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Course, academic year 2023/2024
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Fundamentals of Numerical Mathematics - NMNM201
Title: Základy numerické matematiky
Guaranteed by: Department of Numerical Mathematics (32-KNM)
Faculty: Faculty of Mathematics and Physics
Actual: from 2023
Semester: winter
E-Credits: 8
Hours per week, examination: winter s.:4/2, C+Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: taught
Language: Czech
Teaching methods: full-time
Teaching methods: full-time
Additional information: https://www.karlin.mff.cuni.cz/~blechta/znm/
Guarantor: doc. RNDr. Iveta Hnětynková, Ph.D.
doc. RNDr. Václav Kučera, Ph.D.
Class: M Bc. OM
M Bc. OM > Povinné
M Bc. OM > 2. ročník
Classification: Mathematics > Numerical Analysis
Pre-requisite : {One 1st year Analysis course}
Incompatibility : NNUM105
Interchangeability : NNUM105
Is interchangeable with: NMMB203, NNUM105
In complex pre-requisite: NMNM331
Annotation -
The first course of numerical analysis for students of General Mathematics.
Last update: G_M (16.05.2012)
Aim of the course -

To give a basic knowledge in numerical mathematics.

Last update: Dolejší Vít, prof. RNDr., Ph.D., DSc. (08.06.2015)
Course completion requirements -

Credit requirements:

at seminars, students will be given 6 tasks, which they solve at home. They will submit the solved task (electronically or on paper) no later than one week before the beginning of their exercise to the tutor.

They can get 0 to 6 points for each task.

To obtain the credit it is necessary to obtain at least 2/3 points, ie 24.

The 'nature of the examination of the course' excludes the repetition of that examination, POS, Article 8 (2)

Last update: Kučera Václav, doc. RNDr., Ph.D. (29.10.2019)
Literature -

  • J. Duintjer Tebbens, I. Hnětynková, M. Plešinger, Z. Strakoš, P. Tichý: Analýza metod pro maticové výpočty - Základní metody, Skriptum MFF UK, 2012

  • J. Segethová: Základy numerické matematiky, Skriptum MFF UK, 2002

  • M. Feistauer, V. Kučera: Základy numerické matematiky, Skriptum MFF UK, 2014

  • L. N. Trefethen and D. Bau, III, Numerical linear algebra, SIAM, Philadelphia, PA, 1997

  • A. Quarteroni, R. Sacco and F. Saleri: Numerical mathematics, Springer-Verlag, 2000

  • D. S. Watkins: Fundamentals of Matrix Computations, Willey Interscience, New Yourk, 2010

  • Other sources at: http://msekce.karlin.mff.cuni.cz/~dolejsi/Vyuka/ZNM.html

  • http://www.karlin.mff.cuni.cz/~felcman/nm.pdf

  • http://www.karlin.mff.cuni.cz/~mirektuma/znm/znm2019.pdf

  • Videozáznamy přednášek

Last update: Kučera Václav, doc. RNDr., Ph.D. (30.09.2019)
Teaching methods -

Lectures and tutorials in a lecture hall.

Last update: G_M (27.04.2012)
Requirements to the exam -

Examination according to the syllabus.

Last update: Dolejší Vít, prof. RNDr., Ph.D., DSc. (06.10.2017)
Syllabus -

1. What is numerical mathematics. Examples of applications.

2. Problem types and errors (forward, backward, residual). Stability of algorithms.

3. Schur theorem and its consequences.

4. Orthogonal transformations and QR factorization.

5. Least-squares problems and their solution by SVD and QR factorization.

6. Partial eigenvalue problem. Power method, Arnoldi and Lanczos method.

7. Systems of linear algebraic equations. LU factorization and its stability. Stationary iterative methods.

8. Nonlinear algebraic equations, Newton's method, fixed point iteration.

9. Numerical optimization, descent methods, Newton's method.

10. Orthogonal polynomials.

11. Interpolation of functions, Lagrange interpolation, spline functions.

12. Numerical quadrature, Newton-Cotes and Gauss formulas.

13. Numerical methods for ordinary differential equations, single step and Runge-Kutta methods, multistep methods, stability, orders.

Last update: Kučera Václav, doc. RNDr., Ph.D. (28.08.2023)
Entry requirements -

basic knowledge of calculus and linear algebra

Last update: G_M (27.04.2012)
 
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