## Public University of Navarre

Castellano | Academic year: 2018/2019 | Previous academic years:  2017/2018  |  2016/2017
 Course code: 242602 Subject title: NUMERICAL METHODS Credits: 3 Type of subject: Mandatory Year: 3 Period: 2º S Department: Estadística, Informática y Matemáticas Lecturers BUJANDA CIRAUQUI, BLANCA (Resp) ARRARAS VENTURA, ANDRÉS

Partes de este texto:

### Module/Subject matter

Module: Scientific-technological transversal module.

Subject matter: Further studies in Mathematics and Physics.

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### Descriptors

Numerical Analysis.

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### General proficiencies

• CG3: Knowledge of basic and technological subjects qualifying to learn new methods and theories, and providing versatility to adapt to new situations.
• CG4: Problem solving proficiency with personal initiative, decision making, creativity and critical reasoning. Ability to elaborate and communicate knowledge and skills in the field of Industrial Engineering.

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### Specific proficiencies

• CFB1: Ability to solve mathematical problems in engineering. Ability to apply theoretical knowledge of linear algebra, geometry, differential geometry, differential and integral calculus, ordinary and partial differential equations, numerical methods, algorithmics, statistics and optimization.
• CFB3: Proficiency to use and program computers, operating systems, databases and software with application in engineering.

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### Learning outcomes

At the end of the course, the student is able to:

• LO1: Understand the basic principles and aims of Numerical Analysis.
• LO2: Describe and use direct and iterative methods to solve linear systems and boundary value problems.
• LO3: Describe and use fixed-point iteration methods to solve nonlinear equations and systems.
• LO4: Describe and use Runge-Kutta methods and linear multistep methods to solve initial value problems and initial-boundary value problems.
• LO5: Understand the applicability conditions for each method, and analyze and interpret its results.
• LO6: Understand, run and modify simple programs written in MATLAB/Octave which implement the numerical methods under consideration.

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### Methodology

 Methodology - Activity On-site hours Off-site hours A1: Lectures 24 A2: Practical sessions 6 A3: Self-study 41 A4: Exams and assessment 3 A5: Tutoring 1 Total 34 41

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### Relationship between formative activities and proficiencies

 Formative activity Proficiency A1 CFB1, CFB3 A2 CG3, CG4, CFB1, CFB3 A3 CFB1, CFB3 A4 CG3, CG4, CFB1, CFB3 A5 CG3, CG4, CFB1, CFB3

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English.

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### Evaluation

Continuous assessment is considered along the semester based on the following activities:

 Learning outcome Assessment activity Weight (%) Resit assessment LO1, LO2, LO5, LO6 Midterm exams on lessons 1 and 2 50 Yes (final exam) LO3, LO4, LO5, LO6 Midterm exams on lessons 3 and 4 50 Yes (final exam)

In order to pass the subject, one of the following conditions must be fulfilled:

• the weighted average of the marks of the midterm exams is not less than 5;
• the mark of the final exam covering the whole course (to be scheduled during the resit assessment period) is not less than 5.

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### Contents

• Numerical methods for linear systems: direct and iterative methods.
• Numerical methods for nonlinear equations and systems.
• Numerical methods for ordinary differential equations.
• Numerical methods for partial differential equations.

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### Agenda

1. Introduction to Numerical Analysis.
Preliminaries. Numerical differentiation.

2. Numerical solution of linear systems.
Matrix norms and conditioning. Direct and iterative methods. Application to the solution of boundary value problems.

3. Numerical solution of nonlinear equations and systems.
Fixed-point iteration methods. Newton's method. Quasi-Newton methods.

4. Numerical solution of initial value problems.
Runge-Kutta methods. Linear multistep methods. Stiff problems. Application to the solution of initial-boundary value problems.

Practical sessions:

• Session 1: Numerical solution of linear systems.
• Session 2: Numerical solution of nonlinear equations and systems.
• Session 3: Numerical solution of initial value problems.

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### Bibliography

Acceda a la bibliografía que su profesor ha solicitado a la Biblioteca.

Basic bibliography:

1. R.L. Burden, J.D. Faires. Numerical analysis. Brooks-Cole.
2. J.D. Faires, R.L. Burden. Numerical methods. Brooks-Cole.
3. D. Kincaid, W. Cheney. Numerical analysis. Mathematics of scientific computing. American Mathematical Society.

1. C. Conde, G. Winter. Métodos y algoritmos básicos del álgebra numérica. Editorial Reverté.
2. C. Moler. Numerical computing with MATLAB. SIAM. Electronic edition: http://www.mathworks.es/moler/chapters.html.
3. L.F. Shampine, I. Gladwell, S. Thompson. Solving ODEs with MATLAB. Cambridge University Press.

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### Location

Lecture room building (Arrosadía Campus). The practical sessions will take place at the computer laboratory.

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