Fundamental Numerical Methods and Data Analysis

Table of Contents
List of Figures
List of Tables
Preface
Notes to the Internet Edition
1. Introduction and Fundamental Concepts
1.1 Basic Properties of Sets and Groups
1.2 Scalars, Vectors, and Matrices
1.3 Coordinate Systems and Coordinate Transformations
1.4 Tensors and Transformations
1.5 Operators

Chapter 1 Exercises
Chapter 1 References and Additional Reading
2. The Numerical Methods for Linear Equations and Matrices
2.1 Errors and Their Propagation
2.2 Direct Methods for the Solution of Linear Algebraic Equations
a. Solution by Cramer's Rule
b. Solution by Gaussian Elimination
c. Solution by Gauss Jordan Elimination
d. Solution by Matrix Factorization: The Crout Method
e. The Solution of Tri-diagonal Systems of Linear Equations
2.3 Solution of Linear Equations by Iterative Methods
a. Solution by The Gauss and Gauss-Seidel Iteration Methods
b. The Method of Hotelling and Bodewig
c. Relaxation Methods for the Solution of Linear Equations
d. Convergence and Fixed-point Iteration Theory
2.4 The Similarity Transformations and the Eigenvalues and Vectors of a Matrix

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