Numerical Methods and Methods of Approximation in Science and Engineering - Info and Reading Options

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Cover -- Half Title -- Title Page -- Copyright Page -- Dedication -- Table of Contents -- Preface -- About the Author -- 1: Introduction -- 1.1 Numerical Solutions -- 1.1.1 Numerical Methods without any Approximation -- 1.1.2 Numerical Methods with Approximations -- 1.2 Accuracy of Numerical Solution, Error -- 1.3 Concept of Convergence -- 1.4 Mathematical Models -- 1.5 A Brief Description of Topics and Methods -- 2: Linear Simultaneous Algebraic Equations -- 2.1 Introduction, Matrices, and Vectors -- 2.1.1 Basic Definitions -- 2.1.2 Matrix Algebra -- 2.1.2.1 Addition and Subtraction of Two Matrices -- 2.1.2.2 Multiplication by a Scalar -- 2.1.2.3 Product of Matrices -- 2.1.2.4 Algebraic Properties of Matrix Multiplication -- 2.1.2.5 Decomposition of a Square Matrix into Symmetric and Skew-Symmetric Matrices -- 2.1.2.6 Augmenting a Matrix -- 2.1.2.7 Determinant of a Matrix -- 2.2 Matrix and Vector Notation -- 2.2.1 Elementary Row Operations -- 2.3 Solution Methods -- 2.4 Direct Methods -- 2.4.1 Graphical Method -- 2.4.2 Cramer's Rule -- 2.5 Elimination Methods -- 2.5.1 Gauss Elimination -- 2.5.1.1 Naive Gauss Elimination -- 2.5.1.2 Gauss Elimination with Partial Pivoting -- 2.5.1.3 Gauss Elimination with Full Pivoting -- 2.5.2 Gauss-Jordan Elimination -- 2.5.3 Methods Using [L][U] Decomposition -- 2.5.3.1 Classical [L][U] Decomposition and Solution of [A]{x} = {b}: Cholesky Decomposition -- 2.5.3.2 Determination of the Solution {x} Using [L][U] Decomposition -- 2.5.3.3 Crout Decomposition of [A] into [L][U] and Solution of Linear Algebraic Equations -- 2.5.3.4 Classical or Cholesky Decomposition of [A] in [A]{x} = {b} using Gauss Elimination -- 2.5.3.5 Cholesky Decomposition for a Symmetric Matrix [A] -- 2.5.3.6 Alternate Derivation of [L][U] Decomposition when [A] is Symmetric -- 2.6 Solution of Linear Systems Using the Inverse

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