Chapter One: Vector Analysis The use of vectors and vector analysis ...
Chapter One: Vector Analysis The use of vectors and vector analysis ...
Chapter One: Vector Analysis The use of vectors and vector analysis ...
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Electromagnetic <strong>The</strong>orem<br />
(Dr. Omed Ghareb Abdullah) University <strong>of</strong> Sulaimani –College <strong>of</strong> Science – Physics Department<br />
Problem:<br />
Calculate the curls <strong>of</strong> functions:<br />
3 2 <br />
<br />
<br />
<br />
6 2 3 <br />
<br />
3 2<br />
2 3 <br />
<br />
<br />
<br />
2 3 <br />
<br />
2 3<br />
2 2 <br />
<br />
<br />
<br />
0<br />
<br />
2 2<br />
Product Rules:<br />
<strong>The</strong> calculation <strong>of</strong> ordinary derivatives is facilitated by a number <strong>of</strong> general rules, such as:<br />
<strong>The</strong> sum rule:<br />
<br />
<br />
<br />
<br />
<strong>The</strong> rule for multiplying by a constant:<br />
<br />
<br />
<br />
<strong>The</strong> product rule:<br />
<br />
<br />
<br />
And, the quotient rule:<br />
<br />
<br />
<br />
<strong>The</strong>re are six product rules for Del operator:<br />
Two for gradients:<br />
<br />
<br />
<br />
<br />
<br />
13