Scalar fields: partial derivatives, grad f and |grad f|

[RosanelladC]

Hello All

I'm setting up a worksheet to enable me to check my workings for when I need to solve a two or three dimensional scalar field by hand (cylindrical & spherical polar coordinates).

Mathcad partially differentiate some but not all and it flags some variable. Also, I cannot get grad f or |grad f|.

I'm obviously setting up something incorrectly.

Could someone point me in the right direction, please?

I'm enclosing my worksheet.

[AlanStevens]

The attached shows some modifications to the cylindrical section. It might (or might not!) be of some help.

Alan

[RosanelladC · Accepted solution]

Thank you Alan for the corrected worksheet

Question: I've noticed that MathC does not return a scalar for | grad f | . Should it not return a scalar value instead of a vectorial value, as I'm not working out | grad f | in the direction of its unit vector grad f / | grad f | ?

[AlanStevens]

Rosanella di-Costanzo wrote:

Thank you Alan for the corrected worksheet

Question: I've noticed that MathC does not return a scalar for | grad f | . Should it not return a scalar value instead of a vectorial value, as I'm not working out | grad f | in the direction of its unit vector grad f / | grad f | ?

It does return a scalar value. However, to see this more clearly it's probably best to define ep as a function and then insert specific values when it is called. For example:

(Actually, ep need only be defined as a function of x and y. I've included z above, but it's superfluous).

Alan

[RosanelladC]

Many thanks Alan