By Anthony Croft
ISBN-10: 0273719777
ISBN-13: 9780273719779
Popular electric engineering maths textbook, packed packed with correct smooth purposes and an immense variety of examples and exercises.
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Extra resources for Engineering Mathematics: A Foundation for Electronic, Electrical, Communications and Systems Engineers
Sample text
23 Polynomial equations of higher degree Verify that a = 1 and a = 2 are roots of P{x) = x4 — 2a3 — a + 2 = 0 Solution P(a) = a4 - 2a3 - a+ 2 P(l) = 1-2-1+2 = 0 P(2) = 24 - 2(23) - 2 + 2= 16- 16-2 + 2 = 0 Since P(l) =0 and P(2) = 0, then a = 1 and a = 2 are roots of the given polynomial equation and are sometimes referred to as real roots. Further knowledge is required to find the two remaining roots, which are known as complex roots. This topic is covered in Chapter 9. 21 a formula can be used to solve quadratic equations.
We write this as —2 < r ^ — 1. Case (ii) r + 1 ^ 0 and so r > — 1. r + 2 < 0 and so t < —2. It is impossible to satisfy both r ^ — 1 and t < —2 and so this case yields no values of t. 36 Solve the following inequalities: (a) x2 > 4 Solution 2t + 3 ^ ^ ^ 1 when —2 < / ^ — 1. (b) x2 < 4 x2 > 4 (a) x2 — 4 > 0 (x — 2)(x + 2) > 0 For the product (x — 2)(a: + 2) to be positive requires either (i) x — 2 > 0 and x + 2 > 0 or (ii) x — 2 < 0 and x + 2 < 0. We examine each case in turn. Case (i) x — 2 > 0 and so x > 2.
But these are beyond the scope of this book. 6 Seven-segment displays The number displays found on music systems, video and other electronic equipment commonly employ one or more seven-segment indicators. 3(a). The individual segments are typically illuminated with a light-emitting diode or similar optical device and are either on or off. 3(b), where 1 indicates that the segment is turned on and 0 indicates that it is turned off. 3 (a) Seven-segment LED display, (b) Seven-segment coding. The numbers in the microprocessor system driving the display are typically stored in binary format.
Engineering Mathematics: A Foundation for Electronic, Electrical, Communications and Systems Engineers by Anthony Croft
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