Course code: 504208 |
Subject title: NUMERICAL METHODS |
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Credits: 6 |
Type of subject: Mandatory |
Year: 2 |
Period: 2º S |
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Department: Estadística, Informática y Matemáticas |
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Lecturers: |
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HIGUERAS SANZ, M. INMACULADA (Resp) [Mentoring ] | ARRARAS VENTURA, ANDRÉS [Mentoring ] |

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.

*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.*

*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.*

*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 - 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 |

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*.

- 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.

**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.