# Courses Catalogue

### Syllabus of the course: * General Mathematics II (Exercises) *

In this web page we provide the syllabus of the course General Mathematics II (Exercises), 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-112 |
---|---|

Type | A |

ECTS | 7 |

Hours | 2 |

Semester | Winter |

Instructor | G. Athanasiu |

Program | Monday, 15:00-17:00, Room 3 |

Web page | |

Goal of the course | The course is intended for first year undergraduate students and its purpose is to give a rather complete working knowledge of differential and integral calculus of functions of two and more variables. During the fall semester to course is offered in the form of selfstudy with only one two-hour lecture per week for the students that did not pass it during the spring semester. Emphasis is given in problem solving. |

Syllabus | Vector calculus: Vectors, Vector spaces, scalar, exterior and mixed product. Lines and planes in 3-dimensional Euclidean space. Vector fields. Curves: Parametric representation of curves, in two and three dimensions, velocity and acceleration, moving frame, curvature, torsion. Functions of many variables: Definition of functions of two or more variables, limits, continuity, level surfaces. Partial derivatives, differential, differentiability .Taylor’s expansion of functions of many variables, extrema, extrema under constraints. Coordinate transformation, transformation of partial derivatives, application to the Special Theory of Relativity.Parametric representation of surfaces, curvilinear coordinates. Multiple Integrals: Double integrals, triple integrals, curvilinear integrals, surface integrals, Theorems of Green, Stokes, and Applications in Physics. |

Bibliography | «THOMAS, Απειροστικός Λογισµός» –R. L. Finney, M.D. Weir, F.R. Giordano, (Τόµοι Ι &
ΙΙ) – Μετάφραση Μ. Αντωνογιαννάκης «Ανώτερα Μαθηµατικά», M.R. Spiegel. «Διαφορικός και Ολοκληρωτικός Λογισµός» - M. Spivak. |

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