Book description
Gilat's text is intended for a first course in numerical methods for students in engineering and science, typically taught in the second year of college. The book covers the fundamentals of numerical methods from an applied point of view. They also learn computer programming and use advanced software, specifically MATLAB, as a tool for solving problems. The text prepares students in science and engineering for future courses in their areas of specialization.
Table of contents
- Cover Page
- Title Page
- Copyright
- Preface
- Dedication
- Contents
- Contents
- Chapter 1: Introduction
-
Chapter 2: Mathematical Background
- 2.1 BACKGROUND
- 2.2 CONCEPTS FROM PRE-CALCULUS AND CALCULUS
- 2.3 VECTORS
- 2.4 MATRICES AND LINEAR ALGEBRA
- 2.4.5 Determinant of a Matrix
- 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
-
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 NUMERICAL 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 RANGE–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
- Appendix A: Introductory MATLAB
- Appendix B: MATLAB Programs
- Appendix C: Derivation of the Real Discrete Fourier Transform (DFT)
- Index
Product information
- Title: Numerical Methods for Engineers and Scientists 3rd Edition
- Author(s):
- Release date: October 2013
- Publisher(s): Wiley
- ISBN: 9781118554937
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