exterior differentiation - Maple Help

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difforms[d] - exterior differentiation

Calling Sequence

d(expr)

d(expr, forms)

Parameters

expr

-

expression or list of expressions

forms

-

(optional) list of 1-forms, i.e. wdegree=one

Description

• 

The function d computes the exterior derivative of an expression. If the expression is a list, then d is applied to each element in the list.

• 

When d is called with an expression and a list of 1-forms, any name of type scalar in the expression will be expanded in these 1-forms.  It is assumed that the 1-forms are independent.  For each 1-form, a new scalar is created to be the component for that 1-form.

• 

The command with(difforms,d) allows the use of the abbreviated form of this command.

Examples

withdifforms:

defformf=0,w1=1,w2=1,w3=1,v=1,x=0,y=0,z=0

dx2y

2xydx+x2dy

(1)

dfx,y,z

xfx,y,zdx+yfx,y,zdy+zfx,y,zdz

(2)

df,w1,w2,w3

fw1w1+fw2w2+fw3w3

(3)

df,dx,dy1,v1

fxdx+fy1dy1+fv1v1

(4)

dfw1 &^ w2

&^df,w1,w2+fdw1 &^ w2fw1 &^ dw2

(5)

dxy,y2,w2

ydx+xdy,2ydy,dw2

(6)

See Also

D, diff, difforms, difforms[mixpar]


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