lesson_2_-_Operators

# lesson_2_-_Operators - EE3321 ELECTROMAGNETIC FIELD THEORY...

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EE3321 ELECTROMAGNETIC FIELD THEORY Lecture 2 Highlights 1. Vector Notation a. Unit vectors b. Orthogonal directions Products c. Scalar product d. Magnitude e. Dot (inner) product f. Cross (vector) product 2. Gradient Operator 3. Laplacian Operator 4. Divergence Operator 5. Curl Operator http://mathworld.wolfram.com/

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The gradient is a vector operator denoted and sometimes also called Del or nabla . It is most often applied to a real function of three variables , and may be denoted (1) For general curvilinear coordinates , the gradient is given by (2) which simplifies to (3) in Cartesian coordinates . The direction of is the orientation in which the directional derivative has the largest value and is the value of that directional derivative . Furthermore, if , then the gradient is perpendicular to the level curve through if and perpendicular to the level surface through if . http://mathworld.wolfram.com/
The Laplacian for a scalar function is a scalar differential operator defined by (1) where the are the scale factors of the coordinate system. Note that the operator is commonly written as by mathematicians (Krantz 1999, p. 16). The Laplacian is extremely important in electromagnetics and wave theory, and appears in Laplace's equation (2) the Helmholtz differential equation

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## This note was uploaded on 10/12/2009 for the course EE 3321 taught by Professor Flores during the Fall '08 term at Texas El Paso.

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lesson_2_-_Operators - EE3321 ELECTROMAGNETIC FIELD THEORY...

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