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Extra info for An Analog Electronics Companion

Sample text

Consider now a second order equation (this means that the highest power of the independent variable is 2). 4) If this is plotted as before, the result will look like Fig. 2. If a is positive the curve will be oriented as shown (I), while if a is negative the curve will be inverted (II). The curve is known as a parabola and is the shape of the face of a cone when it is sliced parallel to the side. e. when xϭ0. 5) so the slope now depends on the particular point chosen. 5) allows us to determine the corresponding value of x.

If we have a complex number Zϭxϩjy then this is the vector 0D shown in Fig. 2 where the coordinates of D are simply x and y. 5) 30 Part 1 Mathematical techniques Im Z D y R q x 0 Re Fig. 2 Complex number in polar format. The quantity R is called the modulus or absolute value of Z and is written |Z|. The absolute value is always positive. The angle ␪ is known as the argument or phase of Z. 6) Most functions can be expressed in the form of an infinite series (Boas 1966). Such series provide a means of computing the value of the function to any desired precision or to find approximations.

1) is often quoted as containing five of the most important numbers in mathematics. We shall see later how to evaluate it. In electronics the symbol i is usually used for current so in this subject the symbol j is used instead, but they are identical and can be exchanged anywhere as you wish. In a one-dimensional world there is indeed no meaning to ask what the square root of Ϫ1 is. However, we can consider a simple argument to show what it does mean. Think of all the real numbers plotted along an axis as shown in Fig.

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