The handbook is devoted to common mathematical techniques for university students and practical engineers in electrical engineering. The book consists of the parts: I Fundamentals of Engineering Mathematics, II Algorithms to Solve Common Problems in Electrical Engineering, and III Reference Data.
Part I is divided in 9 Chapters containing definitions, laws, rules, solving methods, and examples. But, Part I is more than a formulary and can be used in a similar manner as a textbook. According to this a number of useful corresponding mathematical formulas are presented separately in 23 appendices which provide for the most part the reference source Part III. Furthermore, Part III contains frequently in electrical engineering used constants, metric units, and alphabets. For readers of Part I, who are interested in derivations, it is referred to selected bibliographies at the end of each chapter. Chapter 1 starts with basic terms of elementary mathematics such as numbers, coordinates, functions, and equations followed by definitions and rules of plane and solid geometry, trigonometry and analytic geometry including common terms of the theory of combinations.
Sequences, series and limits are the subject of Chapter 2.
The fundamentals of the differential and integral calculus of functions in one and several variables, ordinary differential equations of first, second and any order and systems of ordinary differential equations including analytic solving methods and simple examples are presented in Chapter 3. The reader will find line, curved, surface, and volume integrals, Taylor’s and Green’s formula, the integration by part rule and so on.
Chapter 4 is devoted to complex numbers, variables and functions. Starting from a refreshing of complex numbers complex functions and its derivations, analytic and holomorphic functions, Taylor’s and Loraine’s series including the theorem of residues, which provides a powerful tool for calculating complex contour integrals, are treated.
Simple rules for Fourier series and the matrix algebra for real and complex numbers are considered in the Chapters 5 and 6, respectively. Terms such as transposed, adjoint, inverse, symmetrical, Hermitian matrices, determinants, eigenvalues and -vectors are described.
Chapter 7 contains definitions and rules for the vector algebra. Terms such as gradient, divergence, curl, Laplace and Hamiltonian (nabla) operator, important in electrodynamics and optics, including Gauss’ and Stokes’ formulas are introduced.
Fundamentals of probability theory, stochastic processes, and applied statistics are considered in the comprehensive Chapter 8. Section 8.1 starts with definitions and laws for random events and variables. Terms such as disjoint and independent events, conditional probability, probability distribution and probability density function, moments (expectation, variance, and correlation), statistical parameters, and two- and multidimensional Gaussian distributions are treated. Random functions and processes including corresponding probability density functions, moments, correlation functions, derivations and integrations are introduced in Section 8.2. The most common random process in electrical engineering, the Gaussian random process, and four kinds of Markovian processes are demonstrated comprising random flows and fields. The two essential steps of stochastic simulation [- the generation of an uniform distribution, - the transformation of the uniform distribution into a specified (e.g. Gaussian, Rayleigh) distribution] that deals with constructing samples of a random variable or with a random process using a specified probability distribution law are described in Section 8.3.
The next section is about applied statistics that is needed in electrical engineering to describe functions such as signals, noise, and interferences. The engineer has to find certain parameters (e. g. mean, variance, correlation functions, spectrum and so forth) of these processes, known as “statistical analysis” in opposite to the “statistical synthesis” of the previous section. Stationary and non-stationary random processes including accuracy and reliability of the estimates and the least mean square method are considered.
Based on the fact that in contrast to several decades ago a number of mathematical software packages are available today the authors argue that the user does not have to program a numerical algorithm but, he has rather only to write mathematical expressions for using software, e. g. MATHCAD. Thus, Chapter 9 contains among others building blocks for solving the inverse of a matrix or for the solution of an initial value problem of ordinary differential equations. However, one has to say, the user is not confronted in this one-way street with such problems as ill-conditioning of systems of linear algebraic equations or stiffly stable algorithms for systems of ordinary differential equations.
Part II contains building blocks for about 50 common problems in electrical engineering such as electrical circuits and devices, antennas, wave propagation, scattering, filter, signal processing, and stochastic radio engineering. The problems are clearly arranged and well illustrated. Simple examples help the reader to understand the subject. The user is assisted by an Index to find important terms.
However, advanced students and engineers, who have today to solve for instance Maxwell equations numerically, need more comprehensive methods and tools than presented in this handbook.