| First cycle degree courses | Second cycle degree courses | Single cycle degree courses |
| School of Science | ||
| MATHEMATICS | ||
Course unit
THEORY OF APPROXIMATION AND APPLICATIONS
SCN1037767, A.A. 2017/18
Information concerning the students who enrolled in A.Y. 2017/18
THEORY OF APPROXIMATION AND APPLICATIONS
SCN1037767, A.A. 2017/18
Information concerning the students who enrolled in A.Y. 2017/18
Information on the course unit
| Degree course |
Second cycle degree in MATHEMATICS SC1172, Degree course structure A.Y. 2011/12, A.Y. 2017/18 |
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|---|---|---|
| Degree course track | GENERALE [010PD] | |
| Number of ECTS credits allocated | 7.0 | |
| Type of assessment | Mark | |
| Course unit English denomination | THEORY OF APPROXIMATION AND APPLICATIONS | |
| Website of the academic structure | http://matematica.scienze.unipd.it/2017/laurea_magistrale | |
| Department of reference | Department of Mathematics | |
| Mandatory attendance | No | |
| Language of instruction | English | |
| Branch | PADOVA | |
| Single Course unit | The Course unit can be attended under the option Single Course unit attendance | |
| Optional Course unit | The Course unit can be chosen as Optional Course unit |
Lecturers
| Teacher in charge | STEFANO DE MARCHI | MAT/08 |
|---|
Mutuated
| Course unit code | Course unit name | Teacher in charge | Degree course code |
|---|---|---|---|
| INP5070471 | MESH FREE APPROXIMATIONS OF PARTIAL DIFFERENTIAL EQUATIONS | STEFANO DE MARCHI | IN2191 |
ECTS: details
| Type | Scientific-Disciplinary Sector | Credits allocated | |
|---|---|---|---|
| Educational activities in elective or integrative disciplines | MAT/08 | Numerical Analysis | 3.0 |
| Core courses | MAT/08 | Numerical Analysis | 4.0 |
Mode of delivery (when and how)
| Period | First semester |
|---|---|
| Year | 1st Year |
| Teaching method | frontal |
Organisation of didactics
| Type of hours | Credits | Hours of teaching |
Hours of Individual study |
Shifts |
|---|---|---|---|---|
| Laboratory | 1.0 | 8 | 17.0 | No turn |
| Lecture | 6.0 | 48 | 102.0 | No turn |
| Prerequisites: | The course requires the basic courses of Numerical Calculus and Numerical Analysis. It is also useful to have attended a course of Functional Analysis. It is assumed that the students know the programming language Matlab. |
| Target skills and knowledge: | Analysis of some approximation problems in 1-dimension and more dimensions, with the use of polynomials and radial basis functions. Applications: interpolation, hyoerinterpolation, quadrature and solution of PDEs. Error analysis. Solution of test problems by the use of Matlab. |
| Examination methods: | The final exam is a written test on the topics of the course. There will be also an oral part in which the student will discuss the lab exercises given during the course. |
| Assessment criteria: | The student will have to show that he has understood the topics of the course, both from the theoretical and algorithmic point of view, either on the application point of view.
During the lab, it will be important to show familiarity and confidence on the use of Matlab. |
| Course unit contents: | The course can be subdvided in 2 theoretical parts of 24h each, in total 48h corresponding to 6CFU. Moreover there will be 16h of lab exercises.
PART I (24h+2h): from univariate to multivariate polynomial approximation - best approximation approximation - modulus of continuity and Lebesgue constant - nearly optimal distribution of points in 1-dimension - Padua points for interpolation and cubature - (Weakly) admissible meshes - applications and lab (6h) PART II (24h+6h): Radial Basis Functions (RBF) - learning from splines - positive and conditionally definite functions - native spaces, power function and error estimates - application to the solution of elliptic PDEs - applications and lab (10h) |
| Planned learning activities and teaching methods: | The course consists of 48h of frontal teaching lessons and 8h of lab exercises. |
| Additional notes about suggested reading: | - For PART I: teacher's lecture notes(see below)
- For PART II: lectures notes of the teacher and the reference books. |
| Textbooks (and optional supplementary readings) |
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