Numerical Analysis
Code  Completion  Credits  Range  Language 

B4B01NUM  Z,ZK  6  2P+2C  Czech 
 Relations:
 It is not possible to register for the course B4B01NUM if the student is concurrently registered for or has previously completed the course B0B01MVM (mutually exclusive courses).
 Course guarantor:
 Mirko Navara
 Lecturer:
 Mirko Navara
 Tutor:
 Mirko Navara, Aleš Němeček
 Supervisor:
 Department of Mathematics
 Synopsis:

The course introduces to basic numerical methods of interpolation and approximation of functions, numerical differentiation and integration, solution of transcendent equations and systems of linear equations. Emphasis is put on estimation of errors, practical skills with the methods and demonstration of their properties using Maple and computer graphics.
 Requirements:

Linear Algebra, Calculus. Math in Maple (B0B01MVM) is an appropriate/recommended prerequisite.
 Syllabus of lectures:

1. Overview of the subject of Numerical Analysis. Approximation of functions, polynomial interpolation.
2. Errors of polynomial interpolation and their estimation.
3. Hermite interpolating polynomial. Splines.
4. Least squares approximation.
5. Numerical differentiation. Richardson's extrapolation.
6. Numerical integration (quadrature).
7. Error estimates and stepsize control. Gaussian and Romberg integration.
8. Integration over infinite ranges. Tricks for numerical integration.
9. Root separation. Basic rootfinding methods.
10. Iteration method, fixed point theorem.
11. Finitary methods of solution of systems of linear equations.
12. Matrix norms, convergence of sequences of vectors and matrices.
13. Iterative methods of solution of systems of linear equations.
14. Reserve.
 Syllabus of tutorials:

1. Instruction on work in laboratory and Maple.
2. Training in Maple.
3. Polynomial interpolation, estimation of errors.
4. Individual work on assessment tasks.
5. Least squares approximation.
6. Individual work on assessment tasks.
7. Individual work on assessment tasks.
8. Numerical differentiation and integration, modification of tasks.
9. Individual work on assessment tasks.
10. Solution of systems of linear equations.
11. Individual work on assessment tasks.
12. Solution of systems of linear equations.
13. Submission of assessment tasks.
14. Individual work on assessment tasks; assessment.
 Study Objective:

Practical use of numerical methods, also in nonstandard situations, where a modification of the task is needed. Direct motivation to SRL (SelfRegulated Learning).
 Study materials:

[1] Press, W. H., Flannery, B. P., Teukolsky, S. A., Vetterling, W. T.: Numerical Recipes (The Art of Scientific Computing), Cambridge University Press, Cambridge, 2002, ISBN 0521750334.
[2] Knuth, D. E., The Art of Computer Programming, Addison Wesley, Boston, 1997.
[3] Maple User Manuals and Programming Guides, Maplesoft, a division of Waterloo Maple Inc. (http://www.maplesoft.com/documentation_center/)
 Note:
 Further information:
 https://moodle.fel.cvut.cz/courses/B4B01NUM
 Timetable for winter semester 2024/2025:

06:00–08:0008:00–10:0010:00–12:0012:00–14:0014:00–16:0016:00–18:0018:00–20:0020:00–22:0022:00–24:00
Mon Tue Wed Thu Fri  Timetable for summer semester 2024/2025:
 Timetable is not available yet
 The course is a part of the following study plans:

 Open Informatics  Computer Science 2016 (compulsory course of the specialization)
 Open Informatics (compulsory course of the specialization)
 Medical electronics and bioinformatics (compulsory elective course)
 Open Informatics  Artificial Intelligence and Computer Science 2018 (compulsory course of the branch)