Demo01VectorCalc - ECE 3030: Electromagnetic Fields and...

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Unformatted text preview: ECE 3030: Electromagnetic Fields and Waves Fall 2009 DEMO 1 INSTRUCTOR NOTES: Vector Calculus Reminder: Dont do Workshop or Homework items! Date: Tuesday 9/1 1. Do a quick review of notation: unit vectors: x, y, z , or i, j, k , or a x , a y , a z , or a x , a y , a z ( sometimes bold ). We will use the hat notation: x, y, z . coordinate positions: ( x, y, z ), or ( r, , z ), or ( r, , ) ( never bold ) full vectors: E, E , ~ E, E . We will use the over arrow notation: ~ E . differential lengths: d , d x , d y , d z , d s . Use d s for length. differential areas: ~ d a = d x d y~ z , ~ d S , ~ d A , dA . Use ~ d a for area. differential volume: d V ( never a vector) differential vectors: ~ d , ~ d x , ~ d y , ~ d z , or d x x , d y x , or d z z , ~ d S , ~ d a , ~ d A 2. Review r.h. orthogonal coordinate systems (draw each): Cartesian (or rectangular): ( x, y, z ); vector field: ~ A = A x x + A y y + A z z differential examples: ~ d s = d x x , ~ d a = d x d y z , d V = d x d y d z y x z y x z z ( ) z y x , , y P r & Figure 1: Cartesian coordinate system. y x z y x z z y z x y Figure 2: Local unit vectors in the Cartesian coordinate system. Cylindrical: ( r, , z ); vector field: ~ A = A r r + A + A z z differential examples: d s = d x , or ~ d s = d r r , ~ d s = r d , ~ d s = d z z ~ d a = r d d z r , d V = r d r d d z y x z r z ( ) z r , , Figure 3: Cylindrical coordinate system. y x z r z z r Figure 4: Local unit vectors in the Cylindri- cal coordinate system....
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This note was uploaded on 01/16/2010 for the course ECE 3030 at Cornell University (Engineering School).

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Demo01VectorCalc - ECE 3030: Electromagnetic Fields and...

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