Introduction to Linear Algebra in Geology

Introduction to Linear Algebra in Geology
Introduction to Linear Algebra in Geology
Contents
Preface and acknowledgements
Glossary of symbols and conventions
Introduction
1 The solution of simultaneous linear equations
1.1 Basic definitions and introductory examples
1.1.1 Geological examples
1.1.2 Student examples
1.2 Methods of solution of simultaneous linear equations
1.2.1 Gaussian elimination
1.2.2 Student examples
1.2.3 The Gauss-Seidel method
1.2.4 Student examples
1.3 Problem equations
1.3.1 Overdetermined equations
1.3.2 Underdetermined equations
1.3.3 Homogeneous equations
1.3.4 Other geological applications
1.3.5 Student examples
2 Scalars, vectors and matrices
2.1 Scalars and vectors - some basic definitions
2.1.1 Scalars
2.1.2 Vectors
2.1.3 The product of two vectors
2.1.4 Student examples
2.2 Matrices - some basic definitions
2.2.1 Matrix operations - multiplication by a vector
2.2.2 Student examples
2.2.3 Multiplication of two matrices
2.2.4 Powering a matrix
2.2.5 Student examples
3 Determinants and inverses
3.1 Deteminants
3.1.1 The calculation of determinants
3.1.2 Cramer's rule
3.1.3 Calculation of determinants by row reduction
3.1.4 Student examples
3.1.5 Determinants and linear independence
3.1.6 Student examples
3.2 Matrix inversion
3.2.1 Matrix inversion by systematic elimination
3.2.2 Student examples
4 Accuracy and error
4.1 Examples of commonly occurring problems
4.2 Practical error detection during computation
4.2.1 The checksum method
4.2.2 The residual vector method
4.2.3 Scaling
4.2.4 Pivoting
4.2.5 Student examples
4.3 Ill-conditioned equations
4.3.1 Student example
5 A geometrical interpretation of vector and matrix operations
5.1 Points and lines in the plane and in space
5.1.1 Vectors
5.1.2 The angle between two vectors
5.1.3 The concurrence of three straight lines
5.1.4 Relationship between three points
5.1.5 Student examples
5.2 Transformations
5.2.1 Progressive deformation
5.2.2 Student examples
6 Eigenvalues and eigenvectors
6.1 What are eigenvalues and eigenvectors?
6.2 Calculation of eigenvalues and eigenvectors
6.2.1 Solving the characteristic equation
6.2.2 Student examples
6.2.3 An iterative method to find eigenvalues and eigenvectors
6.2.4 Student examples
6.3 The finite strain ellipse - a geometrical interpretation
6.3.1 Student examples
7 Multivariate statistics
7.1 Some basic matrices
7.1.1 Student examples
7.2 Multivariate regression
7.2.1 Student examples
7.3 Discriminant functions
7.3.1 Student example
7.4 Principal components analysis
7.4.1 Student example
8 Review of geological applications
8.1 Markov proc:esses and the simulation of sedimentary sequences
8.2 Differential and partial differential equations
8.3 Well-log analysis and the mixing problem
8.4 Applications in petrological studies
8.5 Tectonic studies
Answers to selected student examples
Chapter 1
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Chapter 7
References
Index