Olive - Maths a students survival guide

Maths A Students Survival Guide This friendly self-help workbook covers mathematics essential to first-year undergraduate scientists and engineers. In the second edition of this highly successful textbook the author has completely revised the existing text and added a totally new chapter on vectors. Mathematics underpins all science and engineering degrees, and this may cause problems for students whose understanding of the subject is weak. In this book Jenny Olive uses her extensive experience of teaching and helping students by giving a clear and confident presentation of the core mathematics needed by students starting science or engineering courses. Each topic is introduced very gently, beginning with simple examples that bring out the basics, and then moving on to tackle more challenging problems. The author takes the time to explain the tricks of the trade and also shortcuts, but is careful to explain common errors allowing students to anticipate and avoid them.

The book contains more than 820 execises, with detailed solutions given in the back to allow students who get stuck to see exactly where they have gone wrong. Topics covered include trigonometry and hyperbolic functions, sequences and series (with detailed coverage of binomial series), differentiation and integration, complex numbers, and vectors. This self-study guide to introductory college mathematics will be invaluable to students who want to brush up on the subject before starting their course, or to help them develop their skills and understanding while at university. Jenny Olive

A Students Survival Guide CAMBRIDGE UNIVERSITY PRESS
Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, So Paulo, Delhi, Mexico City Cambridge University Press
The Edinburgh Building, Cambridge CB2 8RU, UK Published in the United States of America by Cambridge University Press, New York www.cambridge.org
Information on this title: www.cambridge.org/9780521017077 Jenny Olive 1998,2003 This publication is in copyright. Subject to statutory exception
and to the provisions of relevant collective licensing agreements,
no reproduction of any part may take place without
the written permission of Cambridge University Press. I have split the chapters up in the following way so that you can easily find particular topics. I have split the chapters up in the following way so that you can easily find particular topics.

Also, it makes it easy for me to tell you where to go if you need help, and easy for you to find this help.

I would particularly like to thank Rodie and Tony Sudbery for their very helpful ideas and comments on large parts of the text. I am also very grateful to Neil Turok, Eleni Haritou-Monioudis, John Szymanski, Jeremy Jones and David Olive for detailed comments on particular sections, and my father, William Tutton, for his helpful advice on my drawings. I would also like to thank the mathematics department of the University of Wales, Swansea, for helpful discussions concerning the needs of incoming students. The referees also all provided detailed and useful input which was very helpful in structuring the book and I thank them for this. I would also like to thank Rufus Neal, Harriet Millward and Mairi Sutherland for their patient and friendly editorial help and advice, Phil Treble for his great design, and everyone else at Cambridge University Press who has worked on this book.

Finally, I am particularly grateful to my daughter, Rosalind Olive, both for her helpful comments and also for her excellent guinea-pig drawings. For and because of the people I have tought

I have written this book mainly for students who will need to apply maths in science or engineering courses. It is particularly designed to help the foundation or first year of such a course to run smoothly but it could also be useful to specialist maths students whose particular choice of A-level or pre-university course has meant that there are some gaps in the knowledge required as a basis for their University course. Because it starts by laying the basic groundwork of algebra it will also provide a bridge for students who have not studied maths for some time. The book is written in such a way that students can use it to sort out any individual difficulties for themselves without needing help from their lecturers. A message to students I have made this book as much as possible as though I were talking directly to you about the topics which are in it, sorting out possible difficulties and encouraging your thoughts in return.

I want to build up your knowledge and your courage at the same time so that you are able to go forward with confidence in your own ability to handle the techniques which you will need. For this reason, I dont just tell you things, but ask you questions as we go along to give you a chance to think for yourself how the next stage should go. These questions are followed by a heavy rule like the one below. It is very important that you should try to answer these questions yourself, so the rule is there to warn you not to read on too quickly. I have also given you many worked examples of how each new piece of mathematical information is actually used. In particular, I have included some of the off-beat non-standard examples which I know that students often find difficult.

To make the book work for you, it is vital that you do the questions in the exercises as they come because this is how you will learn and absorb the principles so that they become part of your own thinking. As you become more confident and at ease with the methods, you will find that you enjoy doing the questions, and seeing how the maths slots together to solve more complicated problems. Always be prepared to think about a problem and have a go at it dont be afraid of getting it wrong. Students very often underrate what they do themselves, and what they can do. If something doesnt work out, they tend to think that their effort was of no worth but this is not true. Thinking about questions for yourself is how you learn and understand what you are doing. It is much better than just following a template which will only work for very similar problems and then only if you recognise them.

If you really understand what you are doing you will be able to apply these ideas in later work, and this is important for you. Because you may be working from this book on your own, I have given detailed solutions to most of the questions in the exercises so that you can sort out for yourself any problems that you may have had in doing them. (Dont let yourself be tempted just to read through my solutions you will do infinitely better if you write your own solutions first. This is the most important single piece of advice which I can give you.) Also, if you are stuck and have to look at my solution, dont just read through the whole of it. Stop reading at the point that gets you unstuck and see if you can finish the problem yourself. I have also included what I have called thinking points.

These are usually more openended questions designed to lead you forward towards future work. If possible, talk about problems with other students; you will often find that you can help each other and that you spark each others ideas. It is also very sensible to scribble down your thoughts as you go along, and to use your own colour to highlight important results or particular parts of drawings. Doing this makes you think about which are the important bits, and gives you a short-cut when you are revising. There are some pitfalls which many students regularly fall into. These are marked to warn you to take particular notice of the advice there.

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