ADVANCED MODERN ENGINEERING MATHEMATICS JAMES G. Księgarnia

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Preface to the First Edition

Throughout the course of history, engineering and mathematics have developed in parallel. All branches of engineering depend on mathematics for their description and there has been a steady flow of ideas and problems from engineering that has stimulated and sometimes initiated branches of mathematics. Thus it is vital that engineering students receive a thorough grounding in mathematics, with the treatment related to their interests and problems. This has been the motivation in the production of this book - a companion text to Modern Engineering Mathematics, which was designed to provide a first-level core studies course in mathematics for undergraduate programmes in all engineering disciplines.

Skills development

Although the pace of this book is at a somewhat more advanced level than Modern Engineering Mathematics the philosophy of learning by doing is retained with continuing emphasis on the development of students' ability to use mathematics with understanding to solve engineering problems.

Examples and Exercises

The book contains over 320 fully worked examples and more than 750 exercises, with answers to all the questions given. There are copious review exercises at the end of each chapter and these are designed both to reinforce understanding and to extend the range of topics included. In many areas hand-worked exercises can be checked using a suitable software package. It is strongly recommended that this is done whenever possible, not simply to increase confidence, but also to gain insight into the use and the performance of such packages. By this means the student will rapidly develop an appreciation of the need to have a good understanding of the underpinning mathematical theory and of computational problems such as the sensitivity of eigenvalue calculation to rounding errors.

Applications

Recognizing the growing importance of mathematical modelling in engineering practice, each chapter contains specific sections on engineering applications. As in Modern Engineering Mathematics, these sections form an ideal framework for individual, or group, case study assignments leading to a written report and/or oral presentation, thereby helping to reinforce the skills of mathematical modelling, which are seen as essential if engineers are to tackle the increasingly complex systems they are being called upon to analyse and design. Also, recognizing the increased use of numerical methods in problem solving, the treatment of numerical methods is integrated with the analytical work throughout the book. Algorithms are written in pseudocode and, therefore, are readily transferable to any specific language by the user.

Building on the foundations laid in Modern Engineering Mathematics, this book gives an extensive treatment of some of the more advanced areas of mathematics that have applications in various fields of engineering, particularly as tools for computer-based system modelling, analysis and design. In making the choice of material to be included, the authoring team have recognized the increasing importance of digital techniques and statistics in engineering practice. It is believed that the content is sufficiently broad to provide the necessary second-level core studies for most engineering studies, where in each case a selection of the material may be made.

Content

Chapter 1 is designed to develop an understanding of the standard techniques associated with functions of a complex variable which are still seen as an important component of a practising engineer's mathematical 'tool-kit'. The level of treatment recognizes the increasing emphasis in engineering practice on the use of computational methods that has led to less emphasis on the teaching of complex variable theory on engineering undergraduate courses. Chapter 2 and 3 are devoted to Laplace and z transforms, which provide the necessary mathematical foundation for the frequency domain analysis and design of continuous- and discrete-time systems respectively. While Laplace transforms have traditionally been a component of most engineering undergraduate courses, the more recent inclusion of the z transform reflects the increased impact of digital signal processing in many areas of engineering. Chapters 4 and 5 deal with Fourier analysis, which is central to many areas of applications in engineering, particularly in the analysis of signals and systems, with discrete Fourier transforms providing one of the key methods for discrete signal analysis and widely used in fields such as communications theory and speech and image processing.

Matrix techniques provide the framework for much of the developments in modem engineering. Chapter 6 extends the introductory work on matrix algebra covered in Modern Engineering Mathematics to embrace the eigenvalue problem which arises naturally in many fields. In addition, the chapter develops the techniques of matrix analysis, which are used extensively in control and systems engineering among others. Chapter 7 provides a basic introduction to vector calculus, which is seen as necessary to ensure that engineers have a good understanding of the mathematical tools they bring to their tasks when using software packages for the modelling of engineering problems in more than one dimension. Many physical processes fundamental to engineering, such as heat transfer and wave propagation, are governed by partial differential equations; Chapter 8 is devoted to such equations with recognition given to the increasing emphasis on numerical solutions. Optimization, which is dealt with in Chapter 9, is a rapidly developing field that has taken full advantage of numerical methods and developments in computer technology. Indeed, many complex and practical optimization tasks have only become tractable in the last few years. The book concludes with Chapter 10, which is devoted to probability and statistics. In almost all branches of engineering, data from experiments have to be analysed and conclusions drawn, decisions have to be made, production and distribution need to be organized and monitored, and quality has to be controlled. In all these activities, probability and statistics have at least a supporting role to play, and sometimes a central one.

Acknowledgements

A number of individuals have contributed to the development of this book and it is a pleasure to acknowledge their contribution. In particular, the contribution of Dick Clements of Bristol University has been significant, the continuing support and enthusiasm for the project of Sarah Mallen (former development director at Addison-Wesley) has been an inspiration, and the comments and suggestions made by many reviewers during the preparation of the manuscript were extremely valuable. The authoring team also wish to acknowledge the many sources from which exercises have been drawn over many years. Again the authoring team have been fortunate in having an excellent production team at Addison-Wesley. The team wish to thank sincerely all those concerned, in particular the production editor Susan Kcany; without her considerable effort the book would not have been completed. Finally, I would like to thank my wife, Dolan, for her full support throughout the preparation of this book.

Preface to the Second Edition

The revision in this edition reflect both the changes made in the companion text Modern Engineering Mathematics when producing its second edition and the feedback obtained from users of the text.

In general the feedback from users has been positive so changes have been kept to a minimum. Easier examples and exercises have been introduced where appropriate and introductory sections on matrix algebra and vector spaces incorporated in Chapter 6, Matrix Analysis. More significantly a new chapter. Chapter 8, on Numerical Solution of Ordinary Differential Equations has been introduced, reflecting reduced emphasis on this topic in the revised version of the companion text. For those adopting the book as a course text a Solutions Manual for all the exercises is available from the publishers.

Acknowledgements

The authoring team is extremely grateful to all the reviewers and users of the text who have provided valuable comments on the first edition of this book. Most of this was highly constructive and very much appreciated. The team has continued to enjoy the full support of the very enthusiastic production team at Addison Wesley Longman and wishes to thank all those concerned.

989 pages

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