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 | Compulsory |

Year | 2 | Semester | winter |

Study language | Czech | ||

Year of introduction | 2010/2011 | Year of cancellation | |

Intended for the faculties | FMT, HGF, FEI, USP | Intended for study types | Bachelor |

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

Login | Name | Tuitor | Teacher giving lectures |

KRA0220 | Ing. Jan Kracík, Ph.D. | ||

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

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

Form of study | Way of compl. | Extent |

Full-time | Credit and Examination | 3+3 |

Combined | Credit and Examination | 3+3 |

Succesful student will gain deep and wide knowledge of the subject.

Lectures

Tutorials

The subject consists of the basic parts of the n-dimensional calculus theory and practice.

Tom M. Apostol: Calculus, Volume 2, Multi-variable calculus and linear algebra with applications to differential equations and probability, Wiley, New York, 1969
W. E. Boyce, R. C. DiPrima: Elementary differential equations. Wiley, New York 1992

W. Rudin: Principles of Mathematical Analysis. McGraw-Hill Book Company, New York 1964

Students will be continuously addressed assigned projects. During the semester will be held written tests. Terms of the credit: Credit will be awarded to students who successfully manage tests and in those terms, work on projects.

There are not defined other requirements for student.

Subject has no prerequisities.

Subject has no co-requisities.

Real functions of several variables. Euclidean spaces. Topological properties of subsets of Euclidean metric space. Limits and continuity. Partial derivative, the concept of directional derivatives. Total differential and the gradient function. Applications. Geometric interpretation gradient, outline methods steepest descent method. Discussion relationships between the fundamental concepts of calculus. Differentials of higher orders, Taylor polynomials, Taylor's theorem. Theorem of implicit function. Weierstrass theorem on the global extrema, local extrema. Criteria existence of local extreme. Constrained local extrema, Lagrange multipliers method. Search global extremes - practices. Riemann double integral, basic properties. Fubini phrases in double integrals. Substitution theorem for double integrals, applications of double integrals Riemann triple integrals, basic properties. Fubini theorems for integrals. Substitution theorem for integrals. Applications. First order differential equations, the theorem on the existence and uniqueness of the Cauchy problem. Linear differential equation 1 order, the equation with separated variables.

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

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

Exercises evaluation | Credit | 30 | 10 |

Examination | Examination | 70 | 21 |

Show history

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

2019/2020 | (B3942) Nanotechnology | (3942R001) Nanotechnology | P | Czech | Ostrava | 2 | Compulsory | study plan | |||

2019/2020 | (B3942) Nanotechnology | (3942R001) Nanotechnology | P | English | Ostrava | 2 | Compulsory | study plan | |||

2019/2020 | (B0719A270001) Nanotechnology | P | Czech | Ostrava | 1 | Compulsory | study plan | ||||

2018/2019 | (B3942) Nanotechnology | (3942R001) Nanotechnology | P | Czech | Ostrava | 2 | Compulsory | study plan | |||

2018/2019 | (B3942) Nanotechnology | (3942R001) Nanotechnology | P | English | Ostrava | 2 | Compulsory | study plan | |||

2018/2019 | (B1701) Physics | (1702R001) Applied Physics | P | Czech | Ostrava | 2 | Compulsory | study plan | |||

2017/2018 | (B1701) Physics | (1702R001) Applied Physics | P | Czech | Ostrava | 2 | Compulsory | study plan | |||

2017/2018 | (B3942) Nanotechnology | (3942R001) Nanotechnology | P | Czech | Ostrava | 2 | Compulsory | study plan | |||

2016/2017 | (B3942) Nanotechnology | (3942R001) Nanotechnology | P | Czech | Ostrava | 2 | Compulsory | study plan | |||

2016/2017 | (B1701) Physics | (1702R001) Applied physics | P | Czech | Ostrava | 2 | Compulsory | study plan | |||

2016/2017 | (B1701) Physics | (1702R001) Applied Physics | P | Czech | Ostrava | 2 | Compulsory | study plan | |||

2015/2016 | (B1701) Physics | (1702R001) Applied physics | P | Czech | Ostrava | 2 | Compulsory | study plan | |||

2015/2016 | (B3942) Nanotechnology | P | Czech | Ostrava | 2 | Compulsory | study plan | ||||

2015/2016 | (B3942) Nanotechnology | (3942R001) Nanotechnology | P | Czech | Ostrava | 2 | Compulsory | study plan | |||

2014/2015 | (B1701) Physics | (1702R001) Applied physics | P | Czech | Ostrava | 2 | Compulsory | study plan | |||

2014/2015 | (B3942) Nanotechnology | P | Czech | Ostrava | 2 | Compulsory | study plan | ||||

2013/2014 | (B1701) Physics | (1702R001) Applied physics | P | Czech | Ostrava | 2 | Compulsory | study plan | |||

2013/2014 | (B3942) Nanotechnology | P | Czech | Ostrava | 1 | Compulsory | study plan | ||||

2013/2014 | (B3942) Nanotechnology | P | Czech | Ostrava | 2 | Compulsory | study plan | ||||

2012/2013 | (B3942) Nanotechnology | P | Czech | Ostrava | 2 | Compulsory | study plan | ||||

2012/2013 | (B3942) Nanotechnology | (3942R001) Nanotechnology | P | Czech | Ostrava | 2 | Compulsory | study plan | |||

2011/2012 | (B3942) Nanotechnology | P | Czech | Ostrava | 2 | Compulsory | study plan | ||||

2010/2011 | (B3942) Nanotechnology | P | Czech | Ostrava | 2 | Compulsory | study plan |

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