| Course Unit Code | 470-4506/01 |
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| Number of ECTS Credits Allocated | 4 ECTS credits |
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| Type of Course Unit * | Optional |
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| Level of Course Unit * | Second Cycle |
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| Year of Study * | Second Year |
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| Semester when the Course Unit is delivered | Summer Semester |
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| Mode of Delivery | Face-to-face |
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| Language of Instruction | Czech |
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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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| LUK76 | doc. Ing. Dalibor Lukáš, Ph.D. |
| Summary |
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| The course covers fundamental methods of numerical linear and nonlinear algebra, methods of interpolation and approximation, and numerical analysis including an introduction to solution of boundary value problems for partial differential equations. |
| Learning Outcomes of the Course Unit |
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| The aim of the course is to introduce fundamental numerical methods for solution of engineering problems that lead to large-scale linear systems, nonlinear systems, or eigenvalue problems. Further, we shall present interpolation methods and an approximation by the method of least squares. Finally, we shall focus on numerical derivatives, quadrature, and we introduce methods for solution of boundary value problems for partial diferential equations. Each topic will be motivated by an engineering problem. The algorithms will be implemented in Matlab. The students will be also introduced to some libraries of numerical linear algebra such as BLAS, LAPACK, and MUMPS. |
| Course Contents |
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Lectures:
1. Numerical linear algebra - iterative methods for solution to linear systems
2. Numerical linear algebra - the method of conjugate gradients, preconditioning
3. Numerical linear algebra - sparse matrix solvers, parallel frontal method
4. Numerical linear algebra - eigenvalues and eigenvectors, power method, Lanczos method
5. Numerical linear algebra - libraries BLAS, LAPACK, MUMPS
6. Nonlinear systems - bisection, fixed-point iterations, Newton's method
7. Interpolation and approximation - Lagrange interpolation, splines, B-splines, approximation by the method of least squares
8. Numerical analysis - numerical derivative, numerical quadrature
9. Numerical analysis - introduction to numerics for partial differential equations
10. Numerical analysis - principle of the finite element method
Exercises:
1. Numerical linear algebra - iterative methods for solution to linear systems
2. Numerical linear algebra - the method of conjugate gradients, preconditioning
3. Numerical linear algebra - sparse matrix solvers, parallel frontal method
4. Numerical linear algebra - eigenvalues and eigenvectors, power method, Lanczos method
5. Numerical linear algebra - libraries BLAS, LAPACK, MUMPS
6. Nonlinear systems - bisection, fixed-point iterations, Newton's method
7. Interpolation and approximation - Lagrange interpolation, splines, B-splines, approximation by the method of least squares
8. Numerical analysis - numerical derivative, numerical quadrature
9. Numerical analysis - introduction to numerics for partial differential equations
10. Numerical analysis - principle of the finite element method
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| Recommended or Required Reading |
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| Required Reading: |
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| - Quarteroni, A. – Sacco, R. – Saleri, F. Numerical Mathematics. Springer, 2000. |
- Vitásek, E.: Numerické metody. SNTL Praha, 1987.
- Vondrák,V., Pospíšil, L.: Numerické metody 1. MI21, VŠB-TU Ostrava 2012.
http://mi21.vsb.cz/modul/numericke-metody-1
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| Recommended Reading: |
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- W.H., Flannery, B.P., Teukolski, S.A., Vetterling, W.T.: Numerical Recipes in C. Cambridge University Press, Cambridge 1990.
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- W.H., Flannery, B.P., Teukolski, S.A., Vetterling, W.T.: Numerical Recipes in C. Cambridge University Press, Cambridge 1990.
- Quarteroni, A. – Sacco, R. – Saleri, F. Numerical Mathematics. Springer, 2000. |
| Planned learning activities and teaching methods |
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| Lectures, Tutorials |
| Assesment methods and criteria |
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| Task Title | Task Type | Maximum Number of Points
(Act. for Subtasks) | Minimum Number of Points for Task Passing |
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| Credit and Examination | Credit and Examination | 100 (100) | 51 |
| Credit | Credit | 30 | 10 |
| Examination | Examination | 70 | 21 |