Universidad Pública de Navarra - Nafarroako Univertsitate Publikoa

Module/Subject matter

• Subject Matter Level 1: Mathematics
• Subject Matter Level 2: Advanced Mathematics

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Contents

Introduction to numerical techniques. Direct and iterative methods for linear systems. Methods for nonlinear equations and systems. Interpolation. Numerical integration. Numerical treatment of differential equations.

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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.
• 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.

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Specific proficiencies

• CE7- 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.

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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.

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Methodology

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Languages

English.

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Evaluation

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.

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Agenda

1. Introduction to Numerical Analysis. Numerical differentiation.
2. Numerical solution of linear systems.
3. Numerical solution of nonlinear equations and systems.
4. Numerical solution of differential equations.
5. Interpolation. Numerical integration.

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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.

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Location

Universidad Pública de Navarra, Campus Arrosadía, Pamplona.

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