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Numerical Methods for Engineers and Scientists 3rd Edition

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

  1. Cover Page
  2. Title Page
  3. Copyright
  4. Preface
  5. Dedication
  6. Contents
  7. Contents
  8. Chapter 1: Introduction
    1. 1.1 BACKGROUND
    2. 1.2 REPRESENTATION OF NUMBERS ON A COMPUTER
    3. 1.3 ERRORS IN NUMERICAL SOLUTIONS
    4. 1.4 COMPUTERS AND PROGRAMMING
    5. 1.5 PROBLEMS
  9. Chapter 2: Mathematical Background
    1. 2.1 BACKGROUND
    2. 2.2 CONCEPTS FROM PRE-CALCULUS AND CALCULUS
    3. 2.3 VECTORS
    4. 2.4 MATRICES AND LINEAR ALGEBRA
    5. 2.4.5 Determinant of a Matrix
    6. 2.5 ORDINARY DIFFERENTIAL EQUATIONS (ODE)
    7. 2.6 FUNCTIONS OF TWO OR MORE INDEPENDENT VARIABLES
    8. 2.7 TAYLOR SERIES EXPANSION OF FUNCTIONS
    9. 2.8 INNER PRODUCT AND ORTHOGONALITY
    10. 2.9 PROBLEMS
  10. Chapter 3: Solving Nonlinear Equations
    1. 3.1 BACKGROUND
    2. 3.2 ESTIMATION OF ERRORS IN NUMERICAL SOLUTIONS
    3. 3.3 BISECTION METHOD
    4. 3.4 REGULA FALSI METHOD
    5. 3.5 NEWTON'S METHOD
    6. 3.6 SECANT METHOD
    7. 3.7 FIXED-POINT ITERATION METHOD
    8. 3.8 USE OF MATLAB BUILT-IN FUNCTIONS FOR SOLVING NONLINEAR EQUATIONS
    9. 3.9 EQUATIONS WITH MULTIPLE SOLUTIONS
    10. 3.10 SYSTEMS OF NONLINEAR EQUATIONS
    11. 3.11 PROBLEMS
  11. Chapter 4: Solving a System of Linear Equations
    1. 4.1 BACKGROUND
    2. 4.2 GAUSS ELIMINATION METHOD
    3. 4.3 GAUSS ELIMINATION WITH PIVOTING
    4. 4.4 GAUSS–JORDAN ELIMINATION METHOD
    5. 4.5 LU DECOMPOSITION METHOD
    6. 4.6 INVERSE OF A MATRIX
    7. 4.7 ITERATIVE METHODS
    8. 4.8 USE OF MATLAB BUILT-IN FUNCTIONS FOR SOLVING A SYSTEM OF LINEAR EQUATIONS
    9. 4.9 TRIDIAGONAL SYSTEMS OF EQUATIONS
    10. 4.10 ERROR, RESIDUAL, NORMS, AND CONDITION NUMBER
    11. 4.11 ILL-CONDITIONED SYSTEMS
    12. 4.12 PROBLEMS
  12. Chapter 5: Eigenvalues and Eigenvectors
    1. 5.1 BACKGROUND
    2. 5.2 THE CHARACTERISTIC EQUATION
    3. 5.3 THE BASIC POWER METHOD
    4. 5.4 THE INVERSE POWER METHOD
    5. 5.5 THE SHIFTED POWER METHOD
    6. 5.6 THE QR FACTORIZATION AND ITERATION METHOD
    7. 5.7 USE OF MATLAB BUILT-IN FUNCTIONS FOR DETERMINING EIGENVALUES AND EIGENVECTORS
    8. 5.8 PROBLEMS
  13. Chapter 6: Curve Fitting and Interpolation
    1. 6.1 BACKGROUND
    2. 6.2 CURVE FITTING WITH A LINEAR EQUATION
    3. 6.3 CURVE FITTING WITH NONLINEAR EQUATION BY WRITING THE EQUATION IN A LINEAR FORM
    4. 6.4 CURVE FITTING WITH QUADRATIC AND HIGHER-ORDER POLYNOMIALS
    5. 6.5 INTERPOLATION USING A SINGLE POLYNOMIAL
    6. 6.6 PIECEWISE (SPLINE) INTERPOLATION
    7. 6.7 USE OF MATLAB BUILT-IN FUNCTIONS FOR CURVE FITTING AND INTERPOLATION
    8. 6.8 CURVE FITTING WITH A LINEAR COMBINATION OF NONLINEAR FUNCTIONS
    9. 6.9 PROBLEMS
  14. Chapter 7: Fourier Methods
    1. 7.1 BACKGROUND
    2. 7.2 APPROXIMATING A SQUARE WAVE BY A SERIES OF SINE FUNCTIONS
    3. 7.3 GENERAL (INFINITE) FOURIER SERIES
    4. 7.4 COMPLEX FORM OF THE FOURIER SERIES
    5. 7.5 THE DISCRETE FOURIER SERIES AND DISCRETE FOURIER TRANSFORM
    6. 7.6 COMPLEX DISCRETE FOURIER TRANSFORM
