User:Zhennan/Greenstheorem

From SEG Wiki
Jump to navigation Jump to search
ADVERTISEMENT

Green's theorem can find its root in the fundamental theorem of integral calculus. The fundamental theorem of integral calculus expresses the value of a definite integral of a given integrable function over an interval, as the difference between the values of the function 's antiderivative at the endpoints of the interval,

where . This is a fundamental tool to solve problems within a restricted region or interval. The multidimensional extension of this theorem is divergence theorem (also called Gauss's theorem),

where is a volume enclosed by a surface . is a continuously differentiable vector field defined on . Physically, the divergence theorem relates the normal outflow of a vector field through a closed surface to the volume integration of the divergence of that field. Choosing , where and are both twice continously differentiable on the volume , there is Green's theorem (also called the Green's second identity[1]),

References

  1. [1] Aki, K., & Richards, P. G. (2002). Quantitative seismology.