By K. STROUD

The function of this e-book is to supply a whole year's path in arithmetic for these learning within the engineering, technical and medical fields. the cloth has been especially written for classes lead ing to (i) half I of B. Sc. Engineering levels, (ii) better nationwide degree and better nationwide certificates in techno logical matters, and for different classes of a similar point. whereas formal proofs are incorporated the place essential to advertise realizing, the emphasis all through is on supplying the scholar with sound mathematical talents and with a operating wisdom and appreciation of the elemental con cepts concerned. The programmed constitution guarantees that the e-book is extremely fitted to normal type use and for person self-study, and likewise offers a prepared capability for remedial paintings or next revision. The e-book is the end result of a few 8 years' paintings undertaken within the improvement of programmed studying concepts within the division of arithmetic on the Lanchester university of know-how, Coventry. For the J1ast 4 years, the full of the math of the 1st yr of varied Engineering measure classes has been offered in programmed shape, along side seminar and instructional classes. the implications bought have proved to be hugely passable, and extra extension and improvement of those studying suggestions are being pursued. each one programme has been generally demonstrated ahead of being produced in its ultimate shape and has regularly reached a hit point above 80/80, i. e.

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**Additional info for Engineering Mathematics: Programs and Problems**

**Example text**

5( cos 60° + j sin 60°) X 4( cos 30° + j sin 30°) 2( cos 50° + j sin 50°) _ 20( cos 90° + j sin 90°) - 2( cos 50° + j sin 50°) = 10( cos 40° + j sin 40°) What does the following product become? e. (4 X 3 X 2) [cos(20° + 30° + 40°) + j sin(20° + 30° + 40°)} = 24( cos 90° + j sin 90°) 00000000000000000000000000000000000000 Now what about a few revision examples on the work we have done so far? Tum to the next frame.

No matter what the angles are, all we do is (i) multiply the moduli, (ii) add the arguments. So therefore, 4( cos 35° + j sin 35°) X 3( cos 20° + j sin 20°) = 16 00000000000000000000000000000000000000 Now let us see if we can discover a similar set of rules for Division. We already know that to simplify ~ : ~! we first obtain a denominator that is entirely real by multiplying top and bottom by ...................... e. 3 - j4 00000000000000000000000000000000000000 Right. Then let us do the same thing with 'I 'I , 1(cos 9 1 + j sin 9 1) '2 (cos 9 2 + j sin ( 2) (cos 9 1 + j sin 9 d _ (cos 9 1 + j sin 9 d (cos 9 2 - j sin ( 2) '2 (cos 9 2 + j sin ( 2) - '2 (cos 9 2 + j sin 9 2)(cos 9 2 - j sin ( 2) _'I - '2 (cos 9 1 cos 9 2 + j sin 9 1 cos 9 2 - j cos 9 1 sin 9 2 + sin 9 1 sin ( 2 ) (cos 2 9 2 + sin 2 ( 2) _ ,d(cos 91 cos 9 2 + sin 9 1 sin ( 2) + j(sin 9 1 cos 9 2 - cos 9 1 sin ( 2)] ~ 1 = ' 1 [cos (9 1 - ( 2) + j sine9 1 - ( 2)] '2 So, for division, the rule is ..........................

5( cos 60° + j sin 60°) X 4( cos 30° + j sin 30°) 2( cos 50° + j sin 50°) _ 20( cos 90° + j sin 90°) - 2( cos 50° + j sin 50°) = 10( cos 40° + j sin 40°) What does the following product become? e. (4 X 3 X 2) [cos(20° + 30° + 40°) + j sin(20° + 30° + 40°)} = 24( cos 90° + j sin 90°) 00000000000000000000000000000000000000 Now what about a few revision examples on the work we have done so far? Tum to the next frame.