Geometrical
Mathematics for GR
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- Coordinate Systems - Defines
what coordinate systems are.
- Set Theory - The
basic definitions and notations used in set theory is given.
- Affine vs.
Metric Geometry - Describes difference between affine and metric geometry.
- Orthogonal Transformations -
Defines and elaborates of orthogonal transformation.
- Geodesic
Deviation - The relationship for geodesic deviation is provided.
- Geodesics -
Describes what a geodesics is (path of extremal length) and derives the
equations which describe geodesics.
- Introduction
to Manifolds - An introduction to manifolds is given along with the
terminology which goes along with it.
- 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.
- Calculus of Variations - Explains
rudiments of the calculus of variations.
- Metric Tensor -
Defines and describes the metric tensor.
- Total Derivative
- The components of the total derivative are derived in terms of the
Christoffel symbols.
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