION SKILLS
THROUGH THE LABORATORY ACTIVITIES, THE COURSE WILL DEVELOP IN THE STUDENT THE CAPACITY TO MOTIVATE AND DEFEND HIS CHOICES IN THE SOLUTION OF THE CALCULUS PROBLEM, AND WILL SUPPORT THE DEVELOPMENT OF THE CAPACITY TO WORK IN A TEAM.

MAKING JUDGEMENTS:
THE STUDENTS WILL BE GUIDED TO LEARN IN CRITICAL AND RESPONSIBLE WAY EVERYTHING THAT IS EXPLAINED IN THE CLASSROOM, AND TO ENRICH THEIR JUDGMENT CAPACITIES THROUGH THE STUDY OF THE DIDACTIC MATERIAL INDICATED BY THE TEACHER.
THE EVALUATION OF THE DEVELOPED OR USED MATHEMATICAL SOFTWARE, TOGETHER WITH THE COMPARISON OF THE SEVERAL USED ALGORITHMS, AIM TO DEVELOP MATURITY OF JUDGMENT AND CRITICAL SENSE.

LEARNING SKILLS:
THE STUDENTS WILL DEVELOP THE SKILLS THEY NEED IN ORDER TO CONTINUE THE STUDIES WITH HIGH DEGREE OF AUTONOMY.

	Prerequisites
	THEORY OF ORDINARY DIFFERENTIAL EQUATIONS. BASICS ON PROGRAMMING LANGUAGES MATLAB AND C.

	Contents
	NUMERICAL METHODS FOR ORDINARY DIFFERENTIAL EQUATIONS: ANALYTICAL APPROXIMATION METHODS, LNEAR MULTISTEP METHODS, PREDICTOR CORRECTOR METHODS, BDF METHODS, RUNGE-KUTTA METHODS, ERROR ESTIMATIONS, CONSISTENCY, CONVERGENCE, ZERO-STABILITY. THEORY OF WEAK STABILITY. STIFF SYSTEMS. STRUCTURE OF A VARIABLE STEPSIZE ALGORITHM. STARTING PROCEDURES. LOCAL TRUNCATION ERROR ESTIMATION. STRATEGIES FOR STEPSIZE CHANGING. SOFTWARE EVALUATION. ELEMENTS OF PARALLEL CALCULUS: PARALLEL ARCHITECTURES, STANDARD MPI, EVALUATION PARAMETERS, MATRIX-MATRIX OPERATIONS, PARALLELIZATION TECHNIQUES.

Contents

NUMERICAL METHODS FOR ORDINARY DIFFERENTIAL EQUATIONS: ANALYTICAL APPROXIMATION METHODS, LNEAR MULTISTEP METHODS, PREDICTOR CORRECTOR METHODS, BDF METHODS, RUNGE-KUTTA METHODS, ERROR ESTIMATIONS, CONSISTENCY, CONVERGENCE, ZERO-STABILITY. THEORY OF WEAK STABILITY. STIFF SYSTEMS. STRUCTURE OF A VARIABLE STEPSIZE ALGORITHM. STARTING PROCEDURES. LOCAL TRUNCATION ERROR ESTIMATION. STRATEGIES FOR STEPSIZE CHANGING. SOFTWARE EVALUATION.
ELEMENTS OF PARALLEL CALCULUS: PARALLEL ARCHITECTURES, STANDARD MPI, EVALUATION PARAMETERS, MATRIX-MATRIX OPERATIONS, PARALLELIZATION TECHNIQUES.

	Teaching Methods
	LECTURES,PRACTICES,LABORATORY, PROJECTS

	Verification of learning
	1) DEVELOPMENT TEST AND EVALUATION OF MATHEMATICAL SOFTWARE BASED ON THE STUDIED NUMERICAL METHOS 2) ORAL EXAM ON THE THEORETICAL CONTENTS OF THE COURSE

	Texts
	J.D.LAMBERT, NUMERICAL METHODS FOR ORDINARY DIFFERENTIAL SYSTEMS, J. WILEY & SONS, 1991. A. MURLI, LEZIONI DI CALCOLO PARALLELO, LIGUORI, 2006. MPI: HTTP://WWW.NETLIB.ORG/UTK/PAPERS/INTRO-MPI/INTRO-MPI.HTML

	More Information
	BEAPAT@UNISA.IT

BETA VERSION Data source ESSE3 [Ultima Sincronizzazione: 2016-09-30]

Beatrice PATERNOSTER | NUMERICAL CALCULUS II