# SE_01 - Electromagnetics School of Electrical and Computer...

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Electromagnetics School of Electrical and Computer Engineering University of Tehran Supplementary Exercise SE-01 Subject: Vector Analysis Fall Semester 1384 Differential Calculus: Problem 1: (Griffiths P1.12) The height of a certain hill (in meter) is given by ) 12 28 18 4 3 2 ( 10 ) , ( 2 2 + + = y x y x y x y x h where y is the distance (in kilometers) to the north, x is the distance to the east. (a) Where is the top of the hill located? (b) How high is the hill? (c) How steep is the slope (in meter per kilometers) at a point 1kilometer to the north and one kilometer to the east? In what direction is the slop steepest, at that point? Problem 2: (Griffiths P1.13) Let r r be the vector from some fixed point ( ) to the point (x, y, z), and let r be its length. Show that 0 0 0 , , z y x (a) r r r r 2 ) ( 2 = (b) What is the general formula for ) ( n r r ? Problem 3: (Griffiths P1.20) Construct a vector function that has zero divergence and zero curl every where. (A constant will do the job of course, but make it something a little more interesting than

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## This note was uploaded on 02/06/2011 for the course ECE 423 taught by Professor Dolatabadi during the Spring '11 term at Amirkabir University of Technology.

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SE_01 - Electromagnetics School of Electrical and Computer...

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