Angelamaria CARDONE | LABORATORY OF PROGRAMMING AND CALCULUS

cod. 0512300006

LABORATORY OF PROGRAMMING AND CALCULUS

	0512300006
	DEPARTMENT OF MATHEMATICS
	EQF6
	MATHEMATICS
	2024/2025

PERCORSO SHARED STUDY PATHWAY

	OBBLIGATORIO
	YEAR OF COURSE 1
	YEAR OF DIDACTIC SYSTEM 2018
	SPRING SEMESTER

TEACHING UNITS

SSD	CFU	HOURS	ACTIVITY	TYPE OF ACTIVITY
MAT/08	4	32	LESSONS	COMPULSORY SUBJECTS, CHARACTERISTIC OF THE CLASS
MAT/08	2	24	LAB	COMPULSORY SUBJECTS, CHARACTERISTIC OF THE CLASS

PROFESSORS

	ANGELAMARIA CARDONE T Curriculum
	BEATRICE PATERNOSTER Curriculum

EXAMS

Exam	Date	Session
LABORATORIO DI PROGRAMMAZIONE E CALCOLO	10/01/2025 - 09:00	SESSIONE DI RECUPERO
LABORATORIO DI PROGRAMMAZIONE E CALCOLO	31/01/2025 - 09:00	SESSIONE DI RECUPERO
LABORATORIO DI PROGRAMMAZIONE E CALCOLO	27/02/2025 - 09:00	SESSIONE DI RECUPERO

	Objectives
	COURSE AIM THE COURSE AIMS TO ALLOW STUDENTS TO ACQUIRE THE THEORETICAL KNOWLEDGE OF THE MAIN NUMERICAL METHODS AND MATHEMATICAL SOFTWARE DEVELOPMENT SKILLS FOR THE NUMERICAL RESOLUTION OF LINEAR SYSTEMS AND NON-LINEAR EQUATIONS. KNOWLEDGE AND UNDERSTANDING STUDENTS WILL ACQUIRE BASIC KNOWLEDGE ON: • NUMERICAL METHODS FOR SOLVING LINEAR SYSTEMS WITH DIRECT AND ITERATIVE METHODS, AND NON-LINEAR EQUATIONS; • REPRESENTATION OF REAL NUMBERS ON THE CALCULATOR AND ROUNDING ERRORS; • ALGORITHMIC ASPECTS AND PRINCIPLES ON WHICH THE DEVELOPMENT OF EFFICIENT MATHEMATICAL SOFTWARE IN A MATLAB ENVIRONMENT 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 COMPUTING ENVIRONMENT AND THE RELATED SCIENTIFIC COMPUTING FUNCTIONS. KNOWLEDGE AND UNDERSTANDING STUDENTS WILL ACQUIRE BASIC KNOWLEDGE ON: • NUMERICAL METHODS FOR SOLVING LINEAR SYSTEMS WITH DIRECT AND ITERATIVE METHODS, AND NON-LINEAR EQUATIONS; • REPRESENTATION OF REAL NUMBERS ON THE CALCULATOR AND ROUNDING ERRORS; • ALGORITHMIC ASPECTS AND PRINCIPLES ON WHICH THE DEVELOPMENT OF EFFICIENT MATHEMATICAL SOFTWARE IN A MATLAB ENVIRONMENT 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 COMPUTING ENVIRONMENT AND THE RELATED SCIENTIFIC COMPUTING FUNCTIONS. APPLYING KNOWLEDGE AND UNDERSTANDING STUDENTS WILL BE ABLE TO: • SOLVE SOLVE SYSTEMS OF LINEAR EQUATIONS AND NON-LINEAR EQUATIONS THROUGH THE DEVELOPMENT AND USE OF MATHEMATICAL SOFTWARE IN THE MATLAB ENVIRONMENT; • 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; • ANALYZE THE CONVERGENCE OF AN ITERATIVE METHOD; • ESTIMATE THE ACCURACY OF A NUMERICAL METHOD BY CRITICALLY INTERPRETING THE OBTAINED RESULTS; • 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: • 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.

