Advanced Modern Engineering Mathematics (4th Edition)

Book Preface

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. As with the previous editions, this has been the motivation for the production of this fourth edition – a companion text to the fourth edition of Modern Engineering Mathematics, this being designed to provide a first-level core studies course in mathematics for undergraduate programmes in all engineering disciplines. Building on the foundations laid in the companion text, 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. Feedback, from users of the previous editions, on subject content has been highly positive indicating that it is sufficiently broad to provide the necessary second-level, or optional, studies for most engineering programmes, where in each case a selection of the material may be made. Whilst designed primarily for use by engineering students, it is believed that the book is also suitable for use by students of applied mathematics and the physical sciences.

Although the pace of the book is at a somewhat more advanced level than the companion text, 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. Recognizing the increasing importance of mathematical modelling in engineering practice, many of the worked examples and exercises incorporate mathematical models that are designed both to provide relevance and to reinforce the role of mathematics in various branches of engineering. In addition, each chapter contains specific sections on engineering applications, and these form an ideal framework for individual, or group, study assignments, 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. The importance of numerical methods in problem solving is also recognized, and its treatment is integrated with the analytical work throughout the book.

Much of the feedback from users relates to the role and use of software packages, particularly symbolic algebra packages. Without making it an essential requirement the authors have attempted to highlight throughout the text situations where the user could make effective use of software. This also applies to exercises and, indeed, a limited number have been introduced for which the use of such a package is essential. Whilst any appropriate piece of software can be used, the authors recommend the use of MATLAB and/or MAPLE. In this new edition more copious reference to the use of these two packages is made throughout the text, with commands or codes introduced and illustrated. When indicated, students are strongly recommended to use these packages to check their solutions to exercises. This is not only to help develop proficiency in their use, but also to enable students to appreciate the necessity of having a sound knowledge of the underpinning mathematics if such packages are to be used effectively. Throughout the book two icons are used:

• An open screen indicates that the use of a software package would be useful (e.g. for checking solutions) but not essential.
• A closed screen indicates that the use of a software package is essential or highly desirable.

As indicated earlier, feedback on content from users of previous editions has been favourable, and consequently no new chapter has been introduced. However, in response to feedback the order of presentation of chapters has been changed, with a view to making it more logical and appealing to users. This re-ordering has necessitated some redistribution of material both within and across some of the chapters. Another new feature is the introduction of the use of colour. It is hoped that this will make the text more accessible and student-friendly. Also, in response to feedback individual chapters have been reviewed and updated accordingly. The most significant changes are:

• Chapter 1 Matrix Analysis: Inclusion of new sections on ‘Singular value decomposition’ and ‘Lyapunov stability analysis’.
• Chapter 5 Laplace transform: Following re-ordering of chapters a more unified and extended treatment of transfer functions/transfer matrices for continuoustime state-space models has been included.
• Chapter 6 Z-transforms: Inclusion of a new section on ‘Discretization of continuous-time state-space models’.
• Chapter 8 Fourier transform: Inclusion of a new section on ‘Direct design of digital filters and windows’.
• Chapter 9 Partial differential equations: The treatment of first order equations has been extended and a new section on ‘Integral solution’ included.
• Chapter 10 Optimization: Inclusion of a new section on ‘Least squares’.