Introductory Mathematics for Earth Scientists:
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
Edinburgh
Dunedin
2009
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 228 S. graph. Darst. |
| ISBN: | 9781906716004 |
Internformat
MARC
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| 245 | 1 | 0 | |a Introductory Mathematics for Earth Scientists |c Xin-She Yang |
| 264 | 1 | |a Edinburgh |b Dunedin |c 2009 | |
| 300 | |a X, 228 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Earth sciences |x Mathematics | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-017397026 | ||
Datensatz im Suchindex
| _version_ | 1804138939538210816 |
|---|---|
| adam_text | Contents
Preface
ix
1
Preliminary Mathematics I
1
1.1
Functions
.......................... 2
1.1.1
Real Numbers
.................... 2
1.1.2
Functions
...................... 3
1.2
Equations
.......................... 10
1.3
Index Notation
....................... 13
1.3.1
Notations of Indices
................ 13
1.3.2
Graphs of Functions
................ 16
1.4
Applications
......................... 16
1.4.1
Greenhouse Effect
................. 17
1.4.2
Glacier Flow
.................... 18
1.4.3
Airy Isostasy
.................... 19
1.4.4
Size of an Impact Crater
.............. 20
2
Preliminary Mathematics II
21
2.1
Polynomials
......................... 21
2.2
Roots
............................ 22
2.3
Descartes Theorem
.................... 25
2.4
Applications
......................... 27
2.4.1
Stokes Flow
.................... 27
2.4.2
Velocity of a Raindrop
............... 29
3
Binomial Theorem and Sequences
31
3.1
The Binomial Theorem
.................. 31
3.1.1
Factorials
...................... 32
3.1.2
Binomial Theorem and Pascal s Triangle
..... 33
3.2
Sequences
.......................... 34
3.2.1
Fibonacci Sequence
................. 36
3.2.2
Sum of a Series
................... 38
3.2.3
Infinite Series
.................... 41
3.3
Exponentials and Logarithms
............... 42
3.4
Applications
......................... 44
CONTENTS
3.4.1
Carbon
Dioxide................... 44
3.4.2
Folds
......................... 45
3.4.3 Gutenberg-Richter
Law
.............. 45
3.4.4
Distribution of Near-Earth Objects
........ 47
Trigonometry and Spherical Trigonometry
49
4.1
Plane Trigonometry
.................... 49
4.1.1
Trigonometrical Functions
............. 49
4.1.2
Sine Rule
...................... 57
4.1.3
Cosine Rule
..................... 58
4.2
Spherical Trigonometry
.................. 59
4.3
Applications
......................... 61
4.3.1
Travel-Time Curves of Seismic Waves
...... 61
4.3.2
Great-Circle Distance
............... 63
4.3.3
Bubbles and Surface Tension
........... 64
Complex Numbers
67
5.1
Complex Numbers
..................... 67
5.1.1
Imaginary Numbers
................ 67
5.1.2
Polar Form
..................... 70
5.2
Hyperbolic Functions
.................... 72
5.2.1
Hyperbolic Sine and Cosine
............ 72
5.2.2
Hyperbolic Identities
................ 73
5.2.3
Inverse Hyperbolic Functions
........... 74
5.3
Water Waves
........................ 75
Differentiation
77
6.1
Gradient
........................... 77
6.2
Differentiation Rules
.................... 82
6.3
Partial Derivatives
..................... 85
6.4
Maxima or Minima
..................... 87
6.5
Series Expansions
...................... 89
6.6
Applications
......................... 91
6.6.1
Free-Air Gravity
.................. 91
6.6.2
Mantle Convection
................. 92
Integration
95
7.1
Integration
......................... 95
7.2
Integration by Parts
.................... 100
7.3
Integration by Substitution
................ 103
7.4
Bouguer Gravity
...................... 105
CONTENTS
vii
8
Fourier Transforms
107
8.1
Fourier Series
........................ 107
8.2
Fourier Transforms
.....................
