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Aufgabensammlung Elektrotechnik, Bd.2, Magnetisches Feld und by Martin Vömel, Dieter Zastrow

By Martin Vömel, Dieter Zastrow

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Extra resources for Aufgabensammlung Elektrotechnik, Bd.2, Magnetisches Feld und Wechselstrom

Sample text

This example illustrates the simplicity with which we can determine a particular vector component. Unit vectors xˆ i are also called the basis vectors. 3 illustrates the meaning of projection graphically. Here, vector f is projected on x-axis to obtain its x-component f . xˆ . The idea of the expansion of an arbitrary vector in terms of basis vectors can be extended to functions also. Let us consider a function f (x) specified in the interval (a, b). We can expand this function in a set of orthogonal functions u i (x), i = 1, 2, 3, .

This method is limited to solving the Laplace equation in two dimensions and is discussed in Chapter 4. 4. Integral transforms may be used to solve the PDE. Fourier transform method is described in Chapter 5. 5. Computational methods. The development of high-speed computing machines has opened up a number of computational methods. Finite difference method (FDM), finite-difference time-domain (FDTD) method, finite element method (FEM), and method of moments (MoM), in this category, are discussed in the text.

56) and is called group velocity v g . 57) The transportation of energy therefore occurs with the speed of group velocity. 14 Charge and Current Singularities 19 We shall see later that the TEM wave suffers dispersion even in dispersionless medium when the wave equation is discretized for computational methods. This phenomenon is called numerical dispersion and is a characteristic feature of majority of computational methods. 62b) a where C 0 is the capacitance per unit length of the line, and C 0 is the capacitance with the dielectric replaced by air.

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