Checking date: 13/05/2022

Course: 2022/2023

Further topics in numerical methods
Study: Bachelor in Applied Mathematics and Computing (362)

Coordinating teacher: BAYONA REVILLA, VICTOR

Department assigned to the subject: Mathematics Department

Type: Compulsory
ECTS Credits: 6.0 ECTS


Requirements (Subjects that are assumed to be known)
Linear Algebra (Course 1 - Semester 1); Differential Calculus (Course 1 - Semester 1); Programming (Course 1 - Semester 1); Integral Calculus (Course 1 - Semester 2); Programming Techniques (Course 1 - Semester 2); Numerical Methods (Course 2 - Semester 1); Ordinary Differential Equations (Course 3 - Semester 1).
Skills and learning outcomes
Description of contents: programme
1. Approximation 1.1 Uniform approximation 1.2 Approximation in the 2-norm 1.3 Orthogonal polynomials 1.4 Gaussian quadrature 1.5 Trigonometric interpolation and approximation 1.6 The Fast Fourier Transform (FFT) 2. Computation of eigenvalues and eigenvectors 2.1 The power method 2.2 Householder transformation; reduction to tridiagonal forms 2.3 The QR method 2.4 Singular Value Decomposition 3. Ordinary differential equations 3.1 Introduction: existence and uniqueness 3.2 One-step methods 3.3 Runge-kutta methods 3.4 Multistep methods 3.5 System of equations 3.6 Stiff problems
Learning activities and methodology
LEARNING ACTIVITIES AND METHODOLOGY THEORETICAL-PRACTICAL CLASSES. [44 hours with 100% classroom instruction, 1.67 ECTS] Knowledge and concepts students must acquire. Student receive course notes and will have basic reference texts to facilitate following the classes and carrying out follow up work. Students partake in exercises to resolve practical problems and participate in workshops and evaluation tests, all geared towards acquiring the necessary capabilities. TUTORING SESSIONS. [4 hours of tutoring with 100% on-site attendance, 0.15 ECTS] Individualized attendance (individual tutoring) or in-group (group tutoring) for students with a teacher. STUDENT INDIVIDUAL WORK OR GROUP WORK [98 hours with 0 % on-site, 3.72 ECTS] WORKSHOPS AND LABORATORY SESSIONS [8 hours with 100% on site, 0.3 ECTS] FINAL EXAM. [4 hours with 100% on site, 0.15 ECTS] Global assessment of knowledge, skills and capacities acquired throughout the course. METHODOLOGIES THEORY CLASS. Classroom presentations by the teacher with IT and audiovisual support in which the subject's main concepts are developed, while providing material and bibliography to complement student learning. PRACTICAL CLASS. Resolution of practical cases and problem, posed by the teacher, and carried out individually or in a group. TUTORING SESSIONS. Individualized attendance (individual tutoring sessions) or in-group (group tutoring sessions) for students with a teacher as tutor. LABORATORY PRACTICAL SESSIONS. Applied/experimental learning/teaching in workshops and laboratories under the tutor's supervision.
Assessment System
  • % end-of-term-examination 40
  • % of continuous assessment (assigments, laboratory, practicals...) 60
Calendar of Continuous assessment
Basic Bibliography
  • K. Atkinson. Elementary Numerical Analysis. Wiley. 2003
  • R. L. Burden, J. D. Faires. Numerical Analysis. Brooks/Cole. 2010
  • Timothy Sauer. Numerical Analysis. Pearson. 2012
Additional Bibliography
  • A Iserles. A First Course in the Numerical Analysis of Differential Equations. Cambridge University Press. 2009
  • Endre Süli and David F. Mayers. An Introduction to Numerical Analysis. Cambridge. 2003
  • Kendall E. Atkinson. An Introduction to Numerical Analysis (2nd edition). Wiley. 1989
  • Quarteroni, A., Sacco, R., y Saleri, F.. Numerical Mathematics. Springer. 2007
  • S. D. Conte, Carl de Boor. Elementary Numerical Analysis: An Algorithmic Approach . McGraw-Hill . 1980
  • Uri M. Ascher, Chen Greif. A First Course on Numerical Methods. SIAM. 2011
Detailed subject contents or complementary information about assessment system of B.T.

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