How Does Function f Transform in a New Coordinate System?

[sadegh4137]

consider we have function

f= f ( x , y )

that x and y are our coordinate system.
we know that x and y how transform to new coordinate system for example
x' and y'

here arises a question and that
how function f transform to new coordinate system?

 

[mathman]

g(x',y') = f(x(x',y'),y(x',y'))

Based on your description, this is all that one can say.

 

[sadegh4137]

can we say that the form of function can not change?

and for transform a function, its enough that we transform coordinates?

for example
consider have this function
exp( i kx - wt)

and we want to transform this under Galilean transformation can we put x and t exchange by x' and t', without form of function change?

 

[mathman]

For the specific case you described, the form doesn't change. The transformation is linear, but there could be situations where that is not enough.

 

[sadegh4137]

it means you say for all transformation, it enough we transform x and y to x' and y' for example

without think to form of function

some people say it isn't enough beside this, we should know the form of function how will change.

it is true?

 

[mathman]

Look at x²e^y

It is not clear to me what you are trying to ask.