# Matematica | NUMERICAL CALCULUS II

## Matematica NUMERICAL CALCULUS II

 0512300033 DIPARTIMENTO DI MATEMATICA MATHEMATICS 2013/2014

 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
 DAJANA CONTE T BEATRICE PATERNOSTER
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. KNOWLEDGE OF PROGRAMMING IN C AND MATLAB.
Contents
Numerical methods for Ordinary Differential Equations. Linear multistep methods. Predictor-corrector methods. BDF methods. Runge-Kutta methods. Consistency, zero-stability, convergence. Theory of weak stability. Stiff systems. Variable stepsize algorithm, starting procedure for changing stepsize. Software evaluation. Elements of parallel calculus: parallel architectures, usage of MPI interface, evaluations of parallel software. Parallel operations on matrices.
Teaching Methods
Frontal lectures, practice exercises in laboratory, design and usage of mathematical software.
Verification of learning
Design, test and evaluation of mathematical software based on the analyzed numerical methods. Oral exams of the topics 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