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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

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