COURSE AIM
THE COURSE AIMS TO ALLOW STUDENTS TO ACQUIRE THE THEORETICAL KNOWLEDGE OF THE MAIN NUMERICAL METHODS AND MATHEMATICAL SOFTWARE DEVELOPMENT SKILLS FOR THE NUMERICAL RESOLUTION OF LINEAR SYSTEMS AND NON-LINEAR EQUATIONS.

KNOWLEDGE AND UNDERSTANDING
STUDENTS WILL ACQUIRE BASIC KNOWLEDGE ON:
• NUMERICAL METHODS FOR SOLVING LINEAR SYSTEMS WITH DIRECT AND ITERATIVE METHODS, AND NON-LINEAR EQUATIONS;
• REPRESENTATION OF REAL NUMBERS ON THE CALCULATOR AND ROUNDING ERRORS;
• ALGORITHMIC ASPECTS AND PRINCIPLES ON WHICH THE DEVELOPMENT OF EFFICIENT MATHEMATICAL SOFTWARE IN A MATLAB ENVIRONMENT 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 COMPUTING ENVIRONMENT AND THE RELATED SCIENTIFIC COMPUTING FUNCTIONS.

KNOWLEDGE AND UNDERSTANDING
STUDENTS WILL ACQUIRE BASIC KNOWLEDGE ON:
• NUMERICAL METHODS FOR SOLVING LINEAR SYSTEMS WITH DIRECT AND ITERATIVE METHODS, AND NON-LINEAR EQUATIONS;
• REPRESENTATION OF REAL NUMBERS ON THE CALCULATOR AND ROUNDING ERRORS;
• ALGORITHMIC ASPECTS AND PRINCIPLES ON WHICH THE DEVELOPMENT OF EFFICIENT MATHEMATICAL SOFTWARE IN A MATLAB ENVIRONMENT 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 COMPUTING ENVIRONMENT AND THE RELATED SCIENTIFIC COMPUTING FUNCTIONS.

APPLYING KNOWLEDGE AND UNDERSTANDING
STUDENTS WILL BE ABLE TO:
• SOLVE SOLVE SYSTEMS OF LINEAR EQUATIONS AND NON-LINEAR EQUATIONS THROUGH THE DEVELOPMENT AND USE OF MATHEMATICAL SOFTWARE IN THE MATLAB ENVIRONMENT;
• 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;
• ANALYZE THE CONVERGENCE OF AN ITERATIVE METHOD;
• ESTIMATE THE ACCURACY OF A NUMERICAL METHOD BY CRITICALLY INTERPRETING THE OBTAINED RESULTS;
• 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:
• 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
	BASIC LINEAR ALGEBRA (VECTOR AND MATRIX COMPUTATION, LINEAR SYSTEMS ...) AND MATHEMATICAL ANALYSIS (LIMITS, DERIVATIVES).

