# Matematica | NUMERICAL CALCULUS II

## Matematica NUMERICAL CALCULUS II

 0512300033 DIPARTIMENTO DI MATEMATICA MATHEMATICS 2015/2016

 YEAR OF COURSE 3 YEAR OF DIDACTIC SYSTEM 2010 PRIMO SEMESTRE
SSD CFU HOURS ACTIVITY TYPE OF ACTIVITY MAT/08 6 48 LESSONS COMPULSORY SUBJECTS, CHARACTERISTIC OF THE CLASS
 BEATRICE PATERNOSTER T RAFFAELE D'AMBROSIO
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.
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.
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