| Course Unit Code | 310-3142/01 |
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| Number of ECTS Credits Allocated | 2 ECTS credits |
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| Type of Course Unit * | Optional |
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| Level of Course Unit * | First Cycle |
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| Year of Study * | Third 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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| KUC14 | prof. RNDr. Radek Kučera, Ph.D. |
| Summary |
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| The course deals with the matrix calculus and the variational calculus in the context of engineering problems. The course ends by the algorithmization of the finite element method. |
| Learning Outcomes of the Course Unit |
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| The course deals with the matrix calculus and the variational calculus in the context of engineering problems. The course ends by the algorithmization of the finite element method. |
| Course Contents |
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Week. Lecture
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1st Vector space, linear mappings and matricies.
2nd Scalar product and orthogonality, orthogonalization procedure.
3rd Eigenvalues and eigenvectors, spectral decomposition.
4th Singular values and singular decomposition. Generalized inverse.
5th Matrix factorizations. Fast solving of linear systems.
6th Gradient descent method. Preconditioning.
7th Linear, bilinear and quadratic forms. Classification.
8th Weak solutions of differential equations.
9th Theorems on existence of weak solutions.
10th Variational solving differential equations. Ritz-Galerkin method.
11th Fundamentals of the finite element method.
12th Model boundary value problems for ODEs.
13th Model boundary value problems for PDEs.
14th Comparision with the finite difference method. |
| Recommended or Required Reading |
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| Required Reading: |
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1. Van Loan, C. F.: Introduction to scientific computing. Prentice Hall, Upper Saddle River, NJ 07459, 1999, ISBN-13: 9780139491573.
2. Qaurteroni, A., Sacco, R., Saleri, F.: Numerical Mathematics. Springer, 2007, ISBN: 978-3-540-34658-6.
3. Golub G.H., Loan C.F.V.: Matrix Computation. The Johns Hopkins University Press, Baltimore, 1996, ISBN 0-8018-5414-8. |
1. Rektorys, K.: Variační metody. Academia Praha, 1999, ISBN 80-200-0714-8.
2. Práger M.: Numerická analýza. ZUČ Plzeň, 1994. |
| Recommended Reading: |
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1. A. Tveito, R. Winther: Introduction to Partial Differential Equations: A Computational Approach. Springer, Berlin, 2000.
2. http://mi21.vsb.cz/ |
| 1. http://mi21.vsb.cz/ |
| 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 | 20 | 5 |
| Examination | Examination | 80 (80) | 30 |
| Písemná zkouška | Written examination | 60 | 25 |
| Ústní zkouška | Oral examination | 20 | 5 |