	Contents
	•SOLVING A PROBLEM WITH THE COMPUTER: FROM THE REAL PROBLEM TO THE METHOD, THE ALGORITHM, THE CODING, THE ANALYSIS OF THE RESULTS. SOURCES AND ERROR PROPAGATION. CONDITIONING OF A NUMERICAL PROBLEM. STABILITY OF AN ALGORITHM. (2 LESSON HOURS) •NUMBERING SYSTEMS; BINARY SYSTEM. REPRESENTATION OF INFORMATION IN MEMORY. INTEGERS AND OVERFLOWS. REPRESENTATION OF REAL NUMBERS: FIXED POINT, FLOATING POINT. ROUNDING ERROR, MACHINE ACCURACY, MINIMUM NUMBER REPRESENTABLE. NUMERICAL CANCELLATION. EVALUATION OF AN ALGORITHM: COMPLEXITY OF SPACE AND TIME. (6 LESSON HOURS) •REFERENCES TO VECTOR SPACES. VECTORS AND MATRICES, STANDARDS. PARTICULAR MATRICES. POSITIVE DEFINED SYMMETRIC MATRICES: SYLVESTER CRITERION. (2 LESSON HOURS) •NUMERICAL SOLUTION OF LINEAR SYSTEMS; DIRECT AND ITERATIVE METHODS. CONDITIONING INDEX OF LINEAR SYSTEMS.RESOLUTION OF TRIANGULAR SYSTEMS, FORWARD AND BACKWARD SUBSTITUTION METHODS, COMPUTATIONAL COMPLEXITY. METHOD OF GAUSS ELIMINATION AND CALCULATION OF ITS COMPLEXITY; PIVOTING AND SCALING. FACTORING LU. FACTORIZATION OF POSITIVE DEFINITE SYMMETRIC MATRICES: CHOLESKY THEOREM. ITERATIVE METHODS FOR LINEAR SYSTEMS: JACOBI AND GAUSS-SEIDEL METHODS. ITERATIVE METHODS IN MATRIX FORM, ITERATION MATRIX. CONVERGENCE, CONVERGENCE RATE. COMPUTATIONAL COMPLEXITY OF ITERATIVE METHODS. THE SOR METHOD. ITERATIVE METHOD-BASED ALGORITHMS: ERROR ESTIMATION AND CRASH CRITERIA. (16 LESSON HOURS) •REAL ROOTS OF NONLINEAR EQUATIONS. BISECTION METHOD. LOCAL LINEARISATION METHODS. SECANTI METHOD, TANGENT METHOD (NEWTON-RAPHSON). CONVERGENCE THEOREMS, ORDER OF CONVERGENCE. NEWTON’S METHOD FOR MULTIPLE ROOT EQUATIONS. FIXED POINT ITERATIONS, CONVERGENCE THEOREM. COMPUTATIONAL ASPECTS: CONVERGENCE TEST, CONVERGENCE RATE. NUMERICAL CALCULATION OF THE ROOTS OF POLYNOMIALS: PROBLEM OF CONDITIONING. (6 LESSONS) •MATLAB ALGORITHM AND CODING OF PROGRAMMES BASED ON THE MAIN METHODS USED. (24 HOURS LABORATORY )

Contents

•SOLVING A PROBLEM WITH THE COMPUTER: FROM THE REAL PROBLEM TO THE METHOD, THE ALGORITHM, THE CODING, THE ANALYSIS OF THE RESULTS. SOURCES AND ERROR PROPAGATION. CONDITIONING OF A NUMERICAL PROBLEM. STABILITY OF AN ALGORITHM. (2 LESSON HOURS)
•NUMBERING SYSTEMS; BINARY SYSTEM. REPRESENTATION OF INFORMATION IN MEMORY. INTEGERS AND OVERFLOWS. REPRESENTATION OF REAL NUMBERS: FIXED POINT, FLOATING POINT. ROUNDING ERROR, MACHINE ACCURACY, MINIMUM NUMBER REPRESENTABLE. NUMERICAL CANCELLATION. EVALUATION OF AN ALGORITHM: COMPLEXITY OF SPACE AND TIME. (6 LESSON HOURS)
•REFERENCES TO VECTOR SPACES. VECTORS AND MATRICES, STANDARDS. PARTICULAR MATRICES. POSITIVE DEFINED SYMMETRIC MATRICES: SYLVESTER CRITERION. (2 LESSON HOURS)
•NUMERICAL SOLUTION OF LINEAR SYSTEMS; DIRECT AND ITERATIVE METHODS. CONDITIONING INDEX OF LINEAR SYSTEMS.RESOLUTION OF TRIANGULAR SYSTEMS, FORWARD AND BACKWARD SUBSTITUTION METHODS, COMPUTATIONAL COMPLEXITY. METHOD OF GAUSS ELIMINATION AND CALCULATION OF ITS COMPLEXITY; PIVOTING AND SCALING. FACTORING LU. FACTORIZATION OF POSITIVE DEFINITE SYMMETRIC MATRICES: CHOLESKY THEOREM. ITERATIVE METHODS FOR LINEAR SYSTEMS: JACOBI AND GAUSS-SEIDEL METHODS. ITERATIVE METHODS IN MATRIX FORM, ITERATION MATRIX. CONVERGENCE, CONVERGENCE RATE. COMPUTATIONAL COMPLEXITY OF ITERATIVE METHODS. THE SOR METHOD. ITERATIVE METHOD-BASED ALGORITHMS: ERROR ESTIMATION AND CRASH CRITERIA. (16 LESSON HOURS)
•REAL ROOTS OF NONLINEAR EQUATIONS. BISECTION METHOD. LOCAL LINEARISATION METHODS. SECANTI METHOD, TANGENT METHOD (NEWTON-RAPHSON). CONVERGENCE THEOREMS, ORDER OF CONVERGENCE. NEWTON’S METHOD FOR MULTIPLE ROOT EQUATIONS. FIXED POINT ITERATIONS, CONVERGENCE THEOREM. COMPUTATIONAL ASPECTS: CONVERGENCE TEST, CONVERGENCE RATE. NUMERICAL CALCULATION OF THE ROOTS OF POLYNOMIALS: PROBLEM OF CONDITIONING. (6 LESSONS)
•MATLAB ALGORITHM AND CODING OF PROGRAMMES BASED ON THE MAIN METHODS USED. (24 HOURS LABORATORY )

