# Computer science | SCIENTIFIC CALCULUS

## Computer science SCIENTIFIC CALCULUS

 0512100045 COMPUTER SCIENCE EQF6 COMPUTER SCIENCE 2021/2022

 YEAR OF COURSE 3 YEAR OF DIDACTIC SYSTEM 2017 SPRING SEMESTER
SSD CFU HOURS ACTIVITY TYPE OF ACTIVITY MAT/08 6 48 LESSONS SUPPLEMENTARY COMPULSORY SUBJECTS
 DAJANA CONTE T
Objectives
KNOWLEDGE AND UNDERSTANDING
THE AIM OF THE COURSE IS THE THEORETICAL KNOWLEDGE AND CRITICAL ANALYSIS OF THE MAIN NUMERICAL METHODS CONCERNING THE BASIC TOPICS OF NUMERICAL ANALYSIS. PARTICULAR ATTENTION WILL BE PAID TO THE PRINCIPLES ABOUT THE DEVELOPMENT OF EFFICIENT MATHEMATICAL SOFTWARE, WITH REGARD TO THE ESTIMATE OF ACCURACY OF THE OBTAINED RESULTS, THE EVALUATION OF THE PERFORMANCE OF THE DEVELOPED SOFTWARE, THE COMPARISON AMONG DIFFERENT METHODS, THE EXTERNAL AND INTERNAL DOCUMENTATION.

APPLYING KNOWLEDGE AND UNDERSTANDING
THE STUDENT SHOULD BE ABLE:
- TO SOLVE PROBLEMS OF SCIENTIFIC CALCULUS, BY MEANS OF THE DEVELOPMENT AND THE USE OF MATHEMATICAL SOFTWARE AND SUITABLE COMPUTING ENVIRONMENT (MATLAB, OR OCTAVE, OR SCILAB);

- TO CHOOSE THE MOST SUITABLE NUMERICAL METHOD WITH RESPECT TO THE PROBLEM TO SOLVE, BY ANALYZING THE FEATURES OF THE PROBLEM, LIKE THE STRUCTURE OF THE DATA, THE REQUESTED ACCURACY AND THE STABILITY.
Prerequisites
Knowledge on elements of discrete mathematics and matrix theory.
Contents
FLOATING POINT ARITHMETICS, REPRESENTATION OF NUMBERS IN A COMPUTER, ROUND-OFF ERROR, MACHINE PRECISION. CONDITIONING AND STABILITY.

NUMERICAL LINEAR ALGEBRA. LINEAR SYSTEMS: CONDITION NUMBER, TRIANGULAR SYSTEMS, GAUSSIAN ELIMINATION, PIVOTING, LU FACTORIZATION, CHOLESKI FACTORIZATION, ITERATIVE METHODS, CONVERGENCE, SINGULAR VALUE DECOMPOSITION.

APPROXIMATION OF DATA AND FUNCTIONS. POLYNOMIAL INTERPOLATION, ERROR ANALYSIS, CONVERGENCE, SPLINE FUNCTIONS, LEAST-SQUARE APPROXIMATION.

NUMERICAL METHODS FOR EIGENVALUES AND GOOGLE PAGERANK.

INTRODUCTION TO PARALLEL LINEAR ALGEBRA.

ELEMENTS OF PROGRAMMING IN MATLAB/OCTAVE.
Teaching Methods
The lectures are intended to introduce and present methods and algorithms that will be implemented in laboratory and tested on a set of problems.
For each topic, situations of interest in the practice that require the employ of the introduced numerical techniques will also be presented.
The course is enriched by simulations of the exam test (meglio simulation of the exam test enrich the course), in order to assist the preparation of the student.
The e-learning platform will be widely used during the course (especially resources, quiz, forum).
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 SOFTWARE DESIGNED DURING THE COURSE IS USED TO SOLVE A LINEAR SYSTEM BY DIRECT AND ITERATIVE METHODS, A PROBLEM OF APPROXIMATION OF FUNCTIONS AND DATA BY POLYNOMIAL INTERPOLATION, APPROXIMATION IN THE SENSE OF THE LEAST SQUARES AND SPLINES, A PROBLEM OF NUMERICAL APPROXIMATION OF EIGENVALUES OF MATRICES BY THE POWER METHOD; AN ORAL EXAM, BASED ON THE THEORETICAL ITEMS PRESENTED DURING THE LESSONS.

DURING THE COURSE, A MID-TERM TEST WILL BE CARRIED OUT, ACCORDING TO THE SAME RULES OF THE FINAL EXAM.
Texts
G. MONEGATO, FONDAMENTI DI CALCOLO NUMERICO, CLUT 1998

THE SLIDES OF THE LECTURES WILL ALSO BE PROVIDED, AS A GUIDANCE FOR THE ORGANIZATION OF THE STUDY.

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