Understanding Engineering Mathematics

Author: Bill Cox
Publisher: ButterworthHeinemann
Genres: Mathematics
Publish Date: December 11, 2001
ISBN10: 0750650982
Pages: 560
File Type: PDF
Language: English
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This book contains most of the material covered in a typical ﬁrst year mathematics course in an engineering or science programme. It devotes Chapters 1–10 to consolidating the foundations of basic algebra, elementary functions and calculus. Chapters 11–17 cover the range of more advanced topics that are normally treated in the ﬁrst year, such as vectors and matrices, differential equations, partial differentiation and transform methods. With widening participation in higher education, broader school curricula and the wide range of engineering programmes available, the challenges for both teachers and learners in engineering mathematics are now considerable. As a result, a substantial part of many ﬁrst year engineering programmes is dedicated to consolidation of the basic mathematics material covered at preuniversity level. However, individual students have widely varying backgrounds in mathematics and it is difﬁcult for a single mathematics course to address everyone’s needs. This book is designed to help with this by covering the basics in a way that enables students and teachers to quickly identify the strengths and weaknesses of individual students and ‘top up’ where necessary. The structure of the book is therefore somewhat different to the conventional textbook, and ‘To the student’ provides some suggestions on how to use it. Throughout, emphasis is on the key mathematical techniques, coveredlargely in isolation from the applications to avoid cluttering up the explanations. When you teach someone to drive it is best to ﬁnd a quiet road somewhere for them to learn the basic techniques before launching them out onto the High Street! In this book the mathematical techniques are motivated by explaining where you may need them, and each chapter has a short section giving typical applications. More motivational material will also be available on the book website. Rigorous proof for its own sake is avoided, but most things are explained sufﬁciently to give an understanding that the educated engineer should appreciate. Even though you may use mathematics as a tool, it usually helps to have an idea of how and why the tool works. As the book progresses through the more advanced ﬁrst year material there is an increasing expectation on the student to learn independently and ‘ﬁll in the gaps’ for themselves – possibly with the teacher’s help. This is designed to help the student to develop a mature, selfdisciplined approach as they move from the supportive environment of preuniversity to the more independent university environment. In addition the book website (www.bh.com/companions/0750650982) will provide a developing resource to supplement the book and to focus on speciﬁc engineering disciplines where appropriate. In the years that this book has been in development I have beneﬁted from advice and help from too many people to list. The following deserve special mention however. Dave Hatter for having faith in the original idea and combining drink and incisive comment well mixed in the local pub. Peter Jack for many useful discussions and for the best part of the S(ketch) GRAPH acronym (I just supplied the humps and hollows). Val Tyas for typing much of the manuscript, exploring the limits of RSI in the process, and coping cheerfully with my continual changes. The late Lynn Burton for initial work on the manuscript and diagrams. She was still ﬁddling with the diagrams only weeks before she succumbed to cancer after a long and spirited ﬁght. I am especially indebted to her for her friendship and inspiration – she would chuckle at that. I also beneﬁted from an anonymous reviewer who went far beyond the call of duty in providing meticulous, invaluable comment – It’s clear that (s)he is a good teacher. Of course, any remaining errors are my responsibility. The team at Butterworth Heinemann did a wonderful job in dealing with a complicated manuscript – sense of humour essential! Last but not least I must mention the hundreds of students who have kept me in line over the years. I have tried to write the book that would help most of them. I hope they, and their successors, will be pleased with it.
Bill Cox, June 2001
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