COMPETENCES

M05CM01 Knowing the basic techniques of numerical analysis and their translation into algorithms or constructive methods to solve problems.



M05CM02 Programming the studied numerical methods in a computer using a structured language and applying them effectively.



M05CM03 Using packages in which some of the studied methods are applied, and which can serve as a auxiliary tool to one's own codes.



M05CM04 Analyzing the convenience of one or more numerical methods for a given problem, based on the error analysis, the computational cost and other characteristics.



M05CM05 Evaluating the obtained results and drawing conclusions after a computational procedure, and being able to communicate everything both orally and in writing.



LEARNING RESULTS

Using numerical solution algorithms, programming numerical methods in a computer, by implementing these algorithms in a structured programming language, and applying them effectively.

THEORETICAL CONTENTS



1. INTRODUCTION TO NUMERICAL CALCULUS: Computer arithmetic and error propagation.



2. BASIC MATLAB NOTIONS



3. RESOLUTION OF LINEAR SYSTEMS OF EQUATIONS: Direct methods. Minimum square methods and overdetermined systems.



4. RESOLUTION OF NONLINEAR EQUATIONS AND SYSTEMS. Roots searching methods for nonlinear equations. Fix point methods and Newton's method.



PRACTICAL CONTENTS



The computer assignments are associated to the theoretical contents, reinforcing their learning by implementing the studied algorithms in an adequate way.

The theoretical contents will be taught during the master (M) classes, following the lecture notes uploaded in the virtual class at platform eGela. These master lectures will be supplemented with problem sessions (classroom sessions, GA), where the students will solve questions where they will have to apply the acquired theoretical knowledge. In the seminar sessions (S), questions and examples relative to the contents of the course will be developed; these will be usually provided to the students so they can work previously on them, with the aim of facilitating the discussion in the seminar sessions.



In addition, the students will have to do computer assignments oriented to the goals of this course, using a programming language. In this course, we will use MATLAB.

In the ordinary exam call, the continuous assessment system will have the following percentages:



Final exam: 60%

Computer assignments: 10%

Seminars: 10%

Partial exams: 20%



In order to apply this method of evaluation, a minimum grade of 4 out of 10 is required in the final written exam; otherwise, the final grade will be the one obtained in that exam.



FINAL EXAM CRITERIA



The student that does not want to be assessed through the continuous assessment system has the right to do a final assessment exam; however, he or she must give written notice of withdrawal from the continuous assessment system during the first 15 weeks of the autumn term. In that case, the evaluation for that student will be a final assessment exam, plus a complimentary test to be done together with the final exam, that can be an oral exposition, an activity in front of a computer or doing some written assignment; it will measure the acquisition of the course competences will be assessed.



NOT TAKING THE FINAL EXAM



In spite of assessing the activities done during the course, a student who does not take the final exam will obtain the grade "No presentado".

Notes and other teaching materials made available by the instructor in platform eGela.

Basic bibliography

C.B. Moler: Numerical Computing with MATLAB, SIAM, 2004.

J.M. Sanz-Serna: Diez lecciones de Cálculo Numérico, Universidad de Valladolid, 2010.

J. Stoer and R. Bulirsch: Introduction to Numerical Analysis. Springer-Verlag, Inc., 1993.

K.E. Atkinson: An Introduction to Numerical Analysis, John Wiley & Sons, 1989.

U.M. Ascher and C. Greif: A First Course in Numerical Analysis, SIAM, 2011.

M.H. Holmes: Introduction to Scientific Computing and Data Analysis, Springer 2016.

In-depth bibliography

L.N. Trefethen, D. Bau: Numerical Linear Algebra, SIAM, 1997.
N.J. Higham: Accuracy and Stability of Numerical Algoritms, SIAM, 1996.
A. Quarteroni, R.Sacco, F.Saleri: Numerical Mathematics, Springer, 2000.

Journals