曼彻斯特大学电气学院math总结.doc

Mathematics 1. The Laplace Transform The U-I relationship of the inductor is The U-I relationship of the capacitor is Laplace transform in single side Laplace transform table x(t)X(s)1 Time shift property of Laplace transform: S shift property of inverse Laplace transform , (for the differentiation, the ROC will be larger than the original ROC ) . damped 阻尼的 impedance 阻抗 admittance 导纳 factorize 因式分解 electromagnetism 电磁学、电磁 Heaviside function 阶跃方程 proceed开始；继续进行；发生；行进 Ohm’s law欧姆定律 Kichhoff’s law基尔霍夫定律 omit 省略、忽略  2. Vector Calculus Gradient of a scalar field , which transform a scalar to a vector. Divergence of a vector field , which transform a vector to a scalar. And . The relationship between electric field and electrical potential is Laplace’s equation: , which in many cases is valid. The dot product of vectors: The cross product of vectors: The curl of a vector field The sequence of differentiation does not matter and can be changed randomly for most cases, i.e. . For a given vector field , is not a gradient field and conservative field, which is the method to judge if a vector is a gradient field (conservative field) or not. For any vector field , 0. The equation of the tangent line of a given value of t can be written as , where w is another parameter. For any vector field , If the direction is given by a vector with any non-zero length, then the directional derivative of in is . Unit surface normal vector is A line integral of a vector function over a curve C (from point A to point B) is defined as For conservative vectors, ,, (fundamental theorem of line integrals) All gradient fields are conservative, and all conservative fields are gradient fields. density 密度、强度 flux 流量 tangent 切线 ellipse 椭圆 directional derivative 方向导数 normal vector 法向量 implicit 暗含的 orthogonal 正交的 commutative 互易的、互换的 distributive 分配的 associative 结合的 compatible 兼容的 symmetric 对称的 minor 降阶行列式 multiple 倍数 augmented 增广的 pivot 转动 upper/lower trian