Stokes' Theorem - Special Cases

Special Cases

The general form of the Stokes theorem using differential forms is more powerful and easier to use than the special cases. Because in Cartesian coordinates the traditional versions can be formulated without the machinery of differential geometry they are more accessible, older and have familiar names. The traditional forms are often considered more convenient by practicing scientists and engineers but the non-naturalness of the traditional formulation becomes apparent when using other coordinate systems, even familiar ones like spherical or cylindrical coordinates. There is potential for confusion in the way names are applied, and the use of dual formulations.

Read more about this topic:  Stokes' Theorem

Famous quotes containing the words special and/or cases:

    I think those Southern writers [William Faulkner, Carson McCullers] have analyzed very carefully the buildup in the South of a special consciousness brought about by the self- condemnation resulting from slavery, the humiliation following the War Between the States and the hope, sometimes expressed timidly, for redemption.
    Jimmy Carter (James Earl Carter, Jr.)

    Lovers’ quarrels are not generally about money. Divorce cases generally are.
    Mason Cooley (b. 1927)