EE2011 Lecture 1 - Review of Vector Calculus

Or dt z prof joshua le wei li em research group prof

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Unformatted text preview: y y ˆ y ˆ z T ˆ z z dl T dl T dT ˆ x T x T dl ˆ y T y T or z ˆ T a l dl or dT ˆ z Prof Joshua Le-Wei Li, EM Research Group Prof ˆ x dl x y z ˆ T a l directional derivative 17 EE2011: Engineering Electromagnetics Electromagnetics Gradient of a Scalar Field • Example Prof Joshua Le-Wei Li, EM Research Group Prof 18 EE2011: Engineering Electromagnetics Electromagnetics Gradient of a Scalar Field • Gradient Operator in Cylindrical & Spherical Systems – Cylindrical System 1 ˆ ˆ ˆ r z r r z – Spherical System 1 ˆ1 ˆ ˆ R R R R sin Prof Joshua Le-Wei Li, EM Research Group Prof 19 EE2011: Engineering Electromagnetics Electromagnetics Gradient of a Scalar Field • Example Prof Joshua Le-Wei Li, EM Research Group Prof 20 EE2011: Engineering Electromagnetics Electromagnetics Gradient of a Scalar Field • Properties of a Gradient Operator – Addition UV U V – Product UV U V V U – High Order V n nV n 1 V Prof Joshua Le-Wei Li, EM Research Group Prof 21 EE2011: Engineering Electromagnetics Electromagnetics Divergence of a Vector Field • Basic Concept of the Divergence E ds Total flux S F1 F2 F1 E ds F3 F4 F5 ˆ E n1ds Face 1 Face 1 ˆ xE x ˆ yE y ˆ zE z ˆ x1 dydz E ds E Face 1 E x ,1 y z F2 F6 Ex,2 y z E x ,1 E ds Total flux S lim v Ex x y z so F2 F1 x Ey Ex Ez xyz x y z Prof Joshua Le-Wei Li, EM Research Group Prof 22 0 S v Ex x Ey y Ez z Ex xyz x Ev EE2011: Engineering Electromagnetics Electromagnetics Divergence of a Vector Field • Example 1 Prof Joshua Le-Wei Li, EM Research Group Prof 23 EE2011: Engineering Electromagnetics Electromagnetics Divergence of a Vector Field • Divergence...
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