Details

Autor(en) / Beteiligte

• Venkateshan, S. P.,
• Swaminathan, Prasanna,

Titel

Computational methods in engineering

Auflage

First edition

Ort / Verlag

Oxford, United Kingdom : Elsevier,

Erscheinungsjahr

2014

Link zum Volltext

• Elsevier Books AutoHoldings

Beschreibungen/Notizen

• June 2013.
• Includes index.
• Front Cover; Computational Methods in Engineering; Dedication; Copyright Page; Preface; Acknowledgements; Contents; Chapter 1: Preliminaries; 1.1 Introduction; 1.2 Mathematical and computational modeling; 1.3 A brief introduction to MATLAB; Suggested reading; Module I: System of equations and eigenvalues; Chapter 2: Solution of linear equations; 2.1 Analytical methods of solving a set of linear equations; 2.2 Preliminaries; 2.3 Gauss elimination method; 2.4 Gauss Jordan method of determining the inverse matrix; 2.5 LU decomposition or LU factorization; 2.6 Tridiagonal matrix algorithm
• 2.7 QR Factorization2.8 Iterative methods of solution; 2. A MATLAB routines related to Chapter 2; 2.B Suggested reading; Chapter 3: Computation of eigenvalues; 3.1 Examples of eigenvalues; 3.2 Preliminaries on eigenvalues; 3.3 Analytical evaluation of eigenvalues and eigenvectors in simple cases; 3.4 Power method; 3.5 Rayleign Quotient Iteration; 3.6 Eigenvalue eigenvector pair by QR iteration; 3.7 Modification of QR iteration for faster convergence; 3.A MATLAB routines related to Chapter 3; 3.B Suggested reading; Chapter 4: Solution of algebraic equations; 4.1 Univariate nonlinear equation
• 4.2 Multivariate non linear equations4.3 Root finding and optimization; 4.4 Multidimensional unconstrained optimization; 4.5 Examples from engineering applications; 4.A MATLAB routines related to Chapter 4; 4.B Suggested reading; Exercise I; I.1 Solution of linear equations; I.2 Evaluation of eigenvalues; I.3 Solution of algebraic equations; Module II: Interpolation, differentiation and integration; Chapter 5: Interpolation; 5.1 Polynomial interpolation; 5.2 Lagrange interpolating (or interpolation) polynomial; 5.3 Newton Polynomials; 5.4 Error estimates of polynomial approximations
• 5.5 Polynomial approximation using Chebyshev nodes5.6 Piecewise polynomial interpolation; 5.7 Hermite interpolation; 5.8 Spline interpolation and the cubic spline; 5.A MATLAB routines related to Chapter 5; 5.B Suggested reading; Chapter 6: Interpolation in two and three dimensions; 6.1 Interpolation over a rectangle; 6.2 Interpolation over a triangle; 6.3 Interpolation in three dimensions; Chapter 7: Regression or curve fitting; 7.1 Introduction; 7.2 Method of least squares for linear regression; 7.3 Multi-linear regression; 7.4 Polynomial regression; 7.5 Non-linear regression
• 7.A MATLAB routines related to Chapter 77.B Suggested reading; Chapter 8: Numerical Differentiation; 8.1 Introduction; 8.2 Finite difference formulae using Taylor''s series; 8.3 Differentiation of Lagrange and Newton polynomials; 8.4 Numerical partial differentiation; 8.A MATLAB routines related to Chapter 8; Chapter 9: Numerical Integration; 9.1 Introduction; 9.2 Trapezoidal rule; 9.3 Simpson''s rule; 9.4 Integration of functions; 9.5 Quadrature using Chebyshev nodes; 9.6 Gauss quadrature; 9.7 Singular integrals; 9.8 Ingegrals with infinite range; 9.9 Adaptive quadrature
• 9.10 Multiple integrals
• Computational Methods in Engineering brings to light the numerous uses of numerical methods in engineering. It clearly explains the application of these methods mathematically and practically, emphasizing programming aspects when appropriate. By approaching the cross-disciplinary topic of numerical methods with a flexible approach, Computational Methods in Engineering encourages a well-rounded understanding of the subject. This book''s teaching goes beyond the text-detailed exercises (with solutions), real examples of numerical methods in real engineering practices, flowcharts, and MATLAB c
• English
• Description based on online resource; title from PDF title page (ebrary, viewed May 24, 2014).