Universidad Pública de Navarra - Nafarroako Univertsitate Publikoa

Module/Subject matter

Module: Scientific-technological transversal module.

Subject matter: Further studies in Mathematics and Physics.

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Contents

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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

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Languages

English.

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Evaluation

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

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

• the mark of each midterm exam is not less than 2 and the weighted average of the marks of both 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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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

Access the bibliography that your professor has requested from the Library.

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.

Additional bibliography:

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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