Course: Numerical Methods

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Course title Numerical Methods
Course code KMA/NUME
Organizational form of instruction Lecture + Exercise
Level of course Bachelor
Year of study not specified
Semester Winter
Number of ECTS credits 5
Language of instruction Czech
Status of course Compulsory, Compulsory-optional
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
Lecturer(s)
  • Machalová Jitka, RNDr. Ph.D.
  • Kobza Jiří, doc. RNDr. CSc.
  • Ženčák Pavel, RNDr. Ph.D.
  • Burkotová Jana, Mgr. Ph.D.
Course content
1. Computer modelling, algorithms, errors and stability of numerical computations. 2. Approximation of functions - interpolation, least squares approximation using polynomials, splines, systems of orthogonal functions. 3. Numerical differentiation - basic formulas for numerical computing derivatives of functions of one and two variables. 4. Numerical integration: Newton-Cotes formulas, Gauss-type formulas, compound formulas. Error estimates. 5. Solving systems of linear equations - direct methods (Gauss-Jordan, matrix decompositions). 6. Iterative methods (Jacobi, Gauss-Seidel, relaxation and gradient methods) - algorithms, convergence and error estimation problems. 7. Solving nonlinear equations (bisection, regula falsi, fixed point, Newton's methods). 8. Solving systems of nonlinear equations (iterative methods, Newton's method). 9. Roots of polynomials (Horner?s scheme, root estimation and computing). 10. Computing matrix eigenvalues and eigenvectors (position estimates, decomposition and transformations of matrices, applications to difference and differential equations). 11. Methods of approximate and numerical solutions of ordinary differential equations.

Learning activities and teaching methods
Monologic Lecture(Interpretation, Training), Dialogic Lecture (Discussion, Dialog, Brainstorming)
  • Attendace - 52 hours per semester
  • Homework for Teaching - 30 hours per semester
  • Preparation for the Course Credit - 15 hours per semester
  • Preparation for the Exam - 55 hours per semester
Learning outcomes
The course introduces basic methods of function approximation, numerical solution of linear and nonlinear equations and systems of equations, numerical differentiation and integration, and numerical solution of ordinary differential equations. Implementation of the basic methods in MatLab or Maple is also included.
Comprehension Understand the numerical methods of mathematical analysis and linear algebra.
Prerequisites
Basic knowledge of mathematical analysis and linear algebra.

Assessment methods and criteria
Oral exam, Seminar Work

Credit: the student has to pass written tests, seminary work Exam: the student has to understand the subject and be able to prove the principal results
Recommended literature
  • Eldén L. (2004). Introduction to Numerical Computation. Studentliteratur.
  • Horová I., Zelinka J. (2004). Numerické metody. MU Brno.
  • Kobza J. (1993). Numerické metody. PřF UP Olomouc.
  • Linfield G., Penny J. (1995). Numerical Methods Using Matlab. Horwod.
  • Segethová J. (1998). Základy numerické matematiky. Karolinum Praha.
  • Vitásek E. (1982). Numerické metody. SNTL Praha.


Study plans that include the course
Faculty Study plan (Version) Branch of study Category Recommended year of study Recommended semester
Faculty of Science Bioinformatics (1) Informatics courses 3 Winter
Faculty of Science Computer Science (1) Informatics courses 3 Winter
Faculty of Science Applied Computer Science (1) Informatics courses 3 Winter