Numerical Methods for Engineers and Scientists Using MATLAB®, 3rd Edition

Numerical Methods for Engineers and Scientists Using MATLAB®, 3rd Edition

Author: Ramin Esfandiari

Table of Contents

Chapter 1 Introduction to MATLAB ® 10
1.1 MATLAB Built-in Functions
1.2 Vectors and Matrices
1.3 Symbolic Toolbox
1.4 Program Flow Control
1.5 Displaying Formatted Data
1.6 Plotting
1.7 User-Defined Functions and Script Files
Problem Set
Chapter 2 Introduction to Numerical Methods 36
2.1 Errors and Approximations
2.2 Iterative Methods
Problem Set
Chapter 3 Numerical Solution of Equations of a Single Variable 48
3.1 Bracketing Methods
3.2 Fixed-Point Method
3.3 Newton's Method (Newton-Raphson Method)
3.4 Secant Method
3.5 Finding Roots Using the MATLAB Built-in Function fzero
Problem Set
Chapter 4 Numerical Solution of Systems of Equations 72
4.1 Gauss Elimination Method
4.2 LU Factorization Methods
4.3 Iterative Solution of Linear Systems
4.4 Ill-Conditioning and Error Analysis
4.5 Systems of Nonlinear Equations
Problem Set
Chapter 5 Curve Fitting and Interpolation 112
5.1 Linear Regression
5.2 Linearization of Nonlinear Data
5.3 Polynomial Regression
5.4 Polynomial Interpolation
5.5 Spline Interpolation
5.6 Fourier Approximation and Interpolation
Problem Set
Chapter 6 Numerical Differentiation and Integration 156
6.1 Finite-Difference Formulas for Numerical Differentiation
6.2 Numerical Integration: Newton-Cotes Formulas
6.3 Numerical Integration of Analytical Functions: Gaussian Quadrature
Problem Set
Chapter 7 Numerical Solution of Initial-Value Problems 190
7.1 Euler's Method
7.2 Runge-Kutta Methods
7.3 Multistep Methods
7.4 Systems of Initial-Value Problems
7.5 MATLAB Built-in Functions for Initial-Value Problems
Problem Set
Chapter 8 Numerical Solution of Boundary-Value Problems 230
8.1 Shooting Method
8.2 Finite-Difference Method
8.3 MATLAB Built-in Function bvp4c for Boundary-Value Problems
Problem Set
Chapter 9 Numerical Methods for the Eigenvalue Problem 250
9.1 Power Method - Estimation of the Dominant Eigenvalue
9.2 Deflation Methods
9.3 Householder Tridiagonalization and QR Factorization Methods
Problem Set
Chapter 10 Numerical Solution of Partial Differential Equations 276
10.1 Elliptic Partial Differential Equations
10.2 Parabolic Partial Differential Equations
10.3 Hyperbolic Partial Differential Equations
Problem Set
Appendix 1 References 307
Appendix 2 Useful Formulas 308
Index 310

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