Gurantor department | Department of Applied Mathematics | Credits | 6 |

Subject guarantor | Mgr. Bohumil Krajc, Ph.D. | Subject version guarantor | Mgr. Bohumil Krajc, Ph.D. |

Study level | undergraduate or graduate | Requirement | Optional |

Year | 1 | Semester | winter |

Study language | Czech | ||

Year of introduction | 2016/2017 | Year of cancellation | |

Intended for the faculties | FEI | Intended for study types | Follow-up Master |

Instruction secured by | |||
---|---|---|---|

Login | Name | Tuitor | Teacher giving lectures |

KRA04 | Mgr. Bohumil Krajc, Ph.D. | ||

LUK76 | doc. Ing. Dalibor Lukáš, Ph.D. |

Extent of instruction for forms of study | ||
---|---|---|

Form of study | Way of compl. | Extent |

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

Combined | Credit and Examination | 10+10 |

A successful student of the course will have the knowledge and skills of a typical graduate bachelor degree in Computational Mathematics .

Lectures

Tutorials

Project work

Subject contains parts of higher mathematics omitted in some bachelor programs. Mastering selected parts is essential for the successful engineering degree in Computational Mathematics.
In the field of differential calculus of of functions of several variables we concetrate on the following parts: differentiating of composite functions, Taylor polynomials, implicit function theorem, constrained extremes. Students also learn the basic principles and methods of multidimensional integration. Attention to numerical methods is focused on issues of numerical differentiation and integration of functions. Some remarks are dedicated to a function approximation, search for zero points and extremal tasks.
A substantial part of the course is the interpretation of the relevant passages in the field of ordinary differential equations and their systems.

• W. Rudin, Principles of Mathematical Analysis, McGraw-Hill Book Company, New York, 1964
• W. E. Boyce, R. C. DiPrima: Elementary differential equations. Wiley, New York 1992

• M. Braun: Differential Equations and Their Applications. Springer, Berlin 1978.

Students pass out tests and deliver projects.

No additional requirements are imposed on students.

Subject has no prerequisities.

Subject has no co-requisities.

1.Diferential of a function of several variables. Gradient method.
2.Diferential of a composite function. Transformation of variables in the differential expressions.
3.Approximation of function . Taylor's theorem . Conditions for the existence of local extremes.
4.Numerical derivative. Approximate solutions of equations.
5.Theorem about implicitly defined function. Constrained extremes.
6.Construction of integral sums, numerical integration .
7.Definition of multiple integrals. Selected applications.
8.Fubini`s theorems. Substitution in multiple integrals . Geometric interpretation of Jacobian .
9.Theorems about the existence and uniqueness of solutions of initial value problems for ordinary differential equations. Euler's method.
10.Transformation of variables in differential equations .
11.Potential and its use for solving exact equations.
12.Ordinary differential equations of higher orders. Solving linear differential equations. Boundary value problems .

Task name | Type of task | Max. number of points
(act. for subtasks) | Min. number of points |
---|---|---|---|

Credit and Examination | Credit and Examination | 100 (100) | 51 |

Credit | Credit | 30 | 10 |

Examination | Examination | 70 | 21 |

Show history

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

2019/2020 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | P | Czech | Ostrava | 1 | Optional | study plan | ||||

2019/2020 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | K | Czech | Ostrava | 1 | Optional | study plan | ||||

2019/2020 | (N0541A170007) Computational and Applied Mathematics | (S01) Applied Mathematics | P | Czech | Ostrava | 1 | Optional | study plan | ||||

2019/2020 | (N0541A170007) Computational and Applied Mathematics | (S02) Computational Methods and HPC | P | Czech | Ostrava | 1 | Optional | study plan | ||||

2019/2020 | (N0541A170007) Computational and Applied Mathematics | (S01) Applied Mathematics | K | Czech | Ostrava | 1 | Optional | study plan | ||||

2019/2020 | (N0541A170007) Computational and Applied Mathematics | (S02) Computational Methods and HPC | K | Czech | Ostrava | 1 | Optional | study plan | ||||

2018/2019 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | P | Czech | Ostrava | 1 | Optional | study plan | ||||

2018/2019 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | K | Czech | Ostrava | 1 | Optional | study plan | ||||

2017/2018 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | P | Czech | Ostrava | 1 | Optional | study plan | ||||

2017/2018 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | K | Czech | Ostrava | 1 | Optional | study plan | ||||

2016/2017 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | P | Czech | Ostrava | 1 | Optional | study plan | ||||

2016/2017 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | K | Czech | Ostrava | 1 | Optional | study plan |

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