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Numerical Methods For Engineers And Scientists: An Introduction With Applications Using Matlab
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Preface iii Chapter 1 Introduction 1 1.1 Background 1 1.2 Representation of Numbers on a Computer 4 1.3 Errors in Numerical Solutions 10 1.4 Computers and Programming 15 1.5 Problems 18 Chapter 2 Mathematical Background 23 2.1 Background 23 2.2 Concepts from Pre-Calculus and Calculus 24 2.3 Vectors 28 2.4 Matrices and Linear Algebra 32 2.5 Ordinary Differential Equations (ODE) 41 2.6 Functions of Two or More Independent Variables 44 2.7 Taylor Series Expansion of Functions 47 2.8 Inner Product and Orthogonality 50 2.9 Problems 51 Chapter 3 Solving Nonlinear Equations 57 3.1 Background 57 3.2 Estimation of Errors in Numerical Solutions 59 3.3 Bisection Method 61 3.4 Regula Falsi Method 64 3.5 Newton’s Method 66 3.6 Secant Method 71 3.7 Fixed-Point Iteration Method 74 3.8 Use of MATLAB Built-In Functions for Solving Nonlinear Equations 77 3.9 Equations with Multiple Solutions 79 3.10 Systems of Nonlinear Equations 81 3.11 Problems 88 Chapter 4 Solving a System of Linear Equations 99 4.1 Background 99 4.2 Gauss Elimination Method 102 4.3 Gauss Elimination with Pivoting 112 4.4 Gauss–Jordan Eli...
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