    7. 7.7 POWER (ENERGY) SPECTRUM
    8. 7.8 ALIASING AND NYQUIST FREQUENCY
    9. 7.9 ALTERNATIVE FORMS OF THE DISCRETE FOURIER TRANSFORM
    10. 7.10 USE OF MATLAB BUILT-IN FUNCTIONS FOR CALCULATING DISCRETE FOURIER TRANSFORM
    11. 7.11 LEAKAGE AND WINDOWING
    12. 7.12 BANDWIDTH AND FILTERS
    13. 7.13 THE FAST FOURIER TRANSFORM (FFT)
    14. 7.14 PROBLEMS
  15. Chapter 8: Numerical Differentiation
    1. 8.1 BACKGROUND
    2. 8.2 FINITE DIFFERENCE APPROXIMATION OF THE DERIVATIVE
    3. 8.3 FINITE DIFFERENCE FORMULAS USING TAYLOR SERIES EXPANSION
    4. 8.4 SUMMARY OF FINITE DIFFERENCE FORMULAS FOR NUMERICAL DIFFERENTIATION
    5. 8.5 DIFFERENTIATION FORMULAS USING LAGRANGE POLYNOMIALS
    6. 8.6 DIFFERENTIATION USING CURVE FITTING
    7. 8.7 USE OF MATLAB BUILT-IN FUNCTIONS FOR NUMERICAL DIFFERENTIATION
    8. 8.8 RICHARDSON'S EXTRAPOLATION
    9. 8.9 ERROR IN NUMERICAL DIFFERENTIATION
    10. 8.10 NUMERICAL PARTIAL DIFFERENTIATION
    11. 8.11 PROBLEMS
  16. Chapter 9: Numerical Integration
    1. 9.1 BACKGROUND
    2. 9.2 RECTANGLE AND MIDPOINT METHODS
    3. 9.3 TRAPEZOIDAL METHOD
    4. 9.4 SIMPSON'S METHODS
    5. 9.5 GAUSS QUADRATURE
    6. 9.6 EVALUATION OF MULTIPLE INTEGRALS
    7. 9.7 USE OF MATLAB BUILT-IN FUNCTIONS FOR INTEGRATION
    8. 9.8 ESTIMATION OF ERROR IN NUMERICAL INTEGRATION
    9. 9.9 RICHARDSON'S EXTRAPOLATION
    10. 9.10 ROMBERG INTEGRATION
    11. 9.11 IMPROPER INTEGRALS
    12. 9.12 PROBLEMS
  17. Chapter 10: Ordinary Differential Equations: Initial-Value Problems
    1. 10.1 BACKGROUND
    2. 10.2 EULER'S METHODS
    3. 10.3 MODIFIED EULER'S METHOD
    4. 10.4 MIDPOINT METHOD
    5. 10.5 RUNGE–KUTTA METHODS
    6. 10.6 MULTISTEP METHODS
    7. 10.7 PREDICTOR–CORRECTOR METHODS
    8. 10.8 SYSTEM OF FIRST-ORDER ORDINARY DIFFERENTIAL EQUATIONS
    9. 10.9 SOLVING A HIGHER-ORDER INITIAL VALUE PROBLEM
    10. 10.10 USE OF MATLAB BUILT-IN FUNCTIONS FOR SOLVING INITIAL-VALUE PROBLEMS
    11. 10.11 LOCAL TRUNCATION ERROR IN SECOND-ORDER RANGE–KUTTA METHOD
    12. 10.12 STEP SIZE FOR DESIRED ACCURACY
    13. 10.13 STABILITY
    14. 10.14 STIFF ORDINARY DIFFERENTIAL EQUATIONS
    15. 10.15 PROBLEMS
  18. Chapter 11: Ordinary Differential Equations: Boundary-Value Problems
    1. 11.1 BACKGROUND
    2. 11.2 THE SHOOTING METHOD
    3. 11.3 FINITE DIFFERENCE METHOD
    4. 11.4 USE OF MATLAB BUILT-IN FUNCTIONS FOR SOLVING BOUNDARY VALUE PROBLEMS
    5. 11.5 ERROR AND STABILITY IN NUMERICAL SOLUTION OF BOUNDARY VALUE PROBLEMS
    6. 11.6 PROBLEMS
  19. Appendix A: Introductory MATLAB
    1. A.1 BACKGROUND
    2. A.2 STARTING WITH MATLAB
    3. A.3 ARRAYS
    4. A.4 MATHEMATICAL OPERATIONS WITH ARRAYS
    5. A.5 SCRIPT FILES
    6. A.6 PLOTTING
    7. A.7 USER-DEFINED FUNCTIONS AND FUNCTION FILES
    8. A.8 ANONYMOUS FUNCTIONS
    9. A.9 FUNCTION FUNCTIONS
    10. A.10 SUBFUNCTIONS
    11. A.11 PROGRAMMING IN MATLAB
    12. A.12 PROBLEMS
  20. Appendix B: MATLAB Programs
  21. Appendix C: Derivation of the Real Discrete Fourier Transform (DFT)
    1. C.1 ORTHOGONALITY OF SINES AND COSINES FOR DISCRETE POINTS
    2. C.2 DETERMINATION OF THE REAL DFT
  22. Index