Numerical Methods for Engineers and Scientists, 3rd Edition provides engineers with a more concise treatment of the essential topics of numerical methods while emphasizing MATLAB use. The third edition includes a new chapter, with all new content, on Fourier Transform and a new chapter on Eigenvalues (compiled from existing Second Edition content). The focus is placed on the use of anonymous functions instead of inline functions and the uses of subfunctions and nested functions. This updated edition includes 50% new or updated Homework Problems, updated examples, helping engineers test their understanding and reinforce key concepts.
Author(s): Amos Gilat; Vish Subramaniam
Edition: 3
Publisher: Wiley
Year: 2023
Language: english
Pages: 577
Cover
Title Page
Copyright
Preface
Features/pedagogy of the book
Organization of the book
Organization of a typical chapter
The order of topics
MATLAB programs
Third edition
Support material
Contents
Chapter 1: Introduction
1.1 Background
1.2 Representation of Numbers on a Computer
1.3 Errors in Numerical Solutions
1.4 Computers and Programming
1.5 Problems
Chapter 2: Mathematical Background
2.1 Background
2.2 Concepts from Pre-Calculus and calculus
2.3 Vectors
2.4 Matrices and Linear Algebra
2.5 Ordinary Differential Equations (ODE)
2.6 Functions of Two or More Independent Variables
2.7 Taylor Series Expansion of Functions
2.8 Inner Product and Orthogonality
2.9 Problems
Chapter 3: Solving Nonlinear Equations
3.1 Background
3.2 Estimation of Errors in Numerical Solutions
3.3 Bisection Method
3.4 Regula Falsi Method
3.5 Newton’s Method
3.6 Secant Method
3.7 Fixed-Point Iteration Method
3.8 Use of MATLAB Built-In Functions for Solving Nonlinear Equations
3.9 Equations with Multiple Solutions
3.10 Systems of Nonlinear Equations
3.11 Problems
Chapter 4: Solving a System of Linear Equations
4.1 Background
4.2 Gauss Elimination Method
4.3 Gauss Elimination with Pivoting
4.4 Gauss–Jordan Elimination Method
4.5 LU Decomposition Method
4.6 Inverse of a Matrix
4.7 Iterative Methods
4.8 Use of MATLAB Built-In Functions for Solving a System of Linear Equations
4.9 Tridiagonal Systems of Equations
4.10 Error, Residual, Norms, and Condition Number
4.11 Ill-Conditioned Systems
4.12 Problems
Chapter 5: Eigenvalues and Eigenvectors
5.1 Background
5.2 The Characteristic Equation
5.3 The Basic Power Method
5.4 The Inverse Power Method
5.5 The Shifted Power Method
5.6 The QR Factorization and Iteration Method
5.7 Use of MATLAB Built-In Functions for Determining Eigenvalues and Eigenvectors
5.8 Problems
Chapter 6: Curve Fitting and Interpolation
6.1 Background
6.2 Curve Fitting with a Linear Equation
6.3 Curve Fitting with Nonlinear Equation by Writing the Equation in a Linear Form
6.4 Curve Fitting with Quadratic and Higher Order Polynomials
6.5 Interpolation Using a Single Polynomial
6.6 Piecewise (Spline) Interpolation
6.7 Use of MATLAB Built-In Functions for Curve Fitting and Interpolation
6.8 Curve Fitting with a Linear Combination of Nonlinear Functions
6.9 Problems
Chapter 7: Fourier Methods
7.1 Background
7.2 Approximating a Square Wave by a Series of Sine Functions
7.3 General (Infinite) Fourier Series
7.4 Complex Form of the Fourier Series
7.5 The Discrete Fourier Series and Discrete Fourier Transform
7.6 Complex Discrete Fourier Transform
7.7 Power (Energy) Spectrum
7.8 Aliasing and Nyquist Frequency
7.9 Alternative Forms of the Discrete Fourier Transform
7.10 Use of MATLAB Built-In Functions for Calculating Discrete Fourier Transform
7.11 Leakage and Windowing
7.12 Bandwidth and Filters
7.13 The Fast Fourier Transform (FFT)
7.14 Problems
Chapter 8: Numerical Differentiation
8.1 Background
8.2 Finite Difference Approximation of the Derivative
8.3 Finite Difference Formulas Using Taylor Series Expansion
8.4 Summary of Finite Difference Formulas for Numerical Differentiation
8.5 Differentiation Formulas Using Lagrange Polynomials
8.6 Differentiation Using Curve Fitting
8.7 Use of MATLAB Built-In Functions for Nmerical Differentiation
8.8 Richardson’s Extrapolation
8.9 Error in Numerical Differentiation
8.10 Numerical Partial Differentiation
8.11 Problems
Chapter 9: Numerical Integration
9.1 Background
9.2 Rectangle and Midpoint Methods
9.3 Trapezoidal Method
9.4 Simpson’s Methods
9.5 Gauss Quadrature
9.6 Evaluation of Multiple Integrals
9.7 Use of MATLAB Built-In Functions for Integration
9.8 Estimation of Error in Numerical Integration
9.9 Richardson’s Extrapolation
9.10 Romberg Integration
9.11 Improper Integrals
9.12 Problems
Chapter 10: Ordinary Differential Equations: Initial-Value Problems
10.1 Background
10.2 Euler’s Methods
10.3 Modified Euler’s Method
10.4 Midpoint Method
10.5 Runge–Kutta Methods
10.6 Multistep Methods
10.7 Predictor–Corrector Methods
10.8 System of First-Order Ordinary Differential Equations
10.9 Solving a Higher-Order Initial Value Problem
10.10 Use of MATLAB Built-In Functions for Solving Initial-Value Problems
10.11 Local Truncation Error in Second-Order Runge–Kutta Method
10.12 Step Size for Desired Accuracy
10.13 Stability
10.14 Stiff Ordinary Differential Equations
10.15 Problems
Chapter 11: Ordinary Differential Equations: Boundary-Value Problems
11.1 Background
11.2 The Shooting Method
11.3 Finite Difference Method
11.4 Use of MATLAB Built-In Functions for Solving Boundary Value Problems
11.5 Error and Stability in Numerical Solution of Boundary Value Problems
11.6 Problems
Appendix A: Introductory MATLAB
A.1 Background
A.2 Starting with MATLAB
A.3 Arrays
A.4 Mathematical Operations with Arrays
A.5 Script Files
A.6 Plotting
A.7 User-Defined Functions and Function files
A.8 Anonymous Functions
A.9 Function Functions
A.10 Subfunctions
A.11 Programming in MATLAB
A.12 Problems
Appendix B: MATLAB Programs
Appendix C: Derivation of the Real Discrete Fourier Transform (DFT)
C.1 Orthogonality of Sines and Cosines for Discrete Points
C.2 Determination of the Real DFT
Index
