Beatrice PATERNOSTER | NUMERICAL ANALYSIS
Beatrice PATERNOSTER NUMERICAL ANALYSIS
cod. 0522200003
NUMERICAL ANALYSIS
| 0522200003 | |
| DIPARTIMENTO DI MATEMATICA | |
| EQF7 | |
| MATHEMATICS | |
| 2022/2023 |
| YEAR OF COURSE 2 | |
| YEAR OF DIDACTIC SYSTEM 2018 | |
| AUTUMN SEMESTER |
| SSD | CFU | HOURS | ACTIVITY | |
|---|---|---|---|---|
| MAT/08 | 6 | 48 | LESSONS |
| Objectives | |
|---|---|
| 1.KNOWLEDGE AND UNDERSTANDING THE AIM OF THE COURSE IS TO ACQUIRE KNOWLEDGE TO ANALYZE CRITICAL THEORY AND NUMERICAL METHODS RELATING TO THE NUMERICAL TREATMENT OF MAIN PROBLEMS MODELED BY EVOLUTIONARY EQUATIONS, IN PARTICULAR PARTIAL AND DELAY DIFFERENTIAL EQUATIONS. 2.APPLIED KNOWLEDGE AND UNDERSTANDING BY MEANS OF THE PRACTICE IN THE LABORATORY, THE STUDENTS WILL BE ABLE TO EXPERIMENT SOME NUMERICAL METHODS, TO ESTIMATE THE RELIABILITY OF THE OBTAINED RESULTS, TO DEVELOP ELEMENTS OF MATHEMATICAL SOFTWARE, TO USE PACKAGES OF NUMERICAL ANALYSIS AND TO EVALUATE PERFORMANCES. |
| 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. FINITE DIFFERENCE METHODS FOR ELLIPTIC, PARABOLIC AND HYPERBOLIC EQUATIONS. METHODS OF LINES. WEAK FORM OF A DIFFERENTIAL PROBLEM. POLYNOMIAL APPROXIMATION. FINITE ELEMENT METHOD FOR ELLIPTIC EQUATIONS. 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. 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. |
| Teaching Methods | |
|---|---|
| LECTURES, EXERCISES, LABORATORY |
| Verification of learning | |
|---|---|
| THE FINAL EXAM CONSISTS IN THE DISCUSSION ON THE THEORETICAL ISSUES OF THE COURSE, IN ORDER TO CHECK THE ABILITY TO ANALYZE AND PRESENT THE PROPERTIES OF THE NUMERICAL METHODS PRESENTED DURING THE COURSE, AND ON THE NUMERICAL PROJECT DEVELOPED DURING THE COURSE OR A SEMINAR GIVEN BY THE STUDENT ON A SUBJECT OF THE COURSE CHOSEN BY THE STUDENT HIMSELF. |
| 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. |
| More Information | |
|---|---|
| BEAPAT@UNISA.IT THE MATERIAL OF THE COURSE IN 2021-22 IS AVAILABLE TO HTTPS://UNISALERNO.SHAREPOINT.COM/SITES/UNI21-ANALISINUMERICA-052220000364591MATEMATICA/MATERIALE%20DEL%20CORSO/FORMS/ALLITEMS.ASPX |
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