origin of differential forms in Euclidean-flat R^4


read carefully:

aid

 

errata:

\left\{\frac{\partial x}{\partial x}=1,\frac{\partial x}{\partial y }=0,\frac{\partial x}{\partial z}=0,\frac{\partial x}{\partial t}=0\right\}  \longrightarrow dx=[1,0,0,0] ={\rm{grad}}(x)
\left\{\frac{\partial y}{\partial x}=0,\frac{\partial y}{\partial y}=1,\frac{\partial y}{\partial z}=0,\frac{\partial y}{\partial t}=0\right\}  \longrightarrow dy=[0,1,0,0] ={\rm{grad}}(y)
\left\{\frac{\partial z}{\partial x}=0,\frac{\partial z}{\partial y }=0,\frac{\partial z}{\partial z}=1,\frac{\partial z}{\partial t}=0\right\}  \longrightarrow dz=[0,0,1,0] ={\rm{grad}}(z)
\left\{\frac{\partial t}{\partial x}=0,\frac{\partial t}{\partial y }=0,\frac{\partial t}{\partial z}=0,\frac{\partial t}{\partial t}=1\right\}  \longrightarrow dt=[0,0,0,1] ={\rm{grad}}(t)

Leave a comment

Filed under math

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s