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As with the previous editions, the range of material covered in this fifth edition is regarded as appropriate for a first-level core studies course in mathematics for undergraduate courses in all engineering disciplines. Whilst designed primarily for use by engineering students it is believed that the book is also highly suitable for students of the physical sciences and applied mathematics. Additional material appropriate for second-level undergraduate core studies, or possibly elective studies for some engineering disciplines, is contained in the companion text Advanced Modern Engineering Mathematics. The objective of the authoring team remains that of achieving a balance between the development of understanding and the mastering of solution techniques, with the emphasis being on the development of the student’s ability to use mathematics with understanding to solve engineering problems. Consequently, the book is not a collection of recipes and techniques designed to teach students to solve routine exercises, nor is mathematical rigour introduced for its own sake. To achieve the desired objective the text contains:
l Worked examples
Approximately 500 worked examples, many of which incorporate mathematical models and are designed both to provide relevance and to reinforce the role of mathematics in various branches of engineering. In response to feedback from users, additional worked examples have been incorporated within this revised edition.
l Applications
To provide further exposure to the use of mathematical models in engineering practice, each chapter contains sections on engineering applications. 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 develop the skills of mathematical modelling necessary to prepare for the more openended modelling exercises at a later stage of the course.
l Exercises
There are numerous exercise sections throughout the text, and at the end of each chapter there is a comprehensive set of review exercises. While many of the exercise problems are designed to develop skills in mathematical techniques, others are designed to develop understanding and to encourage learning by doing, and some are of an open-ended nature. This book contains over 1200 exercises and answers to all the questions are given. It is hoped that this provision, together with the large number of worked examples and style of presentation, also makes the book suitable for private or directed study. Again in response to feedback from users, the frequency of exercises sections has been increased and additional questions have been added to many of the sections.
l Numerical methods
Recognizing the increasing use of numerical methods in engineering practice, which often complement the use of analytical methods in analysis and design and are of ultimate relevance when solving complex engineering problems, there is wide agreement that they should be integrated within the mathematics curriculum. Consequently the treatment of numerical methods is integrated within 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, in the teaching of mathematics to engineering students. In response, use of such packages continues to be a significant feature of this new edition. Whilst any appropriate software package can be used, the authors recommend the use of MATLAB and/or MAPLE and have continued to adopt their use in this text. Throughout, emphasis will be on the use of MATLAB, with reference made to corresponding MAPLE commands and differences in syntax highlighted. MATLAB/MAPLE commands have been introduced and illustrated, as inserts, throughout the text so that their use can be integrated into the teaching and learning processes. Students are strongly encouraged to use one of these packages to check the answers to the examples and exercises. It is stressed that the MATLAB/MAPLE inserts are not intended to be a first introduction of the package to students; it is anticipated that they will receive an introductory course elsewhere and will be made aware of the excellent ‘help’ facility available. The purpose of incorporating the inserts is not only to improve efficiency in the use of the package but also to provide a facility to help develop a better understanding of the related mathematics.