Fields

- A vector or a tensor
*field*is a mapping that assigns a vector or a tensor to every point of a manifold. - For this to make any sense, there must be a whole vector
space available at each point of the manifold from which
to choose a vector of the vector field. That space is
called a
*tangent space*. - For this, in turn, to make any sense, we must have some means of comparing tangent vector spaces at nearby points. This is usually described in terms of a parallel transport of a vector between those points. Remember that the tangent spaces at two different points are two completely different spaces.
- A structure that comprises a manifold (also called a
*base space*, from every point of which grows a Lie group (a tangent vector space attached to a point of the manifold is a special example of a Lie group) is called a*fibre bundle*. The groups that grow from the points of the manifold are called*fibres*. - All those fibres taken together form a manifold too
which is called a
*total space*.

- A brief review of field theory concepts
- Classification of Field Equations
- Diffusion Equation
- Fortran Shifts
- Parallel Execution
- Fields and Rasters