Geometrical
Math for GR
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- Set Theory - The
basic definitions and notations used in set theory is given.
- Affine vs.
Metric Geometry - Describes difference between affine and metric geometry.
- Geodesics -
Describes what a geodesics is (path of extremal length) and derives the
equations which describe geodesics.
- Geodesic
Deviation - The relationship for geodesic deviation is provided.
- Introduction
to Manifolds - An introduction to manifolds is given along with the
terminology which goes along with it.
- Orthogonal
Transformation - The definition of orthogonal transformation and
an example of such a transformation.
- Tensors - The
Analytic View - An introductions to tensors in which tensors are defined
through their transformation properties
- Tensors - The
Geometric View - An introductions to tensors in which tensors are defined
through their geometric properties
- Parallel Transport - The expression for parallel transport is derived.
The affine connection is introduced.
- Invariance - Defines
and analyses the concept of invariance.
- Metric Tensor -
Defines and describes the metric tensor.
- Total Derivative
- The components of the total derivative are derived in terms of the
Christoffel symbols.
- Vector
Components - The components of a vector are defined.
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