# Question:A potential function in 2D Input mode

## Question:A potential function in 2D Input mode

Maple

Its easy to calculate a potential function for a vectorfield
But now by hand in 2D Input mode ..a struggle

Doing your homework in 2D Input mode is something totally different then the structurized explanations done in Maple input for lessons by an instructor.

Partiel differentation with respect to what variable, is not notated in 2D mode, so a serie of them showing up in the document says nothing.and reexecuting them a couple of times doubles the output if you have used a inline notation.
Basic idea here f-> f ' -> F(f ') = f  and handling variables x,y, and z for integrating/differentation

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 (1)

 (2)

Thats easy to use the ScalarPotential for a manual exercise

Example 2: finding a Potential function

Show that  is conversative and find a potential function for it.

 (3)

 (4)

 (5)

So

Now manual

 (6)

 (7)

 (8)

 (9)

 (10)

 (11)

 (12)

=

 (13)

( to z )

 (14)

=

 (15)

(to y)

 (16)

=

 (17)

(to z)

 (18)

=

 (19)

(to x)

 (20)

=

 (21)

(to y )

 (22)

=

 (23)

( to x )

Test for to be a conservative field

P1=N1 ,  M1=P2, N2=M2

.... integrating F  with respect to x ,holding  y and z fixed
Its a vector form F , probably F must be converted to scalar form? (command?)

 (24)

 (25)

Ok, can integrate to 3 variables now

Now the partial diretives from f

=  + g(y,z) constant of integration of f (the potential function)

So :  + g(y,z) (1) # a total mess as notation here done by me

The logic from this all not yet completely understood and lost oversight , but this equation (1) must be further  integrated/differentiated  to get

Step by step following the text example in Thomas Calculus (page 1075, example 2) in 2 D mode is not going well.