differential geometry

Question

 What is the differential (matrix form) of 

 

Answer 1

Hi  Adnan,

it means:

when you have a point such as A(1,2)  in R^2

this point will have new position base of defined function such as:

A (1 , 2 ) ------> ( 1+2, 1*2, e^1*2 )

A (1 , 2 ) ------> (3. 2, e² )

(1,2) is in coordinate plane but new position is (3. 2, e² ) in the 3 detentions or space

another example what is the origin in R^2 base of above function

O(0,0) -------> ( 0+0. 0*0, e^0*0)

O(0,0) --------> ( 0, 0, 1)

I hope it is useful,

Minoo