By Noel M. Morris
A pocket reference of crucial formulae protecting: digital and electric engineering, measurements and keep watch over, common sense, telecommunications and arithmetic. Of worth to scholars at either BTEC nationwide and better point, in addition to at undergraduate point, specifically these learning digital and electric engineering.
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Additional info for Essential Formulae for Electronic and Electrical Engineers
Sample text
For every quadratic factor (ax 2 + bx + c) of M(x) corresponding partial fraction _P_ + ( In x X 1. For every linear factor (ax + b) of M(x) there is a --=----=--- + -------:: ax 2 + bx + c (ax 2 + bx + c) 2 X sin -t - (a2 - x2 )~ a I -tan -t I x2 + a2 cosh x sinh x sech 2 x a sinh x cosh x tanh x a Integration by parts fu dxdv 'Cover-up' rule If X dx = uv - fv dudx dx f(x) = p(x) (x +a)(x + b)(x +c)··· then the numerators of the separate fractions due to the factors (x +a), (x + b), etc, are determined by 'covering up' each of the factors in turn and evaluating the remainder of the expression by replacing each x term by the value of x which makes the 'covered up' factor zero.
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Function of a [unction If y = f(u ), where u = cp(x ), then dy dy du -=-·dx du dx Maximum and minimum values off(x) A curve has a maximum value at a point if, at that point, d2 y dy dx =0 and dx 2 has a negative value. A curve has a minimum value at a point if, at that point .. d2y dy dx =0 and dx 2 has a pos1t1ve value. 24 dy d 2y If at a point p on a curve dx = 0 and dx 2 = 0, the curve may If f(D) = aoD(n) + atD(n-l) + ... + arD(n-r) + ... +an where ar is a constant and n is a positive integer, then either have a maximum point, or a minimum point, or a d2y point of inflection.