Scalar Value

[MN_10921447]

Hi everyone.

Im trying to calculate the det of the Jacobian however i keep getting this error.
Just what exactly does "scalar value" mean in mathcad? And more importantly, what can i assign u and v to fix this?
In my problem both u ∈ [0,2π] and v ∈ [0,π] but i dont know how to assign these values in mathcad.

[Cornel]

Post your Mathcad file...

Here is an example:

[MN_10921447]

Here it is.

[Cornel]

[MN_10921447]

Thank you. But can you explain to me why it works for you,but it dosent for me? I dont see any difference at the first glance,other then everything being re arranged.

[Cornel · Accepted solution]

Then see this, its your initial Mathcad file. Nothing I changed. You defined in a wrong way the Jacobian matrix...

[MN_10921447]

Oh i see, thank you. The problem is that i dont know how to define partial derivatives in mathcad. Is this also why i cant calculate the surface area of a bohemian dome?

[Cornel]

I am not sure about these formula...

[Werner_E]

---

@Cornel wrote:

Then see this, its your initial Mathcad file. Nothing I changed.

---

Sure you did (apart from correcting the Jacobian definition)!

You change the definition of u and v from ranges to simple scalars. Otherwise you would get the very same error message with the expression in the last line.

@MN_10921447 

Apart from the correct definition of the derivatives in the Jacobian, the main "trick" is this:

Making the determinant a function dependent on r, u and v. Otherwise Prime tries to use the ranges which you defined at the top and fails with the error message you had seen.

BTW, I would do without the u- and v-ranges and use CreateMesh for plotting the sphere:

and ... you could create a vector function and use the built-in "Jacob" function:

Its not necessary to evaluate symbolically, but it sure makes sense, I guess.

[Cornel]

---

@Werner_E wrote:

---

@Cornel wrote:

Then see this, its your initial Mathcad file. Nothing I changed.

---

Sure you did (apart from correcting the Jacobian definition)!

You change the definition of u and v from ranges to simple scalars. Otherwise you would get the very same error message with the expression in the last line.

Yes, true. I didn't notice because from the beginning u and v were changed below in worksheet to scalars by MN guy. If u and v are changed to simple scalars then we can use:

Otherwise, if u and v are range variables then we need to use what also Werner said, DJ(r, u, v):

[MN_10921447]

Oh, wow,I completely missed those too. Its unreal how much trouble one tiny oversight can create. Also i had no idea you can just do everything with vectors.

Thank you.