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

Subject guarantor | prof. RNDr. Jiří Bouchala, Ph.D. | Subject version guarantor | prof. RNDr. Jiří Bouchala, Ph.D. |

Study level | undergraduate or graduate | Requirement | Compulsory |

Year | 1 | Semester | winter |

Study language | English | ||

Year of introduction | 2016/2017 | Year of cancellation | 2020/2021 |

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

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

Login | Name | Tuitor | Teacher giving lectures |

BOU10 | prof. RNDr. Jiří Bouchala, Ph.D. | ||

SIN29 | RNDr. Libor Šindel |

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

Form of study | Way of compl. | Extent |

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

Upon the successful completion of the course, students will be able to actively use new terms in the field of differential
and integral calculus.

Lectures

Tutorials

The aim of the course Differential and Integral Calculus of Functions of Real and Complex Variables is to introduce students to differential and integral calculus of real and complex functions including functional series. Simultaneously, they should acquire a certain computational skill and ability to apply the taught theory on practical problems.

1. James and D.Burley, P.Dyke, J.Searl, N.Steele, J.Wright: Advanced Modern Engineering Mathematics, Addison-Wesley
Publishing Company, 1994.

1. James and D.Burley, P.Dyke, J.Searl, N.Steele, J.Wright: Advanced Modern Engineering Mathematics,Addison-Wesley
Publishing Company, 1994.
2. William L. Briggs, Van Emden Henson: An Owner’s Manual for the Discrete Fourier Transform, SIAM, 1995, ISBN
0-89871-342-0.
3. Michael W. Frazier: An introduction to wavelets through Linear Algebra, Springer, 1999, ISBN 0-387-98639-1

During the semester we will write two tests.

There are no additional requirements on a student.

Subject has no prerequisities.

Subject has no co-requisities.

Lectures + exercises:
Multi-variable Differential and Integral Calculus of Real Functions.
1.Sequence Convergence. Limits, Functions, and Continuity.
2.Total Differential, Partial Derivatives, Directional Derivative, Gradient.
3.Higher Order Differentials, Taylors Polynomial, Taylor’s Theorem.
4.Implicit Function Theorem.
5.Local, Global, and Constrained Extrema, Lagrange multipliers.
6.Double and Triple Integral. Fubini’s Theorem for Double and Triple Integral.
7.Substitution Theorem. Application of Multiple Integrals.
Functions of a Complex Variable.
8.Complex Numbers, Extended Gaussian Images.
9.Complex Functions of a Real and Complex variable.
10.Limits, Continuity, and Complex Functions Derivatives. Conformal Mapping.
11.Complex Function Integration, Cauchy Theorem.
12.Power and Taylor Series. Laurent Series. Rezidue Theorem.
13.Scalar Multiplication, Norm, Orthogonal Systems.
14.Fourier Series.

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 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

2018/2019 | (N2658) Computational Sciences | (2612T078) Computational Sciences | P | English | Ostrava | 1 | Compulsory | study plan | ||||

2017/2018 | (N2658) Computational Sciences | (2612T078) Computational Sciences | P | English | Ostrava | 1 | Compulsory | study plan | ||||

2016/2017 | (N2658) Computational Sciences | (2612T078) Computational Sciences | P | English | Ostrava | 1 | Compulsory | study plan |

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