Engineering mathematics: a foundation for electronic, electrical, communications and systems engineers. (Q2721038)

This third edition of the textbook provides a complete course in engineering mathematics for degree and diploma students in electronic, electrical, communications and systems engineering. The book will be useful for a wider readership -- students in engineering, self-study and continuing education.NEWLINENEWLINENEWLINEIn addition to the previous edition, several new chapters are presented; general references at several points in the text are included for use of modern computer aids, mainly the packages DERIVE and MATLAB; a CD-based testing and assessment package is given in the book; the book is perfectly well designed and printed in 2-colour text. Important results are highlighted.NEWLINENEWLINENEWLINEThe first author, A. Croft, is Manager of the Mathematics Learning Support Center at Loughborough University. The other two authors, R. Davison and M. Hargreaves, are lecturers in the Department of Engineering and Technology at De Montfort University.NEWLINENEWLINENEWLINEThe book contains 29 chapters, four appendices and subject index. The first three chapters provide a convenient review of some important functions and techniques. A new chapter (in comparison with the previous edition) on two and three dimensional co-ordinate systems is included.NEWLINENEWLINENEWLINEThe next chapters cover discrete mathematics (set theory, Boolean algebra, logic gates, binary circuits); sequences, series and power series; two and three dimensional vectors and operations for calculations with them. Mechanical and electrical examples are supplied.NEWLINENEWLINENEWLINEChapter 8 deals with the matrix algebra. Various matrices, determinants, and the inverse matrix are introduced, and the classical matrix operations are studied. Applications of the matrix algebra for solving simultaneous linear equations are presented. For systems of linear equations, both direct (Gaussian elimination) and inverse (Jacobi's and Gauss-Seidel) methods are given. The material has been expanded (in comparison with the second edition) to include eigenvalues and eigenvectors, as well as computer solutions of matrix problems involving matrices. Applications include analysing the movement of robots and the analysis of electrical networks.NEWLINENEWLINENEWLINEClassical material on complex numbers is given in Chapter 9. It includes Cartesian, polar and exponential forms, operations with complex numbers, De Moivre's theorem. Applications in analysing electrical circuits with an a.c. power supply are described.NEWLINENEWLINENEWLINEChapters 10-12 deal with differential calculus and its applications. The notion of differentiation, rules of differentiation, parametric, implicit and logarithmic differentiation, derivatives, are presented. Applications concern analysis of electrical circuits in connection with extremal values of a function of one variable, approximate solutions of nonlinear equations.NEWLINENEWLINENEWLINEChapters 13-17 cover integral calculus. Definite and indefinite integrals, techniques of integration, applications in electronics and electrotechniques are treated. Further topics in integration concern orthogonal functions, improper integrals, integration of piecewise continuous functions and integration of vectors. Some numerical methods of integration are discussed.NEWLINENEWLINENEWLINETaylor and Maclaurin polynomials and series and their applications for electrical network analysis are given in Chapter 18.NEWLINENEWLINENEWLINEOrdinary differential equations are studied in Chapters 19 and 20. The traditional analytical and numerical methods for solving them are presented. Examples from electrotechnics, analog simulation and mechanics are included.NEWLINENEWLINENEWLINEThe Laplace transform is considered in Chapter 21. The exposition includes: definitions, table with Laplace transforms, main theorems (shift, initial and final value), inverse Laplace transforms, transfer function in circuit analysis. Applications for solving differential equations, electrical, electronical and control problems are given.NEWLINENEWLINENEWLINEDifference equations and the \(z\) transform are studied in Chapter 22. The emphasis is given on various engineering applications in communications, control, discretization and \(z\) transform of continuous signals. The relationship between the \(z\) transform and the Laplace transform, shift theorems and complex translation theorem, inversion, are presented.NEWLINENEWLINENEWLINEFourier series, Fourier analysis and Fourier transform in connection with signal processing, communication engineering, filtering, are the next subjects. The properties of the Fourier transform are studied and applications for amplitude modulation are given. The relationship between the Fourier transform and the Laplace transform is presented.NEWLINENEWLINENEWLINECalculus of functions of several variables (partial derivatives, Taylor series, extremal points), vector calculus (partial differentiation, scalar and vector fields, the gradient, divergence and curl operators and their physical interpretations) line integrals and multiple integrals (evaluation, conservative fields, Green's theorem, divergence and Stokes' theorem) as well as applications in electromagnetism are presented in details.NEWLINENEWLINENEWLINEThe last chapters cover probability, statistics and probability distributions with examples from communications.NEWLINENEWLINENEWLINEThe disc includes practice tests at two levels on basic algebra, further algebra, complex numbers, functions, trigonometry, differentiation and integration.NEWLINENEWLINENEWLINEThe textbook has several indisputable advantages. The authors illustrate thoughtful concepts in modern engineering mathematics. Profound engineering examples are in abundance, included in the proper place, as are motivating intelligent applications of mathematics. The exposition is well-organized, lucid, and provides a balanced mathematics curriculum. The key formulas and laws are given on the inside covers. The testing and assessment CD is the next modern item providing feedback for correct understanding and knowledge acquirement.