Checking date: 29/06/2021

Course: 2021/2022

Further topics in numerical methods
(18276)
Study: Bachelor in Applied Mathematics and Computing (362)

Coordinating teacher: BAYONA REVILLA, VICTOR

Department assigned to the subject: Department of Mathematics

Type: Compulsory
ECTS Credits: 6.0 ECTS

Course:
Semester:

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 theory 1.1 The Weierstrass Theorem and Taylor's Theorem 1.2 The minimax approximation problem 1.3 The least squares approximation problem 1.4 Orthogonal polynomials 1.5 Gaussian quadrature 1.6 Trigonometric approximation 1.7 The Fast Fourier Transform (FFT) 2. Computation of eigenvalues and eigenvectors of dense matrices 2.1 The power method 2.2 Reduction to Hessenberg and tridiagonal forms 2.3 The QR method 2.4 Computing eigenvectors 2.5 Computing the Singular Value Decomposition of a matrix 3. Ordinary differential equations 3.1 Existence, uniqueness, and stability theory 3.2 One-step methods 3.3 Multistep methods 3.4 Predictor-corrector methods 3.5 Runge-kutta methods 3.6 System of ordinary differential equations 3.7 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
• S. D. Conte, Carl de Boor. Elementary Numerical Analysis: An Algorithmic Approach. McGraw-Hill. 1980
• Timothy Sauer. Numerical Analysis. Pearson. 2012