Essential Maths for Geoscientists: An Introduction

218 Pages·2014·4.686 MB·English

by  Paul I. Palmer

Paul I. Palmer
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for Geoscientists
An Introduction

Essential Maths for Geoscientists

Essential Maths for
Geoscientists
An Introduction
Paul I. Palmer
School of Geosciences, University of Edinburgh, UK
Thiseditionfirstpublished2014 C⃝2014byJohnWiley&Sons,Ltd
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Palmer,PaulI.
Essentialmathsforgeoscientists:anintroduction/PaulI.Palmer.
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Includesbibliographicalreferencesandindex.
ISBN978-0-470-97193-2(cloth)–ISBN978-0-470-97194-9(pbk.) 1.Geology–Mathematics.
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Contents
Preface xi
1 How Do You Know that Global Warming Is Not a Hoax? 1
2 Preamble 7
2.1 Thescientificmethod:pushingbackthefrontiersofignorance 7
2.2 Subscriptandsuperscripts 9
2.3 Scientificnumberformat 10
2.4 Significantfiguresandroundingnumbers 12
2.5 Unitsanddimensions 13
2.6 Symbolsandnumbers 14
2.7 Mean,medianandvariance:commonlyencounteredstatistics 15
2.8 Guesstimation 19
2.9 Exercises 21
3 Algebra 37
3.1 Introduction 37
3.2 Evaluatingalgebraicequations 37
3.2.1 Preamble:symbolsandnumbers 37
3.2.2 Powers,rootsandbases 38
3.3 Simplifyingalgebraicequations 39
3.4 Factorization 44
3.4.1 Factorizingquadraticequations 46
3.5 Transposingformulae 46
3.6 Wordproblems 49
3.7 Exercises 50
4 Solving Equations 53
4.1 Solvinglinearequations 53
4.1.1 Graphically 54
4.1.2 Analytically 58
4.2 Solvingsimultaneousequations 58
4.3 Solvingquadraticequations 59
viii CONTENTS
4.3.1 Squareroots 60
4.3.2 Completingthesquare 60
4.4 Exercises 62
5 Logarithms and Exponentials 67
5.1 Exponentials 67
5.2 Logarithms 67
5.2.1 Logarithmlaws 68
5.2.2 Solvingexponentialequations 69
5.2.3 Powerlawsandscalingexponents 69
5.3 Log-normalandlog–logplots:whenandhowtousethem 72
5.4 Exercises 74
6 Uncertainties, Errors, and Statistics 77
6.1 Errors 77
6.1.1 Importantdefinitions 78
6.1.2 Measuresoferror 80
6.2 Combiningerrors 83
6.2.1 Equationswithonevariable 83
6.2.2 Equationswithtwoormorevariables 84
6.2.3 Linearequations 84
6.2.4 Products 85
6.2.5 Combiningresultsofdifferentexperiments 86
6.3 Statistics 87
6.3.1 Graphs 87
6.3.2 Descriptivestatistics 89
6.4 Correlations 91
6.5 Exercises 93
7 Trigonometry 95
7.1 Somegeoscienceapplicationsoftrigonometry 95
7.2 Anatomyofatriangle 96
7.3 Angles:degreesandradians 99
7.4 Calculatinganglesgivenatrigonometricratio 100
7.5 Cosineandsinerulesfornon-right-angledtriangles 101
7.6 Exercises 101
8 Vectors 105
8.1 Whatisavector? 105
8.2 Resolvingavector 105
8.3 Vectoralgebra 107
8.3.1 Addingandsubtractingvectors 107