	Teaching Methods
	THE TEACHING (6 CREDITS, 56 HOURS) CONSISTS OF LECTURES (4 CREDITS, 32 HOURS) AND LABORATORY LESSONS (2 CREDITS, 24 HOURS). THE LECTURES WILL PRESENT THE METHODOLOGIES AND ALGORITHMS THAT THEN, DURING THE EXERCISES, WILL BE ENCODED IN SCIENTIFIC COMPUTING ENVIRONMENTS AND TESTED ON SIGNIFICANT TEST EXAMPLES. STUDENTS WILL BE GUIDED IN THE VERIFICATION OF THE ACCURACY, STABILITY AND EFFICIENCY OF THE NUMERICAL METHODS USED. THE FUNCTIONALITIES PROVIDED BY THE E-LEARNING PLATFORM PROVIDED BY THE COURSE OF STUDY (IN PARTICULAR RESOURCES, QUIZZES, FORUMS) WILL ALSO BE USED.

Teaching Methods

THE TEACHING (6 CREDITS, 56 HOURS) CONSISTS OF LECTURES (4 CREDITS, 32 HOURS) AND LABORATORY LESSONS (2 CREDITS, 24 HOURS).
THE LECTURES WILL PRESENT THE METHODOLOGIES AND ALGORITHMS THAT THEN, DURING THE EXERCISES, WILL BE ENCODED IN SCIENTIFIC COMPUTING ENVIRONMENTS AND TESTED ON SIGNIFICANT TEST EXAMPLES. STUDENTS WILL BE GUIDED IN THE VERIFICATION OF THE ACCURACY, STABILITY AND EFFICIENCY OF THE NUMERICAL METHODS USED.

THE FUNCTIONALITIES PROVIDED BY THE E-LEARNING PLATFORM PROVIDED BY THE COURSE OF STUDY (IN PARTICULAR RESOURCES, QUIZZES, FORUMS) WILL ALSO BE USED.

