Universidad Pública de Navarra - Nafarroako Univertsitate Publikoa
Public University of Navarre
| Course code: 504208 | Subject title: NUMERICAL METHODS | ||||
| Credits: 6 | Type of subject: Mandatory | Year: 2 | Period: 2º S | ||
| Department: Estadística, Informática y Matemáticas | |||||
| Lecturers: | |||||
| HIGUERAS SANZ, M. INMACULADA (Resp) [Mentoring ] | ARRARAS VENTURA, ANDRÉS [Mentoring ] | ||||
Contents
Introduction to numerical techniques. Direct and iterative methods for linear systems. Methods for nonlinear equations and systems. Numerical treatment of differential equations. Interpolation. Numerical integration.
General proficiencies
- CB3- That students have the ability to collect and interpret relevant data (usually within their area of study) in order to make judgments that include reflection on relevant issues of a social, scientific or ethical nature.
- CB5- That students have developed those learning skills necessary to undertake further studies with a high degree of autonomy.
Specific proficiencies
- CG1- To apply the acquired analytical and abstraction skills, intuition, and logical thinking to identify and analyze complex problems, and to seek and formulate solutions in a multidisciplinary environment.
- CE18- To analyze, validate and interpret mathematical models of real-world situations, using the tools provided by differential and integral calculus of several variables, complex analysis, integral transforms and numerical methods to solve them.
Learning outcomes
- RA12- To understand the concept of numerical approximation, its importance and limitations.
- RA13- To master the most basic techniques for the numerical solution of nonlinear equations and systems.
- RA14- To master the most common interpolation techniques.
- RA15- To get to know the most usual numerical integration techniques with error estimates.
- RA16- To acquire some basic notions about the numerical solution of differential equations.
Methodology
| Methodology - Activity | On-site hours | Off-site hours |
| A1- Interactive lectures | 42 | |
| A2- Hands-on learning sessions | 14 | |
| A3- Self-study and autonomous work | 88 | |
| A4- Tutorials | 2 | |
| A5- Assessment tests | 4 | |
| Total | 60 | 90 |
Evaluation
| Learning outcome |
Assessment activity |
Weight (%) | It allows test resit |
Minimum required grade |
|---|---|---|---|---|
| RA12 - RA16 | Written tests | 80% | Yes | 5/10 |
| RA12 - RA16 | Assignments and reports | 15% | No | 0 |
| RA12 - RA16 | Active participation | 5% | No | 0 |
If the minimum required grade of the written tests is not reached, the final mark will be, at most, 4.9/10
Continuous assessment is carried out by means of several written tests distributed throughout the semester as follows:
Ordinary assessment:
Written tests (individual):
- Test A: lessons 1, 2 and 3, with a weight of 40% in the final grade.
- Test B: lessons 4 and 5, with a weight of 40% in the final grade.
In order to pass the course, the following two conditions must be fulfilled:
- the average of the grades of Test A and Test B is not less than 5/10;
- the weighted average of the grades of Test A and Test B, the assignments and reports, and the active participation is not less than 5/10 (with the weights indicated in the table).
Resit assessment:
Written test (individual):
- Test R: lessons 1, 2, 3, 4 and 5, with a weight of 80% in the final grade.
In order to pass the course, the following two conditions must be fulfilled:
- the grade of Test R is not less than 5/10;
- the weighted average of the grades of Test R, the assignments and reports, and the active participation is not less than 5/10 (with the weights indicated in the table).
If a student takes part in a number of assessment activities whose total weight is less than 50%, his/her final grade will be Absent.
Agenda
- Introduction to Numerical Analysis. Numerical differentiation.
- Numerical solution of linear systems.
- Numerical solution of nonlinear equations and systems.
- Numerical solution of differential equations.
- Interpolation. Numerical integration.
Bibliography
Access the bibliography that your professor has requested from the Library.
Basic bibliography:
- U.M. Ascher, C. Greif. A First Course in Numerical Methods. SIAM.
- R.L. Burden, J.D. Faires, A.M. Burden. Numerical Analysis. Brooks-Cole.
- J.D. Faires, R. Burden. Numerical Methods. Brooks-Cole.
- J. Kiusalaas. Numerical methods in engineering with Python 3. Cambridge University Press.
Additional bibliography:
- D. Kincaid, W. Cheney. Numerical Analysis. Mathematics of Scientific Computing. American Mathematical Society.
- A. Quarteroni, R. Sacco, F. Saleri. Numerical Mathematics. Springer.