电磁波英文汉语课件讲述.ppt

1-9 格林定理 (标量) 设任意两个标量场? 及?，若在区域 V 中具有连续的二阶偏导数，可以证明该两个标量场? 及? 满足下列等式 S V ?,? 式中S 为包围V 的闭合曲面； 为标量场 ? 在 S 表面的外法线 en 方向上的偏导数。 根据方向导数与梯度的关系，上式又可写成 上两式称为标量第一格林定理。 基于上式还可获得下列两式： 上两式称为标量第二格林定理 1-9 格林定理 (标量) The first vector Green’s theorem: where S is the closed surface bounding the volume V, the direction of the surface element dS is in the outward normal direction, and the second order partial derivatives of two vector fields P and Q exist in the volume V 1-9 Green’s Theorems (Vector) The second vector Green’s theorem: 设任意两个矢量场 P 与 Q ，若在区域 V 中具有连续的二阶偏导数，那么，可以证明该矢量场 P 及 Q 满足下列等式： 式中S 为包围V 的闭合曲面；面元 dS 的方向为S 的外法线方向。上式称为矢量第一格林定理。 1-9 格林定理 (矢量) 基于上式还可获得下式： 此式称为矢量第二格林定理。 1-9 格林定理 (矢量) all Green’s theorems give the relationship between the fields in the volume V and the fields at its boundary S. By using Green’s theorem, the solution of the fields in a region can be expanded in terms of the solution of the fields at the boundary of that region. Green theorem also gives the relationship between two scalar fields or two vector fields. Consequently, if one field is known, then another field can be found out based on Green theorems. 1-9 Green’s Theorems (Summary) 格林定理建立了区域 V 中的场与边界 S 上的场之间的关系。因此，利用格林定理可以将区域中场的求解问题转变为边界上场的求解问题。 格林定理说明了两种标量场或矢量场之间应该满足的关系。因此，如果已知其中一种场的分布特性，即可利用格林定理求解另一种场的分布特性。 1-9 格林定理 (小结) 1-10 Uniqueness Theorem for Vector Fields For a vector field in a region, if its divergence, rotation(Curl), and the tangential component or the normal component at the boundary are given, then the vector field in the region will be determined uniquely. The divergence and the rotation of a vector field represent the sources of the field. Therefore, the above uniqueness theorem shows that the field in the region V will be determined uniquely by its source and boundary condition. The vector field in an unbounded space is uniquely determined only by its divergence and rotation if 1-10 矢量场的惟一性