Essential Maths for Geoscientists: An Introduction

Preface xi1 How Do You Know that Global Warming Is Not a Hoax? 12 Preamble 72.1 The scientific method: pushing back the frontiers of ignorance 72.2 Subscript and superscripts 92.3 Scientific number format 102.4 Significant figures and rounding numbers 122.5 Units and dimensions 132.6 Symbols and numbers 142.7 Mean, median and variance: commonly encountered statistics 152.8 Guesstimation 192.9 Exercises 213 Algebra 373.1 Introduction 373.2 Evaluating algebraic equations 373.2.1 Preamble: symbols and numbers 373.2.2 Powers, roots and bases 383.3 Simplifying algebraic equations 393.4 Factorization 443.4.1 Factorizing quadratic equations 463.5 Transposing formulae 463.6 Word problems 493.7 Exercises 504 Solving Equations 534.1 Solving linear equations 534.1.1 Graphically 544.1.2 Analytically 584.2 Solving simultaneous equations 584.3 Solving quadratic equations 594.3.1 Square roots 604.3.2 Completing the square 604.4 Exercises 625 Logarithms and Exponentials 675.1 Exponentials 675.2 Logarithms 675.2.1 Logarithm laws 685.2.2 Solving exponential equations 695.2.3 Power laws and scaling exponents 695.3 Log-normal and log-log plots: when and how to use them 725.4 Exercises 746 Uncertainties, Errors, and Statistics 776.1 Errors 776.1.1 Important definitions 786.1.2 Measures of error 806.2 Combining errors 836.2.1 Equations with one variable 836.2.2 Equations with two or more variables 846.2.3 Linear equations 846.2.4 Products 856.2.5 Combining results of different experiments 866.3 Statistics 876.3.1 Graphs 876.3.2 Descriptive statistics 896.4 Correlations 916.5 Exercises 937 Trigonometry 957.1 Some geoscience applications of trigonometry 957.2 Anatomy of a triangle 967.3 Angles: degrees and radians 997.4 Calculating angles given a trigonometric ratio 1007.5 Cosine and sine rules for non-right-angled triangles 1017.6 Exercises 1018 Vectors 1058.1 What is a vector? 1058.2 Resolving a vector 1058.3 Vector algebra 1078.3.1 Adding and subtracting vectors 1078.3.2 Multiplying a vector by a scalar 1078.3.3 The resultant of two perpendicular vectors 1078.4 Resolving non-perpendicular vectors 1088.5 Exercises 1109 Calculus 1: Differentiation 1139.1 A graphical interpretation of differentiation 1149.2 A general formula for differentiation 1169.3 The derivative of some common functions 1189.4 Differentiation of the sum and difference of functions 1189.5 Higher derivatives 1209.6 Maxima and minima 1209.7 Exercises 12210 Calculus 2: Integration 12510.1 Introduction 12510.2 Definite integrals 12710.3 Numerical integration 12910.4 Exercises 13011 Bringing It All Together 133A Answers to Problems 143A.1 Chapter 2: Preamble 143A.2 Chapter 3: Algebra 148A.3 Chapter 4: Solving Equations 152A.4 Chapter 5: Logarithms and Exponentials 158A.5 Chapter 6: Uncertainties, Errors, and Statistics 162A.6 Chapter 7: Trigonometry 166A.7 Chapter 8: Vectors 171A.8 Chapter 9: Differentiation 174A.9 Chapter 10: Integration 179A.10 Chapter 11: Bringing it all together 182B A Brief Note on Excel 197C Further Reading 199Index 201