Ill
8.3
DFT and FFT
....................... 112
8.4
Milankovitch Cycles
.................... 114
9
Vectors
117
9.1
Vector Algebra
....................... 117
9.1.1
Vectors
....................... 117
9.1.2
Product of Vectors
................. 122
9.2
Gradient and Laplace Operators
............. 126
9.3
Applications
......................... 129
9.3.1
Mohr-Coulomb Criterion
............. 129
9.3.2
Thrust Faults
.................... 131
9.3.3
Electrical Method in Prospecting
......... 132
10
Matrix Algebra
135
10.1
Matrices
........................... 135
10.2
Transformation and Inverse
................ 138
10.3
Eigenvalues and Eigenvectors
............... 144
10.4
Harmonic Motion
...................... 147
11
Ordinary Differential Equations
149
11.1
Differential Equations
................... 149
11.2
First-Order Equations
................... 150
11.3
Second-Order Equations
.................. 156
11.4
Higher-Order ODEs
.................... 161
11.5
Applications
......................... 163
11.5.1
Climate Changes
.................. 163
11.5.2
Flexura!
Deflection of
Lithosphère
........ 165
11.5.3
Glacial Isostatic Adjustment
........... 168
12
Partial Differential Equations
171
12.1
Introduction
......................... 171
12.2
Classic Equations
...................... 172
12.3
Heat Conduction
...................... 173
12.4
Cooling of the
Lithosphère
................. 176
13
Geostatistics
179
13.1
Random Variables
..................... 179
13.1.1
Probability
..................... 179
13.1.2
Mean and Variance
................. 181
13.2
Sample Mean and Variance
................ 183
13.3
Propagation of Errors
................... 184
13.4
Linear Regression
...................... 188
13.5
Correlation Coefficient
................... 191
viii CONTENTS
13.6
Brownian.
Motion . :....................192
14
Numerical Methods
195
14.1
Finding the roots
...................... 195
14.2
Newton-Raphson Method
................. 196
14.3
Numerical Integration
................... 198
14.4
Numerical Solutions of ODEs
............... 201
14.4.1
Euler
Scheme
.................... 202
14.4.2
Runge-Kutta Method
............... 203
Bibliography
207
A Glossary
211
В
Mathematical Formulae
217
Epilogue
221
Index
223
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| id | DE-604.BV035477437 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T21:36:09Z |
| institution | BVB |
| isbn | 9781906716004 |
| language | English |
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| spelling | Introductory Mathematics for Earth Scientists Xin-She Yang Edinburgh Dunedin 2009 X, 228 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematik Earth sciences Mathematics Mathematik (DE-588)4037944-9 gnd rswk-swf Geowissenschaften (DE-588)4020288-4 gnd rswk-swf Geowissenschaften (DE-588)4020288-4 s Mathematik (DE-588)4037944-9 s DE-604 Yang, Xin-She 1965- Sonstige (DE-588)1043733906 oth Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017397026&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Introductory Mathematics for Earth Scientists Mathematik Earth sciences Mathematics Mathematik (DE-588)4037944-9 gnd Geowissenschaften (DE-588)4020288-4 gnd |
| subject_GND | (DE-588)4037944-9 (DE-588)4020288-4 |
| title | Introductory Mathematics for Earth Scientists |
| title_auth | Introductory Mathematics for Earth Scientists |
| title_exact_search | Introductory Mathematics for Earth Scientists |
| title_full | Introductory Mathematics for Earth Scientists Xin-She Yang |
| title_fullStr | Introductory Mathematics for Earth Scientists Xin-She Yang |
| title_full_unstemmed | Introductory Mathematics for Earth Scientists Xin-She Yang |
| title_short | Introductory Mathematics for Earth Scientists |
| title_sort | introductory mathematics for earth scientists |
| topic | Mathematik Earth sciences Mathematics Mathematik (DE-588)4037944-9 gnd Geowissenschaften (DE-588)4020288-4 gnd |
| topic_facet | Mathematik Earth sciences Mathematics Geowissenschaften |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017397026&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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