Faculty of Mathematics and Computer Science

Calculus on manifolds |

Code |
Semes-ter |
Hours: C+S+L |
Credits |
Type |
Section |

Teaching Staff in Charge |

Assoc.Prof. VARGA Csaba Gyorgy, Ph.D., csvarga@cs.ubbcluj.ro Assoc.Prof. PINTEA Cornel, Ph.D., cpintea@math.ubbcluj.ro |

Aims |

The course is the first step in Differential Topology and Global Analysis. It is necessary for all students which intend to study and to improve these topics in the Master of Science program. |

Content |

1. Differential forms: elements of exterior algebra, determinants, volume and the Hodge operator, exterior differential forms, exterior derivate, interior product, orientability, elements of volume and codifferential.
2. Intagration on differential manifolds and cohomology: integration of exterior differential forms, Stokes theorem, clasical theorems of Green, Gauss and Stokes, Poincare lemma, Mayer-Vietoris exact sequence, Poincare duality, de Rham theorem. 3. Cohomology and Morse theory: elements of Morse theory , aplications in the calculus of cohomology groups, Morse inequalities. |

References |

1. Andrica, D., Critical Point Theory and Some Applications, Univ. of Ankara, 1993, 150 pp.
2. Bredon, G.E., Topology and Geometry, Springer-Verlag, 1993. 3. Conlon, L., Differentiable Manifolds. A First Course, Birkhauser, 1993. 4. Godbillon, C., Elements de topologie algebrique, Hermann, Paris, 1971. |

Assessment |

Exam. |