苏州市申报专业技术职称人员情况简 .pptVIP

Fall 2008 * ELEN 3371 Electromagnetics Fall 2007 * Instructor: Dr. Gleb V. Tcheslavski Contact: gleb@ Office Hours: Room 2030 Class web site: /gleb/em/Index.htm Vector norm Properties: Example: v = (1, 2, 3) Name Symbol value L1 – norm |v|1 6 L2 – norm |v|2 141/2 ? 3.74 L3 – norm |v|3 62/3? 3.3 L4 – norm |v|4 21/471/2? 3.15 L? – norm |v|? 3 (2.2.1) (2.2.2) (2.2.3) (2.2.4) (2.2.5) (2.2.6) Norm(x,p) Vector sum Scalar (dot) product (2.4.1) (2.4.2) (2.4.3) Definitions: Scalar projection: (2.4.5) (2.4.6) dot(A,B) Property: (2.4.4) Vector (cross) product cross(A,B) (2.5.1) Definitions: Properties: In the Cartesian coordinate system: (2.5.2) (2.5.4) (2.5.5) (2.5.3) Triple products 1. Scalar triple product: 2. Vector triple product: (2.6.1) (2.6.2) Note: (2.6.1) represents a circular permutation of vectors. Q: A result of a dot product is a scalar, a result of a vector product is a vector. What is about triple products? Vector fields A vector field is a map f that assigns each vector x a vector function f(x). From Wolfram MathWorld A vector field is a construction, which associates a vector to every point in a (locally) Euclidean space. A vector field is uniquely specified by giving its divergence and curl within a region and its normal component over the boundary. Coordinate systems In a 3D space, a coordinate system can be specified by the intersection of 3 surfaces. An orthogonal coordinate system is defined when these three surfaces are mutually orthogonal at a point. A general orthogonal coordinate system: the unit vectors are mutually orthogonal The cross-product of two unit vectors defines a unit surface, whose unit vector is the third unit vector. Most commonly used coordinate systems – Cartesian; (b) – Cylindrical; (c) – Spherical. In Cartesian CS, directions of unit vectors are independent of their positions; In Cylindrical and Spherical systems, directions of unit vectors depend on positions. Coordinate systems: Cartesian An interse