Matematica | NUMERICAL CALCULUS II

cod. 0512300033

NUMERICAL CALCULUS II

	0512300033
	DIPARTIMENTO DI MATEMATICA

	MATHEMATICS
	2013/2014

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

	DAJANA CONTE T Curriculum
	BEATRICE PATERNOSTER 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. 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.

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