Essentials of Engineering Mathematics: Worked Examples and Problems, second edition
The book is the second edition of a successful and widely popular reference book which was first published in 1992. It contains all of the topics typically covered in the first- and second-year undergraduate mathematics courses taught at technical universities, and, indeed, a lot more. Its contents is admirably wide as it includes everything from basic concepts from algebra, analysis, geometry and even logic to some rather deep and difficult mathematics such as the Fourier and Laplace transforms or differential calculus of several space variables. Yet, the book is quite concise and it does not contain any stuff that would make it unreadable for a mathematical layman. The principal achievement of the book is its great style. It is written in such a way that anyone who needs particular information on some of the many topics covered (typically not a mathematician himself, but somebody in whose work mathematics plays an important role) will obtain this information fast and perfectly clear. The many worked examples are carefully chosen in order to cover all of the typical situations, so the risk of a nasty surprise is decreased to a minimum. The book is organized into short pleasant sections that make it easy to obtain required references. Absolutely no unnecessary heavy abstract mathematics that would obscure the whole thing and scare a potential reader away is used. Compared with the first edition, there is plenty of new material included in this second one. It provides many new examples, new theoretical material (such as new problems involving the mean value theorem for derivatives, extension of the theory of extremes of functions of several variables, the concept direction fields of a first-order ordinary differential equation, Laplace transform etc.). The most important improvement is an introduction to using the symbolic software packages Maple and Matlab in engineering. This is an excellent reference book that nobody interested in either pure or, especially, applied mathematics, should ignore.