	Verification of learning
	LEARNING AUDIT THE EXAMINATION TEST SHALL ASSESS THE KNOWLEDGE ACQUIRED AND THE ABILITY TO APPLY IT TO THE RESOLUTION OF PROBLEMS TYPICAL OF NUMERICAL CALCULATION, INCLUDING THROUGH MATHEMATICAL SOFTWARE WRITTEN IN THE MATLAB/OCTAVE ENVIRONMENT. IT CONSISTS OF TWO TESTS: A PRACTICAL TEST, IN WHICH THE MATLAB COMPUTING ENVIRONMENT AND THE MATHEMATICAL SOFTWARE DESIGNED AND MANUFACTURED DURING THE COURSE FOR PERFORMING EXERCISES RELATING TO: FLOATING-POINT ARITHMETIC, RESOLUTION OF SYSTEMS OF LINEAR EQUATIONS BY DIRECT AND ITERATIVE METHODS, RESOLUTION OF NONLINEAR EQUATIONS; AN ORAL INTERVIEW, FOR THE PURPOSE OF ASSESSING THE THEORETICAL KNOWLEDGE PRESENTED IN THE LECTURE. THE PRACTICAL TEST IS PREPARATORY TO THE ORAL INTERVIEW AND LASTS ABOUT ONE HOUR. THE PRACTICAL TEST WEIGHS ABOUT 40% ON THE FINAL GRADE, THE ORAL INTERVIEW WEIGHS ABOUT 60%. THE INTERVIEW SHALL TAKE PLACE IMMEDIATELY AFTER THE PRACTICAL TEST AND SHALL LAST APPROXIMATELY 30 MINUTES. THE HONOURS MAY BE AWARDED TO STUDENTS WHO DEMONSTRATE THEIR ABILITY TO APPLY THE KNOWLEDGE AND SKILLS ACQUIRED WITH A CRITICAL SENSE AND ORIGINALITY.

Verification of learning

LEARNING AUDIT
THE EXAMINATION TEST SHALL ASSESS THE KNOWLEDGE ACQUIRED AND THE ABILITY TO APPLY IT TO THE RESOLUTION OF PROBLEMS TYPICAL OF NUMERICAL CALCULATION, INCLUDING THROUGH MATHEMATICAL SOFTWARE WRITTEN IN THE MATLAB/OCTAVE ENVIRONMENT.
IT CONSISTS OF TWO TESTS: A PRACTICAL TEST, IN WHICH THE MATLAB COMPUTING ENVIRONMENT AND THE MATHEMATICAL SOFTWARE DESIGNED AND MANUFACTURED DURING THE COURSE FOR PERFORMING EXERCISES RELATING TO: FLOATING-POINT ARITHMETIC, RESOLUTION OF SYSTEMS OF LINEAR EQUATIONS BY DIRECT AND ITERATIVE METHODS, RESOLUTION OF NONLINEAR EQUATIONS; AN ORAL INTERVIEW, FOR THE PURPOSE OF ASSESSING THE THEORETICAL KNOWLEDGE PRESENTED IN THE LECTURE.

THE PRACTICAL TEST IS PREPARATORY TO THE ORAL INTERVIEW AND LASTS ABOUT ONE HOUR. THE PRACTICAL TEST WEIGHS ABOUT 40% ON THE FINAL GRADE, THE ORAL INTERVIEW WEIGHS ABOUT 60%. THE INTERVIEW SHALL TAKE PLACE IMMEDIATELY AFTER THE PRACTICAL TEST AND SHALL LAST APPROXIMATELY 30 MINUTES. THE HONOURS MAY BE AWARDED TO STUDENTS WHO DEMONSTRATE THEIR ABILITY TO APPLY THE KNOWLEDGE AND SKILLS ACQUIRED WITH A CRITICAL SENSE AND ORIGINALITY.

	Texts
	1.G. MONEGATO – METODI E ALGORITMI PER IL CALCOLO NUMERICO – ED. CLUT 2.A. MURLI, G. GIUNTA, G. LACCETTI, M. RIZZARDI - LABORATORIO DI PROGRAMMAZIONE I, LIGUORI EDITORE 3.A. QUARTERONI, F. SALERI, CALCOLO SCIENTIFICO: ESERCIZI E PROBLEMI RISOLTI CON MATLAB E OCTAVE, SPRINGER. 4.SLIDES OF THE COURSE: WWW.ELEARNING.UNISA.IT

	More Information
	ANCARDONE@UNISA.IT

BETA VERSION Data source ESSE3 [Ultima Sincronizzazione: 2024-11-29]

Angelamaria CARDONE | LABORATORY OF PROGRAMMING AND CALCULUS