# Matematica | NUMERICAL CALCULUS I

## Matematica NUMERICAL CALCULUS I

 0512300012 DIPARTIMENTO DI MATEMATICA EQF6 MATHEMATICS 2016/2017

 OBBLIGATORIO YEAR OF COURSE 2 YEAR OF DIDACTIC SYSTEM 2010 SECONDO SEMESTRE
SSD CFU HOURS ACTIVITY TYPE OF ACTIVITY MAT/08 7 56 LESSONS COMPULSORY SUBJECTS, CHARACTERISTIC OF THE CLASS
 BEATRICE PATERNOSTER T ANGELAMARIA CARDONE
Objectives
1.KNOWLEDGE AND UNDERSTANDING
THE AIM OF THE COURSE IS TO DISCUSS THE MAIN PROBLEMS IN THE DEVELOPMENT OF EFFICIENT MATHEMATICAL SOFTWARE. IT IS DEVOTED TO THE THEORETICAL KNOWLEDGE AND A CRITICAL ANALYSIS OF THE MAIN NUMERICAL METHODS FOR THE BASIC ARGUMENTS, LIKE THE APPROXIMATION OF FUNCTIONS AND OF NUMERICAL DATA, THE COMPUTATION OF DEFINITE INTEGRALS, THE NUMERICAL SOLUTION OF NONLINEAR SYSTEMS AND THE COMPUTATION OF THE EIGENVALUES OF A MATRIX. MOREOVER THE STUDENT WILL LEARN THE METHODOLOGY FOR THE PROJECT OF EFFICIENT ALGORITHM AND THE USAGE OF SUITABLE ENVIRONMENTS FOR NUMERICAL COMPUTATION TO SOLVE PROBLEMS OF SCIENTIFIC COMPUTATION.
2.APPLYING KNOWLEDGE AND UNDERSTANDING
BY MEANS OF THE PRACTICE IN THE LABORATORY, THE STUDENTS WILL BE ABLE TO EXPERIMENT NUMERICAL METHODS, TO ESTIMATE THE RELIABILITY OF THE OBTAINED RESULTS, TO DEVELOP ELEMENTS OF MATHEMATICAL SOFTWARE AND EVALUATE PERFORMANCES.
Prerequisites
ELEMENTS OF DISCRETE MATHEMATICS AND LINEAR ALGEBRA. ELEMENTS OF MATHEMATICAL ANALYSIS: CONTINUOUS FUNCTIONS AND MAIN THEOREMS, CONCEPTS OF DERIVATIVE AND INTEGRALS.
Contents
ERROR ANALYSIS AND FLOATING - POINT ARITHMETIC. APPROXIMATION OF DATA AND FUNCTIONS. POLYNOMIAL INTERPOLATION AND SPLINES. LEAST SQUARES APPROXIMATION. ITERATIVE METHODS FOR NONLINEAR EQUATIONS. NUMERICAL QUADRATURE: NEWTON - COTES AND GAUSSIAN FORMULAS. AUTOMATIC INTEGRATORS BASED ON FIXED AND ADAPTATIVE SCHEMES. EIGENVALUES OF MATRICES. ITERATIVE METHODS AND METHODS BASED ON SIMILARITY TRANSFORMATIONS. THE MATLAB PROGRAMMING LANGUAGE. DEVELOPMENT OF CODES RELATED TO THE MAIN ALGORITHMS.
Teaching Methods
LECTURES, EXERCISES IN LABORATORY, DEVELOPMENT OF MATHEMATICAL SOFTWARE
Verification of learning
- FOR STUDENTS THAT ATTEND THE COURSE WITH SUCCESS: ONE SHORT MID-TERM EXAMINATION DURING ON THE DEVELOPMENT OF ELEMENTS OF MATHEMATICAL SOFTWARE, FINAL EXAMINATION
- FOR STUDENTS WHICH ATTEND THE COURSE WITHOUT SUCCESS OR WHICH DON’T ATTEND THE COURSE: TUTORIAL ACTIVITY IN LABORATORY, ORAL EXAMINATION
Texts
G.MONEGATO, FONDAMENTI DI CALCOLO NUMERICO, CLUT
V. COMINCIOLI - ANALISI NUMERICA - ED. MC GRAW HILL