Given a surface defined in parametric equations, find the surface area

[theBEAST]

Homework Statement

The Attempt at a Solution

So I am trying to find the gradient because in class we were taught that the surface area is the magnitude of the gradient divided by the magnitude of the dot product between the gradient and normal to the projected surface.

I noticed in the textbook, the solution uses some sort of vector r_u and r_v, however this was not covered in class so I am somewhat confused.

Is it possible to do this problem with just the knowledge I know?

 

[mighty2000]

Dear student,

Thank you for reaching out and seeking clarification on this topic. I understand your confusion about the use of the vector r_u and r_v in finding the gradient. These vectors represent the partial derivatives of the surface with respect to the u and v parameters, respectively. They can also be thought of as the direction in which the surface is changing the most.

While it is possible to find the gradient using just the knowledge you have, understanding and using these partial derivatives can provide a more accurate and efficient solution. I would suggest reviewing the material on partial derivatives and their applications in order to better understand this concept.

Additionally, I would also recommend seeking guidance from your instructor or TA if you are still struggling with this concept. They can provide further clarification and examples to help you better understand and apply the concept of finding the gradient.

I hope this helps. Keep up the good work and don't hesitate to reach out with any further questions.



Scientist