Vector r v vextendsingle vextendsingle vextendsingle

This preview shows page 11 out of 11 pages.

You've reached the end of this preview.

Unformatted text preview: vector r ∂ v vextendsingle vextendsingle vextendsingle vextendsingle ∂ vector r ∂ u × ∂ vector r ∂ v vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle ∂ vector r ∂ u × ∂ vector r ∂ v vextendsingle vextendsingle vextendsingle vextendsingle du dv = parenleftbigg ∂ vector r ∂ u × ∂ vector r ∂ v parenrightbigg du dv = d vector S . Therefore, integraldisplayintegraldisplay S vector F · d vector S = integraldisplayintegraldisplay S vector F · ˆ n dS . This shows us that the interpretation of this integral is that we are integrating the com- ponent of the vector field that is normal to the surface, i.e. the component of the field that is perpendicular to the surface. Also, this is really an integration of a scalar quantity (or scalar field, vector F · ˆ n ) over the surface. Another way of saying this, is that the integral computes the flux of the vector quantity through the surface....
View Full Document

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern