Gianluca FRASCA CACCIA | NUMERICAL ANALYSIS
Gianluca FRASCA CACCIA NUMERICAL ANALYSIS
cod. 0522200003
NUMERICAL ANALYSIS
| 0522200003 | |
| DEPARTMENT OF MATHEMATICS | |
| EQF7 | |
| MATHEMATICS | |
| 2025/2026 |
| YEAR OF COURSE 1 | |
| YEAR OF DIDACTIC SYSTEM 2018 | |
| AUTUMN SEMESTER |
| SSD | CFU | HOURS | ACTIVITY | |
|---|---|---|---|---|
| MAT/08 | 6 | 48 | LESSONS |
| Objectives | |
|---|---|
| GENERAL AIMTHE COURSE IS AIMED AT ALLOWING STUDENTS TO ACQUIRE THE BASIC THEORETICAL KNOWLEDGE AND SKILLS ON THE MAIN METHODS FOR NUMERICAL SOLVING OF PROBLEMS MODELED BY FUNCTIONAL EQUATIONS, IN PARTICULAR BY PARTIAL DIFFERENTIAL EQUATIONS AND DELAY DIFFERENTIAL EQUATIONS. KNOWLEDGE AND COMPREHENSION SKILLSSTUDENTS WILL ACQUIRE THE BASIC KNOWLEDGE ON • NUMERICAL METHODS FOR ELLIPTICAL, PARABOLIC AND HYPERBOLIC PARTIAL DIFFERENTIAL EQUATIONS; • NUMERICAL METHODS FOR DELAY DIFFERENTIAL EQUATIONS; • NON-STATIONARY NUMERICAL METHODS FOR LARGE LINEAR SYSTEMS; • SINGULAR VALUE DECOMPOSITION. APPLYING KNOWLEDGE AND UNDERSTANDINGSTUDENTS WILL BE ABLE TO • THEORETICALLY AND EXPERIMENTALLY ANALYZE THE PROPERTIES OF NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS; • SOLVE PARTIAL DIFFERENTIAL EQUATIONS BY USING AND/OR DEVELOPING MATHEMATICAL SOFTWARE; • USE NUMERICAL CALCULATION PACKAGES, JUDGEMENT AUTONOMYTHE STUDENT WILL BE ABLE TO: - ASSESS THE LIMITS OF APPLICABILITY OF THE NUMERICAL METHOD; - TO DISCERN THE ACCURACY, RELIABILITY AND EFFICIENCY OF THE NUMERICAL METHOD; - TO SELECT THE MOST SUITABLE NUMERICAL METHOD TO SOLVE THE PROBLEM UNDER CONSIDERATION, BY ANALYSING ITS PECULIAR FEATURES. COMMUNICATIVE SKILLS THE STUDENT WILL BE ABLE TO: - SUPPORT CONVERSATIONS ON ISSUES RELATED TO THE NUMERICAL SOLUTION OF REAL PROBLEMS, USING APPROPRIATE SCIENTIFIC TERMINOLOGY, AND THE TOOLS OF MATHEMATICAL FORMALIZATION; - TO EXPLAIN THE CHOICES MADE IN SOLVING THE MATHEMATICAL PROBLEM. LEARNING SKILL THE STUDENT WILL BE ABLE TO: •LEARN NEW METHODS FOR SOLVING MATHEMATICAL PROBLEMS, EVALUATING THEIR LIMITATIONS AND ADVANTAGES; •CONTINUOUSLY UPDATE THEIR KNOWLEDGE, USING TECHNICAL AND SCIENTIFIC LITERATURE, USING TRADITIONAL BIBLIOGRAPHICAL TOOLS AND DIGITAL RESOURCES. |
| Prerequisites | |
|---|---|
| THEORY OF ORDINARY DIFFERENTIAL EQUATIONS. PROGRAMMING PRINCIPLES. BASIC NOTIONS OF PROGRAMMING LANGUAGES MATLAB. |
| Contents | |
|---|---|
| NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS: BASIC NOTIONS OF THEORY. GENERAL INFORMATION ON NUMERICAL TREATMENT OF SECOND ORDER LINEAR PARTIAL DIFFERENTIAL EQUATIONS (8 HOURS). FINITE DIFFERENCE METHODS FOR ELLIPTIC, PARABOLIC AND HYPERBOLIC EQUATIONS. METHODS OF LINES (14 HOURS). WEAK FORM OF A DIFFERENTIAL PROBLEM. POLYNOMIAL APPROXIMATION. FINITE ELEMENT METHOD FOR ELLIPTIC EQUATIONS (8 HOURS). NUMERICAL METHODS FOR DELAY DIFFERENTIAL EQUATIONS: EXISTANCE AND REGULARITY OF SOLUTION. CRITICAL POINTS. STEP METHOD BASED ON A A CONTINUOUS RUNGE-KUTTA METHOD. MESH-CONSTRAINED METHODS (8 HOURS). NUMERICAL LINEAR ALGEBRA: NON-STATIONARY METHODS FOR THE SOLUTION OF LARGE DIMENSIONE LINEAR SYSTEMS, SINGULAR VALUE DECOMPOSITION AND APPLICATION TO RECOMMENDATION SYSTEMS AND TO ANALYSIS OF DIFFUSION OF FAKE NEWS (10 HOURS). |
| Teaching Methods | |
|---|---|
| THE COURSE CONSISTS OF LECTURES (6 CFU, 48 HOURS). DURING THE LECTURES, EXERCITATIONS, LABORATORY ACTIVITIES FOR THE DEVELOPMENT AND EVALUATION OF MATHEMATIC SOFTWARE WILL ALSO BE CARRIED OUT. |
| Verification of learning | |
|---|---|
| THE EXAMINATION CONSISTS OF AN INTERVIEW ON THE THEORETICAL CONTENT OF THE COURSE, IN ORDER TO VERIFY THE ABILITY TO ANALYSE AND PRESENT RIGOROUSLY THE PROPERTIES OF THE NUMERICAL METHODS PRESENTED IN CLASS. PRAISE MAY BE GIVEN TO STUDENTS WHO DEMONSTRATE THEIR ABILITY TO APPLY THE KNOWLEDGE AND SKILLS ACQUIRED WITH A CRITICAL SENSE AND WITH ORIGINALITY. A PRACTICAL TEST OR SEMINAR (OPTIONAL) ON NUMERICAL RESOLUTION OF AN ELLIPTICAL OR HYPERBOLIC OR PARABOLIC PROBLEM OR OF A DELAY DIFFERENTIAL EQUATION MAY BE PROVIDED, AT THE STUDENT'S CHOICE. THE TEST OR SEMINAR GRANTS A PARTIAL EXEMPTION FROM ONE OF THE QUESTIONS RELATED TO THE CHOSEN TOPIC DURING THE ORAL EXAMINATION OF THE FINAL EXAM. |
| Texts | |
|---|---|
| ISAACSON, H.KELLER- ANALYSIS OF NUMERICAL METHODS - J. WILEY SONS. ALFIO QUARTERONI – MODELLISTICA NUMERICA PER PROBLEMI DIFFERENZIALI, SPRINGER BELLEN, M. ZENNARO: NUMERICAL METHODS FOR DELAY DIFFERENTIAL EQUATIONS. OXFORD UNIVERSITY PRESS, 2003. SLIDES AND NOTES OF THE COURSE IN A.A. 2023-24 ARE AVAILABLE ON MS-TEAMS AL LINK HTTPS://UNISALERNO.SHAREPOINT.COM/:F:/S/UNI23-ANALISINUMERICA-052220000374019NESSUNPARTIZIONAMENTOMA/EMB_HWOZBBDMM_YIYRWAHVIBUZOV77XWUDUXBCMVJ8LEBA?E=UZ6SFN |
| More Information | |
|---|---|
| BEAPAT@UNISA.IT, ANCARDONE@UNISA.IT |
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