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Code: | M2008 | Acronym: | M2008 | Level: | 200 |

Keywords | |
---|---|

Classification | Keyword |

OFICIAL | Mathematics |

Active? | Yes |

Responsible unit: | Department of Mathematics |

Course/CS Responsible: | First Degree in Mathematics |

Acronym | No. of Students | Study Plan | Curricular Years | Credits UCN | Credits ECTS | Contact hours | Total Time |
---|---|---|---|---|---|---|---|

L:B | 0 | Official Study Plan | 3 | - | 6 | 56 | 162 |

L:CC | 0 | Plano de estudos a partir de 2014 | 2 | - | 6 | 56 | 162 |

3 | |||||||

L:F | 26 | Official Study Plan | 2 | - | 6 | 56 | 162 |

3 | |||||||

L:G | 0 | study plan from 2017/18 | 2 | - | 6 | 56 | 162 |

3 | |||||||

L:M | 114 | Official Study Plan | 2 | - | 6 | 56 | 162 |

L:Q | 5 | study plan from 2016/17 | 3 | - | 6 | 56 | 162 |

Teacher | Responsibility |
---|---|

Semyon Borisovich Yakubovich |

Theoretical classes: | 2,00 |

Theoretical and practical : | 2,00 |

Type | Teacher | Classes | Hour |
---|---|---|---|

Theoretical classes | Totals | 1 | 2,00 |

Semyon Borisovich Yakubovich | 2,00 | ||

Theoretical and practical | Totals | 3 | 6,00 |

Semyon Borisovich Yakubovich | 6,00 |

Studies of methods of integration, extension of definitions of the various elementary functions to the case of complex variable. Studies some applications in other areas of Mathematics and Natural Sciences. Required knowledge of Real Analysis and Linear Algebra.

Elementary functions: Polynomial, rational function, root function, exponential function, logarithm, trigonometric functions, inverse trigonometric functions.

Complex sequences: Limits of successions of complex numbers, Bolzano-Weierstrass's theorem, Cauchy criterion.

Complex functions: Curves, plane sets, limit and continuity.

Holomorphic functions: Derivative and differential, Cauchy-Riemann equations.

Integral: Integral along a curve, primitive, Cauchy's theorem for continuously differentiable functions.

Cauchy integral formula and fundamental theorems of Complex Analysis: Cauchy integral formula, Cauchy inequality, Liouville's theorem, fundamental algebra theorem, Morera's theorem.

Analytic functions: Power series, uniform convergence, radius of convergence, Abel's theorem, Taylor series, uniqueness theorem.

Laurent's series and singularities: Laurent's theorem, classification of singular points.

Residuals: Residual calculus, residual theorem and applications, logarithmic residue, Rouché's theorem. Principle of isolated zeros, module theorem. Principle of analytic continuation. Analytic continuation of elementary functions. Integrate with parameters. Analytical properties of the integrals. Laplace, Fourier and Mellin transforms. Euler gama- function. Analytic continuation of the gama- function. Functions meromorfas and intéiras. Weierstrass Theorem: any continuous function is a uniform limit of polynomial functions.

Bibliography:

1. G.Smirnov 'Complex Analysis and Applications', Escolar Editora, Lisbon, 2003.

2. Coimbra de Matos, José Carlos Santos, 'Course of Complex Analysis', Escolar Editora, Lisboa, 2000.

4. S. Lang, 'Complex Analysis', Springer-Verlag, 1999.

5. L.V. Ahlfors, 'Complex Analysis', McGraw-Hill, 1979.

Physical sciences > Mathematics > Mathematical analysis

designation | Weight (%) |
---|---|

Exame | 100,00 |

Total: |
100,00 |

designation | Time (hours) |
---|---|

Estudo autónomo | 100,00 |

Frequência das aulas | 56,00 |

Trabalho escrito | 6,00 |

Total: |
162,00 |

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Page created on: 2023-02-01 at 14:49:31 | Reports Portal

Page created on: 2023-02-01 at 14:49:31 | Reports Portal