| Course Unit Code | Course Unit Title | Number of ECTS Credits Allocated |
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| 714-0886/01 | Numerical Methods | 5 ECTS credits |
| Type of Course Unit | Compulsory |
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| Level of Course Unit | First Cycle |
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| Year of Study | |
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| Semester when the Course Unit is delivered | Winter, Summer Semester |
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| Mode of Delivery | Face-to-face |
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| Language of Instruction | Czech, English |
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| Prerequisites and Co-Requisites | Course succeeds to compulsory courses of previous semester |
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| Name of Lecturer(s) | Personal ID | Name |
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| KUC14 | doc. RNDr. Radek Kučera, Ph.D. |
| Learning Outcomes of the Course Unit |
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The course is an introduction to the numerical methods. The main goal consists in explanations of fundamental numerical principles so that students should be able to decide about an appropriate method for problems arising in the other courses or in the technical practice. An important ingredient is the algorithmic implementation of numerical methods and the usage of the standard numerical software.
The graduate of this course should know:
• to recognize problems suitable for solving by numerical procedures and to find an appropriate numerical method;
• to decide whether the computed solution is sufficiently accurate and, in case of need, to assess reasons of inaccuracies;
• to propose an algorithmic procedure for solving the problem and to choice a suitable computer environment for its realization.
It is necessary to complete Mathematics 1 and Mathematics 2 courses or their equivalents. |
| Recommended Optional Programme Components |
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| Common optional components are not offered, students of special interest can participate in departmental activities or can arrange consulting hours with lecturer. |
| Course Contents |
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Program of lectures
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Week. Lecture
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1st Course contents, the issue of errors, stability calculations.
2nd Solution of nonlinear equations, separation of roots, the simplest method.
3rd Newton's method and simple iterations.
4th Direct methods for solving linear equations, Gaussian elimination and LU-decomposition.
5th Eigenvalues and eigenvectors, numerical calculation.
6th Iterative methods for solving linear equations.
7th Interpolation by polynomials and splines.
8th Least squares approximation.
9th Numerical differentiation and integration.
10th Extrapolation in the calculation of integrals. Gaussian integration formulas.
11th One-step method for solving initial value problems for ordinary differential equations.
12th Multistep methods.
13th Ordinary differential equations of higher order.
14th Systems of differential equations.
Program of the excercises and the exam questions are analogous.
Matalb program is used in the excersises. |
| Recommended or Required Reading |
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| Required Reading: |
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1. Qaurteroni, A., Sacco, R., Saleri, F.: Numerical Mathematics. Springer, 2007.
2. Süli, E., Mayers, D.: An introduction to Numerical Analysis. Cambridge University Press, 2003. |
1. Qaurteroni, A., Sacco, R., Saleri, F.: Numerical Mathematics. Springer, 2007.
2. Süli, E., Mayers, D.: An introduction to Numerical Analysis. Cambridge University Press, 2003. |
| Recommended Reading: |
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1. Van Loan, C. F.: Introduction to scientific computing. Prentice Hall, Upper Saddle River, NJ 07459, 1999.
|
| 1. Van Loan, C. F.: Introduction to scientific computing. Prentice Hall, Upper Saddle River, NJ 07459, 1999. |
| Planned learning activities and teaching methods |
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| Lectures, Individual consultations, Tutorials |
| Assesment methods and criteria |
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| Tasks are not Defined |
| Work placement(s) |
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| Course does not contain work placement. |
