# Matematica | NUMERICAL CALCULUS I

## Matematica NUMERICAL CALCULUS I

 0512300012 DIPARTIMENTO DI MATEMATICA EQF6 MATHEMATICS 2022/2023

 OBBLIGATORIO YEAR OF COURSE 2 YEAR OF DIDACTIC SYSTEM 2018 SPRING SEMESTER
SSD CFU HOURS ACTIVITY TYPE OF ACTIVITY MAT/08 7 56 LESSONS COMPULSORY SUBJECTS, CHARACTERISTIC OF THE CLASS
 BEATRICE PATERNOSTER T ANGELAMARIA CARDONE
ExamDate
APPELLO CALCOLO NUMERICO I24/02/2023 - 09:00
CALCOLO NEMRICO I RIC. FREQ.24/02/2023 - 09:00
Objectives
1.KNOWLEDGE AND UNDERSTANDING
THE AIM OF THE COURSE IS TO GET THEORETICAL KNOWLEDGE AND TO PERFORM 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. THE COURSE IS ALSO DEVOTED TO THE ANALISYS OF THE MAIN PROBLEMS IN THE DEVELOPMENT OF EFFICIENT MATHEMATICAL SOFTWARE. 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, 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. EULER METHOD FOR NUMERIAL SOLUTION OF CHAUCHY INITIAL VALUE PROBLEM. THE MATLAB PROGRAMMING LANGUAGE. DEVELOPMENT OF CODES RELATED TO THE MAIN ALGORITHMS.
Teaching Methods
LECTURES, PRACTICES,LABORATORY, PROJECTS ON DEVELOPMENT AND EVALUATION OF MATHEMATICAL SOFTWARE
Verification of learning
THE FINAL EXAM EVALUATES THE ACQUIRED KNOWLEDGE AND THE ABILITY TO APPLY IT TO SOLVING TYPICAL PROBLEMS OF SCIENTIFIC COMPUTING.

IT CONSISTS IN TWO PARTS: A PRACTICAL TEST, IN WHICH THE MATHEMATICAL SOFTWARE DESIGNED DURING THE COURSE IS USED TO SOLVE SOME QUADRATURE PROBLEMS, PROBLEMS OF APPROXIMATION OF FUNCTIONS AND DATA BY POLYNOMIAL INTERPOLATION, APPROXIMATION IN THE SENSE OF THE LEAST SQUARES AND SPLINES, AND NUMERICAL APPROXIMATION OF EIGENVALUES OF MATRICES; AN ORAL EXAM, BASED ON THE THEORETICAL ITEMS PRESENTED DURING THE LESSONS.
Texts
G.MONEGATO, FONDAMENTI DI CALCOLO NUMERICO, CLUT
V. COMINCIOLI - ANALISI NUMERICA - ED. MC GRAW HILL