# Courses Catalogue

### Syllabus of the course: * Mathematics for Physics II *

In this web page we provide the syllabus of the course Mathematics for Physics II, offered by the Department of Physics.

The list of the courses offered during the current accademic year is available here.

The list of all courses offered by the Department of Physics is available here.

Code | Φ-311 |
---|---|

Type | B |

ECTS | 6 |

Hours | 4 |

Semester | Spring |

Instructor | P. Ditsas, N. Tsamis |

Program | Monday, 11:00-13:00, Room 1 Wednesday, 11:00-13:00, Room 1 |

Web page | |

Goal of the course | This course aims to provide 3rd and 4th year student with mathematical tool to handle advanced problems in modern theoretical physics. |

Syllabus | - Introductory Complex Analysis: Complex numbers. The complex plane. - Complex functions: Complex functions. Branch points. Multivalued functions. Continuity and the derivative of complex functions. Cauchy-Riemann conditions. - Analytic Functions: Analytic functions and applications. Cauchy's theorem and integration. Derivatives of analytic functions. Taylor and Laurent series.Classification of singular points. - Applications of Residues: Calculation of definite integrals. Calculation of generalized integrals. - Functional Spaces: Linear Operators, Fourier Series and Transformations. Distributions, Delta function. - Linear Differential Operators: Operator Algebra. Conjugation.Operator Specturm. - Applications to Green's Functions: Inhomogenous linear differential equations. Sturm-Liouville problems. Analytic properties of Green's functions. The resolvent. |

Bibliography | R.Churchill-J.Brown : Complex functions and Applications |

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