Gurantor department | Department of Applied Mathematics | Credits | 8 |

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

Study level | undergraduate or graduate | Requirement | Choice-compulsory |

Year | 2 | Semester | winter |

Study language | Czech | ||

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

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

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

Login | Name | Tuitor | Teacher giving lectures |

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

VLA04 | Ing. Oldřich Vlach, 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.

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

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

Continuous assessment: Students will keep homework and projects. During the semester will be held two written tests rated in total a maximum of 20 points. The projects can acquire a maximum 10 points. Terms of the credit: Credit will be granted if the student receives written tests and projects at least 10 points.

There are not defined other requirements for student.

Subject has no prerequisities.

Subject has no co-requisities.

Lectures: 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 on the links between the basic 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 for the existence of local extreme. Constrained local extrema, Lagrange multipliers method. Search global extremes - practices. Riemann double integral, basic properties. Fubini's theorem for double integrals. Substitution theorem for double integrals, applications, Riemann double integral triple integrals, basic properties. Fubini theorem for integrals. Substitution theorem for integrals. Applications. Practice: Investigation of different topological and metric properties of subsets eukleidovského space. Determining the limit of a sequence of points in Euclidean space. Discussion of terms limits and continuity of functions of several variables. Methods of calculating the limit, the verification link. The calculations of partial derivatives and directional derivatives. Gradient. Geometric interpretation. Calculations of higher order differentials. Application of Taylor's theorem for functions of several variables. Working with functions defined implicitly. Search for extremes of functions of several variables - local and constrained local extremes. Finding the global minima. Calculation of double integrals - Fubini's theorem. Calculation of double inegrálu - substitution to polar coordinates. Applications. The calculation of triple integrals - Fubini's theorem. Substitution into cylindrical and spherical coordinates. Applications of triple integrals. Projects: Solving difficult problems of differential and integral calculus of functions of several 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 | |
---|---|---|---|---|---|---|---|---|---|---|---|

2014/2015 | (B2647) Information and Communication Technology | (1103R031) Computational Mathematics | P | Czech | Ostrava | 2 | Choice-compulsory | study plan | |||

2014/2015 | (B2647) Information and Communication Technology | (1103R031) Computational Mathematics | K | Czech | Ostrava | 2 | Choice-compulsory | study plan | |||

2013/2014 | (B2647) Information and Communication Technology | (1103R031) Computational Mathematics | P | Czech | Ostrava | 2 | Choice-compulsory | study plan | |||

2013/2014 | (B2647) Information and Communication Technology | (1103R031) Computational Mathematics | K | Czech | Ostrava | 2 | Choice-compulsory | study plan | |||

2012/2013 | (B2647) Information and Communication Technology | (1103R031) Computational Mathematics | P | Czech | Ostrava | 2 | Choice-compulsory | study plan | |||

2012/2013 | (B2647) Information and Communication Technology | (1103R031) Computational Mathematics | K | Czech | Ostrava | 2 | Choice-compulsory | study plan | |||

2011/2012 | (B2647) Information and Communication Technology | (1103R031) Computational Mathematics | P | Czech | Ostrava | 2 | Choice-compulsory | study plan | |||

2011/2012 | (B2647) Information and Communication Technology | (1103R031) Computational Mathematics | K | Czech | Ostrava | 2 | Choice-compulsory | study plan | |||

2010/2011 | (B2647) Information and Communication Technology | (1103R031) Computational Mathematics | P | Czech | Ostrava | 2 | Choice-compulsory | study plan | |||

2010/2011 | (B2647) Information and Communication Technology | (1103R031) Computational Mathematics | K | Czech | Ostrava | 2 | Choice-compulsory | study plan |

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