First Order Differential Calculus on Manifolds
Alexandre De Paris
A program of the course at the 4-th Italian Diffiety School,
(Forino, July 17-29, 2000)
(Preliminary version)

  1. Tangent vectors and absolute and relative vector fields. D functor
  2. The flow of a vector field. Lie derivative of vector fields. Commutators and Lie algebrae
  3. Tangent covectors and differential forms. Tensors. Main operations on tensors. Algebra of differential forms
  4. Behaviour of differential forms and covariant tensors with respect to differentiable mappings of manifolds. Lie derivatives of covariant tensors.
  5. Exterior differential and de Rham cohomology
  6. Cartan's formula and homotopy property of de Rham cohomology
  7. Integration theory as de Rham cohomology

Passing the exam during the school required 9 solved problems. To pass the exam by email one should solve 11 problems.
The exam has been passed by the following students:
  1. Diego Catalano
  2. Giovanna Ilardi
  3. Emanuele Castagna
  4. Stefania Donadio
  5. Rossella Piscopo
  6. Massimiliano Malgieri
  7. Beniamino Cappelletti

Questions and suggestions should go to Jet NESTRUEV, jet @