Introductory Mathematics for Earth Scientists

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ISBN: 9781906716004 | 1906716005
Cover: Paperback
Copyright: 7/15/2009

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Any quantitative work in earth sciences requires mathematical analysis. Many mathematical methods are essential to the modeling and analysis of the geological, geophysical, and environmental processes widely studied in earth sciences. This book provides a

Preface	p. ix
Preliminary Mathematics I	p. 1
Functions	p. 2
Real Numbers	p. 2
Functions	p. 3
Equations	p. 10
Index Notation	p. 13
Notations of Indices	p. 13
Graphs of Functions	p. 16
Applications	p. 16
Greenhouse Effect	p. 17
Glacier Flow	p. 18
Airy Isostasy	p. 19
Size of an Impact Crater	p. 20
Preliminary Mathematics II	p. 21
Polynomials	p. 21
Roots	p. 22
Descartes' Theorem	p. 25
Applications	p. 27
Stokes' Flow	p. 27
Velocity of a Raindrop	p. 29
Binomial Theorem and Sequences	p. 31
The Binomial Theorem	p. 31
The Binomial Theorem	p. 31
Factorials	p. 32
Binomial Theorem and Pascal's Triangle	p. 33
Sequences	p. 34
Fibonacci Sequence	p. 36
Sum of a Series	p. 38
Infinite Series	p. 41
Exponentials and Logarithms	p. 42
Applications	p. 44
Carbon Dioxide	p. 44
Folds	p. 45
Gutenberg-Richter Law	p. 45
Distribution of Near-Earth Objects	p. 47
Trigonometry and Spherical Trigonometry	p. 49
Plane Trigonometry	p. 49
Trigonometrical Function	p. 49
Sine Rule	p. 57
Cosine Rule	p. 58
Spherical Trigonometry	p. 59
Applications	p. 61
Travel-Time Curves of Seismic Waves	p. 61
Great-Circle Distance	p. 63
Bubbles and Surface Tension	p. 64
Complex Numbers	p. 67
Complex Numbers	p. 67
Imaginary Numbers	p. 67
Polar Form	p. 70
Hyperbolic Functions	p. 72
Hyperbolic Sine and Cosine	p. 72
Hyperbolic Identities	p. 73
Inverse Hyperbolic Functions	p. 74
Water Waves	p. 75
Differentiation	p. 77
Gradient	p. 77
Differentiation Rules	p. 82
Partial Derivatives	p. 85
Maxima or Minima	p. 87
Series Expansions	p. 89
Applications	p. 91
Free-Air Gravity	p. 91
Mantle Convection	p. 92
Integration	p. 95
Integration	p. 95
Integration by Parts	p. 100
Integration by Substitution	p. 103
Bouguer Gravity	p. 105
Fourier Transforms	p. 107
Fourier Series	p. 107
Fourier Transforms	p. 111
DFT and FFT	p. 112
Milankovitch Cycles	p. 114
Vectors	p. 117
Vector Algebra	p. 117
Vectors	p. 117
Product of Vectors	p. 122
Gradient and Laplace Operators	p. 126
Applications	p. 129
Mohr-Coulomb Criterion	p. 129
Thrust Faults	p. 131
Electrical Method in Prospecting	p. 132
Matrix Algebra	p. 135
Matrices	p. 135
Transformation and Inverse	p. 138
Eigenvalues and Eigenvectors	p. 144
Harmonic Motion	p. 147
Ordinary Differential Equations	p. 149
Differential Equations	p. 149
First-Order Equations	p. 150
Second-Order Equations	p. 156
Higher-Order ODEs	p. 161
Applications	p. 163
Climate Changes	p. 163
Flexural Deflection of Lithosphere	p. 165
Glacial Isostatic Adjustment	p. 168
Partial Differential Equations	p. 171
Introduction	p. 171
Classic Equations	p. 172
Heat Conduction	p. 173
Cooling of the Lithosphere	p. 176
Geostatistics	p. 179
Random Variables	p. 179
Probability	p. 179
Mean and Variance	p. 181
Sample Mean and Variance	p. 183
Propagation of Errors	p. 184
Linear Regression	p. 188
Correlation Coefficient	p. 191
Brownian Motion	p. 192
Numerical Methods	p. 195
Finding the roots	p. 195
Newton-Raphson Method	p. 196
Numerical Integration	p. 198
Numerical Solutions of ODEs	p. 201
Euler Scheme	p. 202
Runge-Kutta Method	p. 203
Bibliography	p. 207
Glossary	p. 211
Mathematical Formulae	p. 217
Epilogue	p. 221
Index	p. 223
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Introductory Mathematics for Earth Scientists

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