Elements of Differential Calculus over Commutative Algebras:
Algebraic Tools
Smooth Manifolds
Vector Bundles
Vector Fields
Differential Forms
Lie Derivative
Basic Differential Calculus on Fat Manifolds:
Basic Definitions
The Lie Algebra of Der-operators
Fat Vector Fields
Fat Fields and Vector Fields on the Total Space
Induced Der-operators
Fat Trajectories
Inner Structures
Linear Connections:
Basic Definitions and Examples
Parallel Translation
Curvature
Operations with Linear Connections
Linear Connections and Inner Structures
Covariant Differential:
Fat de Rham Complexes
Covariant Differential
Compatible Linear Connections
Linear Connections Along Fat Maps
Covariant Lie Derivative
Gauge/Fat Structures and Linear Connections
Cohomological Aspects of Linear Connections:
An Introductory Example
Cohomology of Flat Linear Connections
Maxwell's Equations
Homotopy Formula for Linear Connections
Characteristic Classes
