Q10Mathematics I
Question
2 marks
State Stokes theorem.
Answer
Stokes' Theorem establishes a profound mathematical equivalence between the macroscopic circulation (line integral) of a vector field around a closed curve and the microscopic rotation (surface integral of the curl) over any bounding surface.
In advanced vector calculus, Stokes' Theorem serves as the higher-dimensional generalization of Green's Theorem. It rigidly states that the circulation of a continuous vector field exactly around a closed boundary curve equals the total surface flux of its curl.
This absolute theorem mathematically connects 1D line integrals to 2D surface integrals, provided the surface orientation strictly follows the right-hand rule relative to the boundary curve's defined path.