EE2011 Lecture 1 - Review of Vector Calculus

Coordinate systems prof joshua le wei li em research

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Unformatted text preview: Systems • Summary of Coordinate Systems Prof Joshua Le-Wei Li, EM Research Group Prof 12 EE2011: Engineering Electromagnetics Electromagnetics Coordinate System Transformations • Summary of Coordinate Transformations Prof Joshua Le-Wei Li, EM Research Group Prof 13 EE2011: Engineering Electromagnetics Electromagnetics Summary • Why do we use more than 1 coordinate system? ˆˆˆ • Why is it that the base vectors (x, y , z ) are ˆ independent of the location of a point, but r and ˆ are not? • What are the cyclic relations for the base vectors in (a) Cartesian coordinates, (b) cylindrical coordinates, and (c) spherical coordinates? • How is the position vector of a point in cylindrical coordinates related to its position vector in spherical coordinates? Prof Joshua Le-Wei Li, EM Research Group Prof 14 EE2011: Engineering Electromagnetics Electromagnetics Lecture 1: Review of Vector Calculus – Part -II • Gradient of a Scalar Field – Gradient Operator in Cylindrical & Spherical Systems – Properties of a Gradient Operator • Divergence of a Vector Field – Divergence Theorem Curl of a Vector Field – Vector Identities Involving the Curl – Stokes’s Theorem • Laplacian Operator Prof Joshua Le-Wei Li, EM Research Group Prof 15 EE2011: Engineering Electromagnetics Electromagnetics Vector Line Integrals F dl FA dl A FB dl FC dl B C FA A FB B FC C F vector field vector line FA FB FC ABC y C A FA 15a B FC x FB Example FA 4x ˆ FB 2y ˆ FC 7z ˆ F dl A 3x ˆ B 4y ˆ Cz ˆ FA dl A FB dl B FC dl C FA A FB B FC C 12 8 7 27 1...
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