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Course info
SLO / PROG1
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Course description
Department/Unit / Abbreviation
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SLO
/
PROG1
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Academic Year
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2024/2025
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Academic Year
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2024/2025
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Title
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Computer programming and numer. methods
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Form of course completion
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Exam
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Form of course completion
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Exam
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Long Title
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Computer programming and numerical methods
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Accredited / Credits
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Yes,
5
Cred.
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Type of completion
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Combined
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Type of completion
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Combined
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Time requirements
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Přednáška
2
[Hours/Week]
Exercise
1
[Hours/Week]
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Course credit prior to examination
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Yes
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Course credit prior to examination
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Yes
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Automatic acceptance of credit before examination
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No
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Included in study average
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YES
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Language of instruction
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Czech, English
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Occ/max
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|
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Automatic acceptance of credit before examination
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No
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Summer semester
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0 / -
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0 / -
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0 / -
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Included in study average
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YES
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Winter semester
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0 / -
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0 / -
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0 / -
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Repeated registration
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NO
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Repeated registration
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NO
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Timetable
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Yes
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Semester taught
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Winter semester
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Semester taught
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Winter semester
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Minimum (B + C) students
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not determined
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Optional course |
Yes
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Optional course
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Yes
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Language of instruction
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Czech, English
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Internship duration
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0
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No. of hours of on-premise lessons |
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Evaluation scale |
A|B|C|D|E|F |
Periodicity |
každý rok
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Evaluation scale for credit before examination |
S|N |
Periodicita upřesnění |
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Fundamental theoretical course |
No
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Fundamental course |
No
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Fundamental theoretical course |
No
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Evaluation scale |
A|B|C|D|E|F |
Evaluation scale for credit before examination |
S|N |
Substituted course
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OPT/PROG1
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Preclusive courses
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N/A
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Prerequisite courses
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N/A
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Informally recommended courses
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N/A
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Courses depending on this Course
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N/A
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Histogram of students' grades over the years:
Graphic PNG
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XLS
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Course objectives:
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The aim consists in application of mathematical analysis and algebra knowledge for understanding the basic numerical methods usable in scientific calculations and practically demonstrate how these algorithms work when implemented in the computer environment.
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Requirements on student
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Passing the oral examination
Practical application of a given numerical method in the form of the software programme compiled in one of the following programming environment: C, FORTRAN, PASCAL, BASIC, MATLAB etc.
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Content
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- Computation errors - influence of finite number of digits on the accuracy of the computation
- Algebraic methods - systems of linear algebraic equations (systems with non-empty null-space, predetermined systems), three-diagonal scheme, Gauss and Gauss-Jordan method, LU decomposition, inversion of matrices, zero points of the polynomial expressions (Lin- Bairstow method, method of Siljakov coefficients, Laguerre method), eigenvalues and eigenvectors of the matrices (general problem, symmetric matrices, LU and QR algorithms)
- Solving of systems of nonlinear equations - bisection of the interval, Newton method of the tangents, Richmond method of tangential hyperboles, their generalization for the systems of equations, Čebyšev iteration methods, Warner scheme (generalized method of tangents), gradient methods
- Interpolation, numerical differentiation and integration - Laguerre polynomials, the best trigonometric polynomials, Fourier series, discrete and fast Fourier transform, cubic splines, Čebyšev approximation (Remez algorithm), numerical differentiation and integration (trapezoidal formula, Newton-Cotes quadrature formula, Simpson formula, Gauss methods, special formula)
- Numerical solutions of ordinary differential equations - problem with initial condition (Euler method, Runge-Kutta methods, Merson method, automatic choice of integration step, implicit integration methods, stability convergence, correctness), boundary problem (method of shooting, linear systems of differential equations, analytical solutions, problems of existence of numerical solutions, construction of difference schemes, Marcuk identity)
- Minimization of functions and optimization - minimization of functions of one variable (golden section, differential methods), simplex method of minimization of functions of more variables, gradient methods (method of conjugated vectors, Powell quadratic convergent method), linear programming, combinatory problems (permutation problems - lexicographical selection, problem of traveling salesman, method of simulative annealing, evolution algorithms - self-organized migration algorithms)
- Basics of numerical solving of partial differential equations - difference scheme, fully conservative difference scheme
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Activities
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Fields of study
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Guarantors and lecturers
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Literature
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Recommended:
Flannery, B. P., Teukolsky S. A., Vetterling W. T. Numerical Recipes - The Art of Scientific Computing. Cambridge University Press, 1986.
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Recommended:
Kubíček M. Numerické algoritmy řešení chemicko-inženýrských úloh. SNTL Praha, 1983.
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Recommended:
Vitásek E. Numerické metody. SNTL Praha, 1982.
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On-line library catalogues
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Time requirements
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All forms of study
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Activities
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Time requirements for activity [h]
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Attendace
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39
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Preparation for the Exam
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45
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Preparation for the Course Credit
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35
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Homework for Teaching
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31
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Total
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150
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Prerequisites - other information about course preconditions |
basics of mathematical analysis and algebra, programming language ? basic, fortran, C, Matlab etc. |
Competences acquired |
Application Apply knowledge of mathematical analysis and algebra and understand the basic numerical methods usable in scientific calculations, show how these algorithms work implemented in the computer. |
Teaching methods |
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Assessment methods |
- Oral exam
- Student performance
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