An introduction to differential geometry with applications to mechanics and relativity -- Max Lipyanskiy, March 5, 2003

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We will introduce the concept of a metric and connection on an open subset of R^n. 
As an application, we will construct a geometric model for the 1-dimensional motion 
of a particle subject to a potential force. In addition, we will demonstrate how a 
geometric description of flat space-time naturally leads to the Special Theory of 
Relativity.