Differential geometry and complex analysis 1984/85, 1985/86.

For 3rd year mathematics students. 
Official name: Istituzioni di Geometria superiore.
DIFFERENTIAL GEOMETRY

Complex numbers
n-th roots
The complex numbers as matrices
Differentiable functions of several real variables
Curve integrals
Surfaces and hypersurfaces
Classical tensor calculus
Tensor product of modules
Tensor algebra
Exterior algebra
Determinants from exterior algebra
Alternating differential forms
Rotation and divergence
General transformation formulas for integrals
Differentiable manifolds
Differentiable mappings between manifolds
Directional derivative in R^d
Tangent space
The tangent bundle as a differentiable variety
Tangent vectors as derivations
Tangent vectors as elements of (Ann/Ann^2)'
Tangent vectors as tangent vectors of curves
Vector fields and sections
Integral curves of a vector field
Differential forms on a variety
Mapping and derivation of differential forms
The simplicial Stokes theorem
Stokes' theorem for chains

HOLOMORPHIC FUNCTIONS

Cauchy's integral theorem
Cauchy's integral formula
Power series in the complex field
Every holomorphic function is analytic
First applications
The identity theorem
Isolated singular points and Laurent series
Theorem of residues
Applications of the theorem of residues
Harmonic functions