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第12講 Parametrized Surfaces and Tangent Vectors

L12_A
       1. Definition: Parametrized Surfaces and Regular Parametrized Surfaces
       2. Example: The Tangent Surface
 
L12_B 
       1. Proposition: A Regular Parametrized Surface Is Locally 
           a Regular Surface
       2. Definition: Tangent Vectors
 
L12_C 
       1. Proposition: Relation Between T_p(S) and dx_q(R^2)
       2. Proposition: The Tangent Plane to f^{-1}(a) Is the Kernel of df_p

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