2. Professors
  3. CONTE Dajana
  4. Teaching

SCIENTIFIC CALCULUS

Dajana CONTE SCIENTIFIC CALCULUS

0512100045
COMPUTER SCIENCE
Bachelor or equivalent first cycle
COMPUTER SCIENCE
2026/2027

YEAR OF COURSE 3
YEAR OF DIDACTIC SYSTEM 2017
SPRING SEMESTER
CFUHOURSACTIVITY
648LESSONS
DAJANA CONTE T Curriculum
Objectives
COURSE AIM
THE COURSE IS AIMED AT ACQUIRING THEORETICAL KNOWLEDGE OF THE MAIN NUMERICAL METHODS AND MATHEMATICAL SOFTWARE DEVELOPMENT SKILLS FOR THE NUMERICAL RESOLUTION OF SCIENTIFIC CALCULUS PROBLEMS OF INTEREST IN COMPUTER SCIENCE.

KNOWLEDGE AND UNDERSTANDING
STUDENTS WILL ACQUIRE BASIC KNOWLEDGE ON:
•NUMERICAL METHODS RELATED TO THE FOLLOWING TOPICS: NUMERICAL RESOLUTION OF LINEAR SYSTEMS WITH DIRECT AND ITERATIVE METHODS, APPROXIMATION OF DATA AND FUNCTIONS, CALCULATION OF EIGENVALUES OF MATRICES;
•ALGORITHMIC ASPECTS AND PRINCIPLES ON WHICH THE DEVELOPMENT OF EFFICIENT MATHEMATICAL SOFTWARE IN SCIENTIFIC COMPUTING ENVIRONMENTS (MATLAB OR PYTHON) IS BASED, WITH REFERENCE TO THE ESTIMATION OF THE RELIABILITY OF THE OBTAINED RESULTS AND THE EVALUATION OF THE PERFORMANCE OF THE DEVELOPED SOFTWARE;
•BASIC KNOWLEDGE OF THE MATLAB (OR PYTHON) COMPUTING ENVIRONMENT AND THE RELATED SCIENTIFIC COMPUTING FUNCTIONS.

APPLYING KNOWLEDGE AND UNDERSTANDING
STUDENTS WILL BE ABLE TO:
•SOLVE SCIENTIFIC CALCULUS PROBLEMS PRESENT IN VARIOUS COMPUTER SCIENCE APPLICATIONS THROUGH THE DEVELOPMENT AND USE OF MATHEMATICAL SOFTWARE AND APPROPRIATE COMPUTING ENVIRONMENTS (MATLAB/PYTHON);
•CARRY OUT TESTING AND EVALUATION OF MATHEMATICAL SOFTWARE IN TERMS OF ACCURACY AND EFFICIENCY, ALSO BY COMPARING PERFORMANCE BETWEEN DIFFERENT CODES.

MAKING JUDGMENTS
STUDENTS WILL BE ABLE TO:
•CHOOSE THE MOST SUITABLE NUMERICAL METHOD FOR THE PROBLEM UNDER EXAMINATION THROUGH THE ANALYSIS OF THE CHARACTERISTICS OF THE PROBLEM ITSELF, SUCH AS DATA STRUCTURE, REQUIRED ACCURACY;
•ANALYZE THE CONVERGENCE OF AN ITERATIVE METHOD;
•ESTIMATE THE ACCURACY OF A NUMERICAL METHOD BY CRITICALLY INTERPRETING THE RESULTS OBTAINED;
•PROVIDE THEORETICAL JUSTIFICATIONS FOR THE EFFECTIVENESS OF DIFFERENT METHODS FOR SOLVING THE PROBLEMS STUDIED;
•RECOGNIZE ERRORS RESULTING FROM MACHINE OPERATIONS (IN FLOATING POINT ARITHMETIC).

COMMUNICATION SKILLS
STUDENTS WILL BE ABLE TO:
•DESCRIBE THE RESULTS OBTAINED USING GRAPHS AND TABLES;
•COMMUNICATE THE KNOWLEDGE ACQUIRED IN WRITTEN AND ORAL FORM WITH CORRECT TECHNICAL-SCIENTIFIC LANGUAGE.

LEARNING SKILL
STUDENTS WILL BE ABLE TO:
•APPLY THE KNOWLEDGE ACQUIRED TO CONTEXTS DIFFERENT FROM THOSE PRESENTED DURING THE COURSE;
•LEARN NEW METHODS FOR DEVELOPING MATHEMATICAL SOFTWARE, APPRECIATING THEIR LIMITS AND ADVANTAGES;
•PROCEED WITH THE CONTINUOUS UPDATING OF ONE'S KNOWLEDGE, USING TECHNICAL AND SCIENTIFIC LITERATURE, USING TRADITIONAL BIBLIOGRAPHIC TOOLS AND DIGITAL RESOURCES.


Prerequisites
Knowledge on elements of discrete mathematics and matrix theory.
Contents
FOR EACH TOPIC THE HOURS OF LECTURES (F) AND LABORATORY (L) ARE INDICATED

REPRESENTATION OF REAL NUMBERS IN A COMPUTER, ROUND-OFF ERROR, MACHINE PRECISION. CONDITIONING AND STABILITY. (6F+6L)

MATHEMATICS OF WEB AND GOOGLE'S PAGERANK PROBLEM. FORMULATION OF PAGERANK PROBLEM AS LINEAR SYSTEM. LINEAR SYSTEMS: CONDITION NUMBER, TRIANGULAR SYSTEMS, GAUSSIAN ELIMINATION, PIVOTING, ITERATIVE METHODS, CONVERGENCE. FACTORIZATION OF MATRICES AND APPLICATIONS IN IMAGE COMPRESSION. (8F+8L)

FORMULATION OF GOOGLE'S PAGERANK AS AN EIGENVALUE PROBLEM AND POWER'S METHOD. (3F+3L)

MATHEMATICAL FUNCTIONS FOR COMPUTER GRAPHICS: POLYNOMIAL AND SPLINE INTERPOLATION. APPLICATIONS OF POLYNOMIAL INTERPOLATION TO CRYPTOGRAPHY. LEAST-SQUARE APPROXIMATION OF EXPERIMENTAL DATA. (5F+5L)

INTRODUCTION TO PARALLEL LINEAR ALGEBRA. NOTES TO TWITTER'S PAGERANK AND PARALLEL ALGORITHM FOR ITS CALCULATION. (2F+2L)

ELEMENTS OF PROGRAMMING IN MATLAB/OCTAVE/PYTHON.
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.
More Information

•HTTP://ELEARNING.INFORMATICA.UNISA.IT
  BETA VERSION Data source ESSE3 [Ultima Sincronizzazione: 2026-07-31]