| First cycle degree courses | Second cycle degree courses | Single cycle degree courses |
| School of Science | ||
| MATHEMATICS | ||
Course unit
NUMERICAL METHODS FOR DIFFERENTIAL EQUATIONS
SCP3051019, A.A. 2019/20
Information concerning the students who enrolled in A.Y. 2019/20
NUMERICAL METHODS FOR DIFFERENTIAL EQUATIONS
SCP3051019, A.A. 2019/20
Information concerning the students who enrolled in A.Y. 2019/20
Information on the course unit
| Degree course |
Second cycle degree in MATHEMATICS SC1172, Degree course structure A.Y. 2011/12, A.Y. 2019/20 |
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|---|---|---|
| Degree course track | GENERALE [010PD] | |
| Number of ECTS credits allocated | 7.0 | |
| Type of assessment | Mark | |
| Course unit English denomination | NUMERICAL METHODS FOR DIFFERENTIAL EQUATIONS | |
| Website of the academic structure | http://matematica.scienze.unipd.it/2019/laurea_magistrale | |
| Department of reference | Department of Mathematics | |
| Mandatory attendance | No | |
| Language of instruction | Italian | |
| 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 | MARIO PUTTI | MAT/08 | |
|---|---|---|---|
| Other lecturers | STEFANO DE MARCHI | MAT/08 |
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 |
Course unit organization
| Period | Second semester |
|---|---|
| Year | 1st Year |
| Teaching method | frontal |
| Type of hours | Credits | Teaching hours |
Hours of Individual study |
Shifts |
|---|---|---|---|---|
| Laboratory | 1.0 | 16 | 9.0 | No turn |
| Lecture | 6.0 | 48 | 102.0 | No turn |
| Start of activities | 02/03/2020 |
|---|---|
| End of activities | 12/06/2020 |
| Show course schedule | 2019/20 Reg.2011 course timetable |
Examination board
Examination board not defined
| Prerequisites: | Mathematical Analysis 1 and 2, with elements of Differential Equations and functional analysis. Numerical Analysis and linear algebra. The lab projects require some knowledge of Matlab programming. |
| Target skills and knowledge: | The course deals with methods of scientific computing and numerical analysis for the solution of partial differential equations. We will address both application and implementation issues as well as theoretical results. The course will also address many of the instruments that are necessary to complete the numerical solution of a PDE, such as solution of ODEs, solution of large sparse linear systems of equations. The lab projects will provide the students with the opportunity to challenge themselves in practical implementation issues. |
| Examination methods: | Oral examination with discussion on the lab projects. |
| Assessment criteria: | 30% lab projects
70% oral discussion |
| Course unit contents: | Ordinary differential equations. Generalities, existence and uniqueness. Discrete methods: one step-methods, Runge-Kutta methods. stability and convergemce. Multi-step methods. Stiff problems, linear and nonlinear stability, implementation.
Partial differential equations: characterization with description of most important model problems. FEM methods for elliptic equations: variational formulation, Hilbert spaces; boundary conditions (Dirichlet, Neumann, Cauchy). Abstract FEM formulation: energy norm, discretization, error estimates, regularity of the solution. Parabolic equations: spatio-temporal discretizations. Error and stability estimates for Euler and Crank-Nicolson methods. Applications to nonlinear problems. |
| Planned learning activities and teaching methods: | Classroom and computer laboratory. The theoretical notions will be discussed on the blackboard. The implementation issues and usage of the different algorithms will be discussed in the computer lab. |
| Additional notes about suggested reading: | Lecture notes written by the teacher will be available for most of the material. |
| Textbooks (and optional supplementary readings) |
|
- Lecturing
- Questioning
- Loading of files and pages (web pages, Moodle, ...)
- Moodle (files, quizzes, workshops, ...)
- Matlab