Gianluca FRASCA CACCIA | NUMERICAL CALCULUS I
Gianluca FRASCA CACCIA NUMERICAL CALCULUS I
cod. 0512300012
NUMERICAL CALCULUS I
| 0512300012 | |
| DEPARTMENT OF MATHEMATICS | |
| EQF6 | |
| MATHEMATICS | |
| 2025/2026 |
| YEAR OF COURSE 1 | |
| YEAR OF DIDACTIC SYSTEM 2018 | |
| SPRING SEMESTER |
| SSD | CFU | HOURS | ACTIVITY | |
|---|---|---|---|---|
| MAT/08 | 7 | 56 | LESSONS |
| Objectives | |
|---|---|
| COURSE AIM.THE COURSE AIMS TO ALLOW STUDENTS TO ACQUIRE BASIC THEORETICAL KNOWLEDGE ON THE MAIN METHODS AND MATHEMATICAL SOFTWARE DEVELOPMENT SKILLS, FOR THE APPROXIMATION OF DATA AND FUNCTIONS, THE NUMERICAL COMPUTATION OF DEFINED INTEGRALS, THE NUMERICAL SOLUTION OF NONLINEAR SYSTEMS, THE COMPUTATION OF EIGENVALUES OF MATRICES. KNOWLEDGE AND UNDERSTANDING SKILLS STUDENTS WILL ACQUIRE THE BASIC KNOWLEDGE ON •APPROXIMATION OF DATA AND FUNCTIONS; •NUMERICAL COMPUTATION OF DEFINED INTEGRALS; •NUMERICAL SOLUTION OF NON-LINEAR SYSTEMS; •NUMERICAL COMPUTATION OF EIGENVALUES OF MATRICES; •DEVELOPMENT OF EFFICIENT MATHEMATICAL SOFTWARE; •MATLAB ENVIRONMENT FOR SOLVING SCIENTIFIC PROBLEMS. APPLYING KNOWLEDGE AND UNDERSTANDINGSTUDENTS WILL BE ABLE TO: •APPROXIMATE DATA AND FUNCTIONS, NUMERICALLY COMPUTE DEFINED INTEGRALS AND EIGENVALUES OF MATRICES, SOLVING NONLINEAR SYSTEMS, USING MATHEMATICAL SOFTWARE; •THEORETICALLY AND EXPERIMENTALLY ANALYZE THE PROPERTIES OF THE NUMERICAL METHODS STUDIED, ANALYZING THE ERROR AND THE CONVERGENCE; •TEST AND EVALUATE MATHEMATICAL SOFTWARE IN TERMS OF ACCURACY AND EFFICIENCY; •COMPARE THE PERFORMANCES OF DIFFERENT CODES. JUDGEMENT AUTONOMY THE STUDENT WILL BE ABLE TO: - SELECT THE MOST SUITABLE NUMERICAL METHOD TO SOLVE THE PROBLEM UNDER CONSIDERATION, BY ANALYSING ITS MATHEMATICAL PROPERTIES. - DISCERN THE ACCURACY, RELIABILITY AND EFFICIENCY OF THE NUMERICAL METHOD, CRITICALLY INTERPRETING THE EXPERIMENTAL RESULTS; - PROVIDE THEORETICAL JUSTIFICATION FOR THE EFFECTIVENESS OF DIFFERENT METHODS TO SOLVE THE PROBLEMS UNDER CONSIDERATION. COMMUNICATIVE SKILLS. THE STUDENT WILL BE ABLE TO: - REPRESENT THE RESULTS OBTAINED BY MEANS OF TABLES AND GRAPHS, ACCOMPANIED BY DESCRIPTIVE TEXT; - COMMUNICATE THE KNOWLEDGE ACQUIRED, USING APPROPRIATE SCIENTIFIC TERMINOLOGY, AND THE TOOLS OF MATHEMATICAL FORMALISATION; - EXPLAIN THE CHOICES MADE IN SOLVING THE CALCULATION PROBLEM; - TO INTERACT IN CRANE WORK LEARNING ABILITY THE STUDENT WILL BE ABLE TO: - LEARN NEW NUMERICAL METHODS FOR SOLVING MATHEMATICAL PROBLEMS, APPRECIATING THEIR LIMITATIONS AND ADVANTAGES; - CONTINUOUSLY UPDATE THEIR KNOWLEDGE, USING TECHNICAL AND SCIENTIFIC LITERATURE, USING TRADITIONAL BIBLIOGRAPHICAL TOOLS AND DIGITAL RESOURCES. |
