Maths a student's survival guide

Описание

A Student’s 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
Maths
A Student’s Survival Guide
CAMBRIDGE UNIVERSITY PRESS Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São 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
First published 1998 Reprinted 2000, 2002 (with corrections) Second edition published 2003 7th printing 2013
A catalogue record for this publication is available from the British Library
ISBN 978-0-521-01707-7 Paperback
Cambridge University Press has no responsibility for the persistence or accuracy of URLs for external or third-party internet websites referred to in this publication, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate.
Contents
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.
Introduction
Introduction to the second edition
1Basic algebra: some reminders of how it works
1.AHandling unknown quantities
(a)Where do you start? Self-test 1
(b)A mind-reading explained
(c)Some basic rules
(d)Working out in the right order
(e)Using negative numbers
(f)Putting into brackets, or factorising
1.BMultiplications and factorising: the next stage
(a)Self-test 2
(b)Multiplying out two brackets
(c)More factorisation: putting things back into brackets
1.CUsing fractions
(a)Equivalent fractions and cancelling down
(b)Tidying up more complicated fractions
(c)Adding fractions in arithmetic and algebra
(d)Repeated factors in adding fractions
(e)Subtracting fractions
(f)Multiplying fractions
(g)Dividing fractions
1.DThe three rules for working with powers
(a)Handling powers which are whole numbers
(b)Some special cases
1.EThe different kinds of numbers
(a)The counting numbers and zero
(b)Including negative numbers: the set of integers
(c)Including fractions: the set of rational numbers
(d)Including everything on the number line: the set of real numbers
(e)Complex numbers: a very brief forwards look
1.FWorking with different kinds of number: some examples
(a)Other number bases: the binary system
(b)Prime numbers and factors
(c)A useful application - simplifying square roots
(d)Simplifying fractions with √ signs underneath
2Graphs and equations
2.ASolving simple equations
(a)Do you need help with this? Self-test 3
(b)Rules for solving simple equations
(c)Solving equations involving fractions
(d)A practical application – rearranging formulas to fit different situations
2.BIntroducing graphs
(a)Self-test 4
(b)A reminder on plotting graphs
(c)The midpoint of the straight line joining two points
(d)Steepness or gradient
(e)Sketching straight lines
(f)Finding equations of straight lines
(g)The distance between two points
(h)The relation between the gradients of two perpendicular lines
(i)Dividing a straight line in a given ratio
2.CRelating equations to graphs: simultaneous equations
(a)What do simultaneous equations mean?
(b)Methods of solving simultaneous equations
2.DQuadratic equations and the graphs which show them
(a)What do the graphs which show quadratic equations look like?
(b)The method of completing the square
(c)Sketching the curves which give quadratic equations
(d)The ‘formula’ for quadratic equations
(e)Special properties of the roots of quadratic equations
(f)Getting useful information from ‘ b 2 – 4ac’
(g)A practical example of using quadratic equations
(h)All equations are equal – but are some more equal than others?
2.EFurther equations – the Remainder and Factor Theorems
(a)Cubic expressions and equations
(b)Doing long division in algebra
(c)Avoiding long division – the Remainder and Factor Theorems
(d)Three examples of using these theorems, and a red herring
3Relations and functions
3.ATwo special kinds of relationship
(a)Direct proportion
(b)Some physical examples of direct proportion
(c)More exotic examples
(d)Partial direct proportion – lines not through the origin
(e)Inverse proportion
(f)Some examples of mixed variation

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