Gurantor department | Department of Mathematics and Descriptive Geometry | Credits | 2 |

Subject guarantor | prof. RNDr. Radek Kučera, Ph.D. | Subject version guarantor | prof. RNDr. Radek Kučera, Ph.D. |

Study level | undergraduate or graduate | ||

Study language | Czech | ||

Year of introduction | 2019/2020 | Year of cancellation | |

Intended for the faculties | FS | Intended for study types | Bachelor |

Instruction secured by | |||
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Login | Name | Tuitor | Teacher giving lectures |

KUC14 | prof. RNDr. Radek Kučera, Ph.D. |

Extent of instruction for forms of study | ||
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Form of study | Way of compl. | Extent |

Full-time | Credit and Examination | 2+2 |

Mathematics is essential part of education on technical universities. It should be considered rather the method in the study of technical courses than a goal. Thus the goal of mathematics is train logical reasoning than mere list of mathematical notions, algorithms and methods. Students should learn how to analyze problems, distinguish between important and unimportant, suggest a method of solution, verify each step of a method, generalize achieved results, analyze correctness of achieved results with respect to given conditions, apply these methods while solving technical problems, understand that mathematical methods and theoretical advancements outreach the field mathematics.

Lectures

Tutorials

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.

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. A. Tveito, R. Winther: Introduction to Partial Differential Equations: A Computational Approach. Springer, Berlin, 2000.
2. http://mi21.vsb.cz/

Tests and credits
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Exercises
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Conditions for obtaining credit points (CP):
- participation in exercises, 20% can be to apologize
- completion of three written tests, 0-15 CP
- completion of two programs, 5 CP
Exam
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- written exam 0-60 CP, successful completion at least 25 CP
- oral exam 0-20 CP, successful completion at least 5 CP
The exam questions are analogous to the program of the lectures.

The mandatory participation is 80%.

Subject has no prerequisities.

Subject has no co-requisities.

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.

Conditions for completion are defined only for particular subject version and form of study

Academic year | Programme | Field of study | Spec. | Form | Study language | Tut. centre | Year | W | S | Type of duty | |
---|---|---|---|---|---|---|---|---|---|---|---|

2019/2020 | (B2341) Engineering | (3902R001) Applied Informatics and Control | P | Czech | Ostrava | 3 | Optional | study plan | |||

2019/2020 | (B2341) Engineering | (2302R003) Transport Machinery and Material Handling | P | Czech | Ostrava | 3 | Optional | study plan | |||

2019/2020 | (B2341) Engineering | (3901R003) Applied Mechanics | P | Czech | Ostrava | 3 | Optional | study plan | |||

2019/2020 | (B2341) Engineering | (2302R007) Hydraulics and Pneumatics | P | Czech | Ostrava | 3 | Optional | study plan | |||

2019/2020 | (B2341) Engineering | (2302R010) Design of Machines and Equipment | (21) Design of Production Machines and Equipment | P | Czech | Ostrava | 3 | Optional | study plan | ||

2019/2020 | (B2341) Engineering | (2302R010) Design of Machines and Equipment | (40) Design of Machines and Equipment | P | Czech | Ostrava | 3 | Optional | study plan | ||

2019/2020 | (B2341) Engineering | (2302R010) Design of Machines and Equipment | (60) Industrial Design | P | Czech | Ostrava | 3 | Optional | study plan | ||

2019/2020 | (B2341) Engineering | (2302R010) Design of Machines and Equipment | (70) Earth, Mining and Building Machines | P | Czech | Ostrava | 3 | Optional | study plan | ||

2019/2020 | (B2341) Engineering | (3907R009) Operation of Energy Equipment | P | Czech | Ostrava | 3 | Optional | study plan | |||

2019/2020 | (B2341) Engineering | (3904R016) Environmental Engineering | P | Czech | Ostrava | 3 | Optional | study plan | |||

2019/2020 | (B2341) Engineering | (2301R013) Robotics | P | Czech | Ostrava | 3 | Optional | study plan | |||

2019/2020 | (B2341) Engineering | (2301R023) Technical Diagnostics, Service and Management | P | Czech | Ostrava | 3 | Optional | study plan | |||

2019/2020 | (B2341) Engineering | (2301R040) Industrial Engineering | P | Czech | Ostrava | 3 | Optional | study plan | |||

2019/2020 | (B2341) Engineering | (2303R002) Mechanical Engineering Technology | P | Czech | Ostrava | 3 | Optional | study plan | |||

2019/2020 | (B2341) Engineering | (2303R002) Mechanical Engineering Technology | P | Czech | Šumperk | 3 | Optional | study plan | |||

2019/2020 | (B2341) Engineering | (2301R003) Transport Equipment and Technology | P | Czech | Ostrava | 3 | Optional | study plan |

Block name | Academic year | Form of study | Study language | Year | W | S | Type of block | Block owner |
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