Gurantor department | Department of Applied Mathematics | Credits | 4 |

Subject guarantor | Mgr. Petr Vodstrčil, Ph.D. | Subject version guarantor | Mgr. Petr Vodstrčil, Ph.D. |

Study level | undergraduate or graduate | Requirement | Compulsory |

Year | 1 | Semester | summer |

Study language | English | ||

Year of introduction | 2015/2016 | Year of cancellation | |

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

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

VOD03 | Mgr. Petr Vodstrčil, 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 |

Combined | Credit and Examination | 10+10 |

Students will get basic practical skills for work with fundamental concepts, methods and applications of differential and integral calculus of one-variable real functions.

Lectures

Tutorials

In the first part of this subject, there are fundamental properties of the set of real numbers mentioned. Further, basic properties of elementary functions are recalled. Then limit of sequence, limit of function, and continuity of function are defined and their basic properties are studied. Differential and integral calculus of one-variable real functions is essence of this course.

J. Bouchala, M. Sadowská: Mathematical Analysis I, VŠB-TUO.

L. Gillman, R. H. McDowell: Calculus, New York, W.W. Norton & Comp. Inc. 1973.

During the semester we will write 6 tests.

No additional requirements are imposed on the student.

Subject has no prerequisities.

Subject has no co-requisities.

Lectures:
Real numbers. Supremum and infimum. Principle of mathematical induction.
Real one-variable functions and their basic properties.
Elementary functions.
Sequences of real numbers. Limit of sequence.
Theorems on limit of sequences, calculation of limits.
Limit of a function. Theorems on limits.
Continuity of a function. Theorems on limits and continuity of composite function.
Derivative and differential of a function. Calculation of derivatives.
Basic theorems of differential calculus. L'Hospital rule.
Intervals of monotony of a function. Local extremes of a function.
Convexity and concavity. Asymptotes of graphs. Course of a function.
Global extremes of a function. Weierstrass-theorem.
Taylor's theorem.
Fundamental principles of integral calculus.
Exercises:
Application of principle of mathematical induction. Supremum and infimum of various sets.
Functions and their properties. Graph of a function. Functions with absolute value.
Elementary functions. Calculation of inverse function.
Finding domain of definition of a function. Arithmetic and geometric sequence.
Calculation of limits of sequences.
Calculation of limits of functions.
Limits of functions. Continuity of a function.
Calculation of derivatives.
Tangent and normal line. L'Hospital rule.
Monotony of a function. Local extremes.
Convexity and concavity, asymptotes. Course of a function.
Global extremes of a function.
Taylor's polynom and error estimation.
Calculation of antiderivatives and Riemann integrals.

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 | (B2660) Computer Systems for the Industry of the 21st. Century | P | English | Ostrava | 1 | Compulsory | study plan | ||||

2019/2020 | (B2649) Electrical Engineering | P | English | Ostrava | 1 | Compulsory | study plan | ||||

2019/2020 | (B2649) Electrical Engineering | K | English | Ostrava | 1 | Compulsory | study plan | ||||

2018/2019 | (B2660) Computer Systems for the Industry of the 21st. Century | P | English | Ostrava | 1 | Compulsory | study plan | ||||

2018/2019 | (B3973) Automotive Electronic Systems | P | English | Ostrava | 1 | Compulsory | study plan | ||||

2018/2019 | (B2649) Electrical Engineering | P | English | Ostrava | 1 | Compulsory | study plan | ||||

2018/2019 | (B2649) Electrical Engineering | K | English | Ostrava | 1 | Compulsory | study plan | ||||

2017/2018 | (B2649) Electrical Engineering | P | English | Ostrava | 1 | Compulsory | study plan | ||||

2017/2018 | (B2649) Electrical Engineering | K | English | Ostrava | 1 | Compulsory | study plan | ||||

2017/2018 | (B2660) Computer Systems for the Industry of the 21st. Century | P | English | Ostrava | 1 | Compulsory | study plan | ||||

2017/2018 | (B3973) Automotive Electronic Systems | P | English | Ostrava | 1 | Compulsory | study plan | ||||

2016/2017 | (B2649) Electrical Engineering | P | English | Ostrava | 1 | Compulsory | study plan | ||||

2016/2017 | (B2649) Electrical Engineering | K | English | Ostrava | 1 | Compulsory | study plan | ||||

2016/2017 | (B2660) Computer Systems for the Industry of the 21st. Century | P | English | Ostrava | 1 | Compulsory | study plan | ||||

2015/2016 | (B2649) Electrical Engineering | P | English | Ostrava | 1 | Compulsory | study plan | ||||

2015/2016 | (B2649) Electrical Engineering | K | English | Ostrava | 1 | Compulsory | study plan |

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