Numerical Analysis
Code  Completion  Credits  Range  Language 

B4B01NUM  Z,ZK  6  2P+2C  Czech 
 Lecturer:
 Mirko Navara (guarantor)
 Tutor:
 Aleš Němeček, Mirko Navara (guarantor)
 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.
 Syllabus of lectures:

1. Overview of the subject of Numerical Analysis.
2. Sources of errors in numerical computations.
3. Approximation of functions, polynomial interpolation.
4. Errors of polynomial interpolation and their estimation.
5. Hermite interpolating polynomial. Splines.
6. Least squares approximation.
7. Basic rootfinding methods.
8. Iteration method, fixed point theorem.
9. Basic theorem of algebra, root separation and finding roots of polynomials,
10. Solution of systems of linear equations.
11. Numerical differentiation.
12. Numerical integration (quadrature); error estimates and stepsize control.
13. Gaussian and Romberg integration.
 Syllabus of tutorials:

1. Instruction on work in laboratory and Maple.
2. Individual work  training in Maple.
3. Polynomial interpolation, estimation of errors.
4. Individual work on assessment tasks.
5. Individual work on assessment tasks.
6. Least squares approximation.
7. Individual work on assessment tasks.
8. Rootfinding methods, root separation.
9. Individual work on assessment tasks.
10. Solution of systems of linear equations.
11. Numerical differentiation.
12. Numerical differentiation and integration, modification of tasks.
13. 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.
 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:
 http://math.feld.cvut.cz/nemecek/nummet.html
 Timetable for winter semester 2019/2020:

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 Fri Thu Fri  Timetable for summer semester 2019/2020:
 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)