 Checking date: 31/01/2023

Course: 2023/2024

Numerical methods
(16493)
Bachelor in Data Science and Engineering (Plan: 392 - Estudio: 350)

Coordinating teacher: TERAN VERGARA, FERNANDO DE

Department assigned to the subject: Mathematics Department

Type: Compulsory
ECTS Credits: 6.0 ECTS

Course:
Semester:

Requirements (Subjects that are assumed to be known)
Lineal Algebra, Programming, Calculus I, Calculus II
Objectives
Using NUMERICAL METHODS (NM) to calculate approximate solutions of mathematical models Study the stability and accuracy of NM. Calculate numerical solution of systems of nonlinear equations. Approximate the minimum of a function of several variables. Developing, analyzing, and implementing finite difference methods. Solving ordinary differential equations and systems by numerical integration methods. Using the software environments to discuss the efficiency, pros and cons of different NM.
Skills and learning outcomes
Description of contents: programme
1. Fundamentals (floating point, errors, stability, algorithms...). 2. Solution of linear systems of equations. 3. Numerical solution of equations and systems of nonlinear equations. 4. Interpolation and approximation of functions. 5. Least squares problems. 6. Numerical optimization. 7. Numerical integration. 8. Numerical differentiation: numerical solution of ODEs. 9. Fast Fourier Transform.
Learning activities and methodology
This is a "hands on" course. In the large-group lectures the theoretical contents will be introduced, and they will be delivered in a blackboard standard room. However, the small-group lectures will take place in the computer Lab, and students are supposed to follow the explanations of the instructor performing in real time the exercises, examples and other proposed activities. Students must become acquainted with MATLAB. The course will start learning how to program MATLAB. After and introduction to the course, every two weeks (as a general rule), one of the topics of the course will be discussed in the classroom and practices related to these topics will be proposed to the students. Usually the practices involve to solve a simple problem by writing the appropriate code.
Assessment System
• % end-of-term-examination 50
• % of continuous assessment (assigments, laboratory, practicals...) 50
Calendar of Continuous assessment
Basic Bibliography
• [A] K. Atkinson. Elementary Numerical Analysis. John Wiley & Sons. 2004
• [BF] R. L. Burden, J. D. Faires. Numerical Methods. Brooks/Cole, Cengage Learning. 2003
• [QSG] A. Quarteroni, F. Saleri, P. Gervasio. Scientific computing with MATLAB and Octave. Springer. 2010
• [QSS] A. Quarteroni, R. Sacco, F. Saleri. Numerical Mathematics. Springer. 2007 Electronic Resources *
• [BC] A. Belegundu, T. Chandrupatla. Optimization Concepts and Applications in Engineering. Cambridge University Press. 2011
• [BV] S. Boyd, L. Vanderberghe. Convex Optimization. Cambridge University Press. 2004
• [DCM] S. Dunn, A. Constantinides, P. Moghe. Numerical Methods in Biomedical Engineering. Elsevier Academic Press. 2010
• [DH] P. Deuflhard, A. Hohmann. Numerical Analysis in Modern Scientific Computing. An Introduction. Springer. 2003
• [FJNT] P.E. Frandsen, K. Jonasson, H.B. Nielsen, O. Tingleff. Unconstrained Optimization. IMM, DTU. 1999
• [HH] D. Higham, N. J. Higham. Matlab Guide. SIAM. 2017
• [HJ] R. A. Horn, C. R. Johnson. Matrix Analysis, 2nd ed.. Cambridge University Press. 2013
• [H] N. J. Higham. Accuracy and Stability of Numerical Methods. SIAM. 1998
• [K] C. Kelley. Iterative Methods for Optimization. SIAM (available online). 1999
• [NW] J. Nocedal, S. J. Wright. Numerical Optimization, 2nd ed.. Springer. 2006
• [TB] L. N. Trefethen, D. Bau. [TB] L. N. Trefethen, D. Bau. SIAM. 1997 Electronic Resources *
(*) Access to some electronic resources may be restricted to members of the university community and require validation through Campus Global. If you try to connect from outside of the University you will need to set up a VPN

The course syllabus may change due academic events or other reasons.