An Introduction to Numerical Methods : a MATLAB Approach, Fourth Edition

"Previous editions of this popular textbook offered an accessible and practical introduction to numerical analysis. An Introduction to Numerical Methods: A MATLAB® Approach, Fourth Edition continues to present a wide range of useful and important algorithms for scientific and engineering applic...

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Bibliographic Details
Main Authors Kharab, Abdelwahab (Author), Guenther, Ronald B. (Author)
Format Electronic eBook
LanguageEnglish
Published Boca Raton, FL : CRC Press, 2018.
EditionFourth edition.
Subjects
Mathematical physics.
Mechanics, Applied.
Mechanical engineering.
Numerical analysis.
elektronické knihy
electronic books
Online AccessFull text
ISBN9781315107042
131510704X
9781351605922
1351605925
9781351605915
1351605917
9781351605908
1351605909
9781523120475
1523120479
9781138093072
1138093076
Physical Description1 online resource : text file, PDF

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TOC from ObalkyKnih.cz
Table of Contents:
  • Cover; Half Title; Title Page; Copyright Page; Dedication; Table of Contents; Preface; 1: Introduction; 1.1 ABOUT MATLAB and MATLAB GUI (Graphical User Interface); 1.2 AN INTRODUCTION TO MATLAB; 1.2.1 Matrices and matrix computation; 1.2.2 Polynomials; 1.2.3 Output format; 1.2.4 Planar plots; 1.2.5 3-D mesh plots; 1.2.6 Function files; 1.2.7 Defining functions; 1.2.8 Relations and loops; 1.3 TAYLOR SERIES; 2: Number System and Errors; 2.1 FLOATING-POINT ARITHMETIC; 2.2 ROUND-OFF ERRORS; 2.3 TRUNCATION ERROR; 2.4 INTERVAL ARITHMETIC; 3: Roots of Equations; 3.1 THE BISECTION METHOD.
  • 3.2 FIXED POINT ITERATION3.3 THE SECANT METHOD; 3.4 NEWTON'S METHOD; 3.5 CONVERGENCE OF THE NEWTON AND SECANT METHODS; 3.6 MULTIPLE ROOTS AND THE MODIFIED NEWTON METHOD; 3.7 NEWTON'S METHOD FOR NONLINEAR SYSTEMS; APPLIED PROBLEMS; 4: System of Linear Equations; 4.1 MATRICES AND MATRIX OPERATIONS; 4.2 NAIVE GAUSSIAN ELIMINATION; 4.3 GAUSSIAN ELIMINATION WITH SCALED PARTIAL PIVOTING; 4.4 LU DECOMPOSITION; 4.4.1 Crout's and Cholesky's methods; 4.4.2 Gaussian elimination method; 4.5 ITERATIVE METHODS; 4.5.1 Jacobi iterative method; 4.5.2 Gauss-Seidel iterative method; 4.5.3 Convergence.
  • APPLIED PROBLEMS5: Interpolation; 5.1 POLYNOMIAL INTERPOLATION THEORY; 5.2 NEWTON'S DIVIDED-DIFFERENCE INTERPOLATING POLYNOMIAL; 5.3 THE ERROR OF THE INTERPOLATING POLYNOMIAL; 5.4 LAGRANGE INTERPOLATING POLYNOMIAL; APPLIED PROBLEMS; 6: Interpolation with Spline Functions; 6.1 PIECEWISE LINEAR INTERPOLATION; 6.2 QUADRATIC SPLINE; 6.3 NATURAL CUBIC SPLINES; APPLIED PROBLEMS; 7: The Method of Least-Squares; 7.1 LINEAR LEAST-SQUARES; 7.2 LEAST-SQUARES POLYNOMIAL; 7.3 NONLINEAR LEAST-SQUARES; 7.3.1 Exponential form; 7.3.2 Hyperbolic form; APPLIED PROBLEMS; 8: Numerical Optimization.
  • 8.1 ANALYSIS OF SINGLE-VARIABLE FUNCTIONS8.2 LINE SEARCH METHODS; 8.2.1 Newton's method; 8.2.2 Golden section search; 8.2.3 Fibonacci Search; 8.2.4 Parabolic Interpolation; 8.3 MINIMIZATION USING DERIVATIVES; 8.3.1 Newton's method; 8.3.2 Newton's method; APPLIED PROBLEMS; 9: Numerical Differentiation; 9.1 NUMERICAL DIFFERENTIATION; 9.2 RICHARDSON'S FORMULA; APPLIED PROBLEMS; 10: Numerical Integration; 10.1 TRANPEZOIDAL RULE; 10.2 SIMPSON'S RULE; 10.3 ROMBERG ALGORITHM; 10.4 GAUSSIAN QUADRATURE; APPLED PROBLEMS; 11: Numerical Methods for Linear Integral Equations; 11.1 INTRODUCTION.
  • 11.2 QUADRATURE RULES11.2.1 Trapezoidal rule; 11.2.2 The Gauss-Nyström method; 11.3 THE SUCCESSIVE APPROXIMATION METHOD; 11.4 SCHMIDT's METHOD; 11.5 VOLTERRA-TYPE INTEGRAL EQUATIONS; 11.5.1 Euler's method; 11.5.2 Heun's method; APPLED PROBLEMS; 12: Numerical Methods for Differential Equations; 12.1 EULER'S METHOD; 12.2 ERROR ANALYSIS; 12.3 HIGHER-ORDER TAYLOR SERIES METHODS; 12.4 RUNGE-KUTTA METHODS; 12.5 MULTISTEP METHODS; 12.6 ADAMS-BASHFORTH METHODS; 12.7 PREDICTOR-CORRECTOR METHODS; 12.8 ADAMS-MOULTION; 12.9 NUMERICAL STABILITY.

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