| 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 (2 HOURS). •APPROXIMATION OF DATA AND FUNCTIONS. POLYNOMIAL INTERPOLATION AND SPLINES. LEAST SQUARES APPROXIMATION. ITERATIVE METHODS FOR NONLINEAR EQUATIONS. (13 HOURS) •NUMERICAL QUADRATURE: NEWTON - COTES AND GAUSSIAN FORMULAS. AUTOMATIC INTEGRATORS BASED ON FIXED AND ADAPTATIVE SCHEMES. (17 HOURS) •EIGENVALUES OF MATRICES. ITERATIVE METHODS AND METHODS BASED ON SIMILARITY TRANSFORMATIONS. (4 HOURS) •EULER METHOD FOR NUMERIAL SOLUTION OF CHAUCHY INITIAL VALUE PROBLEM. (2 HOURS) •THE MATLAB PROGRAMMING LANGUAGE. DEVELOPMENT OF CODES RELATED TO THE MAIN ALGORITHMS. (16 HOURS) TEACHING METHODS THE COURSE CONSISTS OF LECTURES (7 CFU, 56 HOURS). DURING THE LECTURES, EXERCITATIONS, LABORATORY ACTIVITIES AND PROJECTS FOR THE DEVELOPMENT AND EVALUATION OF MATHEMATIC SOFTWARE WILL ALSO BE CARRIED OUT. |
| Teaching Methods | |
|---|---|
| THE COURSE CONSISTS OF LECTURES (7 CFU, 56 HOURS). DURING THE LECTURES, EXERCITATIONS, LABORATORY ACTIVITIES AND PROJECTS FOR THE DEVELOPMENT AND EVALUATION OF MATHEMATIC SOFTWARE WILL ALSO BE CARRIED OUT. |
| 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. 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. THERE MAY BE TWO PRACTICAL TESTS DURING THE COURSE (OPTIONAL): ONE ON THE APPROXIMATION OF DATA AND FUNCTIONS IN MATLAB; ONE ON NUMERICAL QUADRATURE, WHICH CONSISTS IN THE DISCUSSION OF A DESIGN AND COMPUTATION OF INTEGRALS DEFINED IN MATLAB, USING THE CODES DEVELOPED DURING THE COURSE. THEY CONSTITUTE PARTIAL EXEMPTION FROM THE PRACTICAL TEST DURING THE FINAL EXAM. |
| Texts | |
|---|---|
| - G.MONEGATO, FONDAMENTI DI CALCOLO NUMERICO, CLUT •R. D’AMBROSIO, NUMERICAL APPROXIMATION OF ORDINARY DIFFERENTIAL PROBLEMS: FROM DETERMINISTIC TO STOCHASTIC NUMERICAL METHODS, SPRINGER (ES. 1.4 – FAKE NEWS DIFFUSING AS EPIDEMICS) - SLIDES AND NOTES OF THE COURSE ARE AVAILABLE ON THE MS-TEAMS PLATFORM AT THE LINK HTTPS://UNISALERNO.SHAREPOINT.COM/:F:/S/UNI23-CALCOLONUMERICOI-051230001273991NESSUNPARTIZIONAMENTOM/EMFGRMZ3HFNMTVZ203SOUPEBNWYO8D-EZ7UH1RGWJUU92G?E=45LHOD |
| More Information | |
|---|---|
| BEAPAT@UNISA.IT; ANCARDONE@UNISA.IT |
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