Gianluca FRASCA CACCIA | SCIENTIFIC COMPUTING
Gianluca FRASCA CACCIA SCIENTIFIC COMPUTING
cod. 0522200045
SCIENTIFIC COMPUTING
| 0522200045 | |
| DEPARTMENT OF MATHEMATICS | |
| EQF7 | |
| MATHEMATICS | |
| 2024/2025 |
| OBBLIGATORIO | |
| YEAR OF COURSE 1 | |
| YEAR OF DIDACTIC SYSTEM 2018 | |
| AUTUMN SEMESTER |
| SSD | CFU | HOURS | ACTIVITY | |
|---|---|---|---|---|
| MAT/08 | 6 | 48 | LESSONS |
| Objectives | |
|---|---|
| COURSE AIM THE TEACHING IS AIMED AT ACQUIRING THEORETICAL KNOWLEDGE AND CRITICALLY ANALYZING THE MAIN NUMERICAL METHODS RELATING TO THE NUMERICAL RESOLUTION OF PROBLEMS MODELED BY ORDINARY DIFFERENTIAL EQUATIONS (ODES), ALSO DEVELOPING THE RELATED MATHEMATICAL SOFTWARE. KNOWLEDGE AND UNDERSTANDING STUDENTS WILL ACQUIRE BASIC KNOWLEDGE ON: •NUMERICAL METHODS FOR SOLVING ODES; •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. APPLYING KNOWLEDGE AND UNDERSTANDING STUDENTS WILL BE ABLE TO: •SOLVE SYSTEMS OF ODES USING MATHEMATICAL SOFTWARE; •THEORETICALLY AND EXPERIMENTALLY ANALYZE THE PROPERTIES OF NUMERICAL METHODS FOR ODES: CONVERGENCE AND STABILITY; •CARRY OUT TESTING AND EVALUATION OF MATHEMATICAL SOFTWARE IN TERMS OF ACCURACY AND EFFICIENCY, ALSO BY COMPARING PERFORMANCE AMONG DIFFERENT CODES. MAKING JUDGMENTS STUDENTS WILL BE ABLE TO: •CHOOSE THE MOST SUITABLE NUMERICAL METHOD FOR THE PROBLEM UNDER CONSIDERATION THROUGH THE ANALYSIS OF THE CHARACTERISTICS OF THE PROBLEM ITSELF; •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 STUDIED PROBLEMS. COMMUNICATION SKILLS STUDENTS WILL BE ABLE TO: •DESCRIBE THE OBTAINED RESULTS USING GRAPHS AND TABLES; •COMMUNICATE THE ACQUIRED KNOWLEDGE IN WRITTEN AND ORAL FORM WITH CORRECT TECHNICAL-SCIENTIFIC LANGUAGE. LEARNING SKILL STUDENTS WILL BE ABLE TO: •APPLY THE ACQUIRED KNOWLEDGE 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 | |
|---|---|
| THEORY OF ORDINARY DIFFERENTIAL EQUATIONS. BASICS ON PROGRAMMING LANGUAGE MATLAB |
| Contents | |
|---|---|
| NUMERICAL METHODS FOR ORDINARY DIFFERENTIAL EQUATIONS, MULTISTEP LINEAR METHODS (8 HOURS). PREDICTOR-CORRECTOR METHODS (4 HOURS). RUNGE-KUTTA METHODS (4 HOURS). ORDER AND ERROR ESTIMATES (6 HOURS). CONSISTENCY, CONVERGENCE, ZERO-STABILITY (8 HOURS). WEAK STABILITY THEORY, STIFF SYSTEMS (6 HOURS). STRUCTURE OF A VARIABLE PITCH ALGORITHM: STARTING PROCEDURES, ESTIMATION OF THE TRUNCATION ERROR, STRATEGIES FOR PITCH CHANGE, SOFTWARE EVALUATION (4 HOURS). APPROXIMATION OF THE NUMERICAL SOLUTION WITH NON-POLYNOMIAL BASES (2 HOURS). INTRODUCTION TO NUMERICAL METHODS FOR STOCHASTIC DIFFERENTIAL EQUATIONS: WEAK AND STRONG CONVERGENCE, EULER-MARUYAMA METHOD (6 HOURS). |
| Teaching Methods | |
|---|---|
| THE COURSE IS DIVIDED INTO FRONTAL LESSONS (6 CREDITS, 48 HOURS). DURING THE LESSONS, EXERCISES, LABORATORY ACTIVITIES WILL ALSO BE CARRIED OUT AND PROJECTS WILL BE CARRIED OUT FOR THE DEVELOPMENT AND EVALUATION OF MATHEMATICAL SOFTWARE. THE FRONTAL LESSONS WILL PRESENT THE METHODOLOGIES AND THE ALGORITHMS THAT THEN, DURING THE EXERCISES, WILL BE CODED IN SCIENTIFIC CALCULATION ENVIRONMENTS AND TESTED ON TEST PROBLEMS OF INTEREST. PART OF THE EXERCISES WILL BE DEDICATED TO PROJECT ACTIVITIES IN SMALL GROUPS, FOR THE PURPOSE OF DEVELOPING MATHEMATICAL SOFTWARE AND TESTING IT ON TEST PROBLEMS PROVIDED BY THE TEACHER, VERIFYING THE PROPERTIES OF ACCURACY, STABILITY AND EFFICIENCY OF THE METHODS. WORKING IN SMALL GROUPS ALSO AIMS TO GET STUDENTS USED TO GROUP WORK. |
| Verification of learning | |
|---|---|
| THE FINAL EXAM CONSISTS IN THE DISCUSSION OF A PRACTICAL PART IN THE LABORATORY AND AN ORAL PART ON THE CONTENTS OF THE COURSE. THE PRACTICAL PARTY REGARDS THE USE OF THE MATHEMATICAL SOFTWARE DEVELOPED DURING THE TEACHING, TO BE APPLIED TO CERTAIN TEST PROBLEMS BASED ON ORDINARY DIFFERENTIAL EQUATIONS, TO CHECK THE ABILITY TO APPLY THE ACQUIRED KNOWLEDGE. THE ORAL PART REGARDS THE THEORETICAL CONTENTS OF TEACHING, IN ORDER TO CHECK THE ABILITY TO ANALYZING AND PRESENTING WITH RIGOR THE PROPERTIES OF NUMERICAL METHODS FOR ORDINARY DIFFERENTIAL EQUATIONS PRESENTED DURING THE LESSONS. THE PRACTICAL TEST IS PREPARATORY TO THE ORAL INTERVIEW AND LASTS ABOUT AN HOUR. THE PRACTICAL TEST WEIGHS ABOUT 40% ON THE FINAL MARK, THE ORAL INTERVIEW WEIGHS ABOUT 60%. THE INTERVIEW TAKES PLACE IMMEDIATELY AFTER THE PRACTICAL TEST AND LASTS ABOUT 30 MINUTES. HONORS CAN BE AWARDED TO STUDENTS WHO DEMONSTRATE THAT THEY ARE ABLE TO APPLY THE ACQUIRED KNOWLEDGE AND SKILLS WITH A CRITICAL SENSE AND WITH ORIGINALITY. |
| Texts | |
|---|---|
| J.D.LAMBERT, NUMERICAL METHODS FOR ORDINARY DIFFERENTIAL SYSTEMS, J. WILEY & SONS, 1991. R. D’AMBROSIO, NUMERICAL APPROXIMATION OF ORDINARY DIFFERENTIAL PROBLEMS, FROM DETERMINISTIC TO STOCHASTIC NUMERICAL METHODS, SPRINGER, 2023. SLIDES ON THE TEAMS CHANNEL OF THE COURSE: THE MATERIAL OF ACADEMIC YEAR 2023/2024 IS ON: HTTPS://UNISALERNO.SHAREPOINT.COM/:F:/S/UNI23-CALCOLOSCIENTIFICO-052220004577735NESSUNPARTIZIONAMENT/EIYTI4AANU1HNYIW_AFFEI4BCM3BIXUW2DATFN_YTKPOLA?E=XKYLJF |
| More Information | |
|---|---|
| TEACHERS' E-MAIL: BEAPAT@UNISA.IT, DAJCONTE@UNISA.IT |
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