Applied Numerical Methods for Engineers and Scientists / Edition 1

Applied Numerical Methods for Engineers and Scientists / Edition 1

by Singiresu S. Rao
     
 

ISBN-10: 013089480X

ISBN-13: 9780130894809

Pub. Date: 09/28/2001

Publisher: Pearson

This comprehensive book includes over 800 problems including open ended, project type and design problems. Chapter topics include Introduction to Numerical Methods; Solution of Nonlinear Equations; Simultaneous Linear Algebraic Equations; Solution of Matrix Eigenvalue Problem; Curve Fitting and Interpolation; Statistical Methods; Numerical

Overview

This comprehensive book includes over 800 problems including open ended, project type and design problems. Chapter topics include Introduction to Numerical Methods; Solution of Nonlinear Equations; Simultaneous Linear Algebraic Equations; Solution of Matrix Eigenvalue Problem; Curve Fitting and Interpolation; Statistical Methods; Numerical Differentiation; Numerical Integration; Numerical Solution of Ordinary Differential Equations: Initial Value Problems; Numerical Solution of Ordinary Differential Equations: Boundary Value Problems; Numerical Solution of Partial Differential Equations; Numerical Methods of Optimization ;Finite Element Method. This book is intended as a reference for numerical methods in engineering.

Product Details

ISBN-13:
9780130894809
Publisher:
Pearson
Publication date:
09/28/2001
Edition description:
New Edition
Pages:
880
Product dimensions:
7.00(w) x 9.00(h) x 2.00(d)

Table of Contents

(NOTE: Each chapter concludes with References and Bibliography, Review Questions, and Problems.)

1. Introduction to Numerical Methods.

Importance of Numerical Methods in Engineering. Computers. Computer Programming Languages. Data Representation. Programming Structure. Errors. Numerical Methods Considered. Software for Numerical Analysis. Use of Software Packages. Computer Programs.

2. Solution of Nonlinear Equations.

Introduction. Engineering Applications. Incremental Search Method. Bisection Method. Newton-Raphson Method. Secant Method. Regula Falsi Method. Fixed Point Iteration or Successive Substitution Method. Determination of Multiple Roots. Bairstow's Method. Muller's Method. Newton-Raphson Method for Simultaneous Nonlinear Equations. Unconstrained Minimization. Convergence of Methods. Choice of Method. Use of Software Packages. Computer Programs.

3. Solution of Simultaneous Linear Algebraic Equations.

Introduction. Engineering Applications. Vector and Matrix Norms. Basic Concepts of Solution. Linearly Independent Equations. Ill-Conditioned Equations. Graphical Interpretation of the Solution. Solution Using Cramer's Rule. Gauss Elimination Method. Gauss-Jordan Elimination Procedure. LU Decomposition Method. Jacobi Iteration Method. Gauss-Seidel Iteration Method. Relaxation Methods. Simultaneous Linear Equations with Complex Coefficients and Constants. Matrix Inversion. Equations with Special Form of Coefficient Matrix. Overdetermined, Underdetermined, and Homogeneous Equations. Comparative Efficiencies of Various Methods and Recommendations. Choice of the Method. Use of Software Packages. Computer Programs.

4. Solution of Matrix Eigenvalue Problem.

Introduction. Engineering Applications. Conversion of General Eigenvalue Problem to Standard Form. Methods of Solving Eigenvalue Problems. Solution of the Characteristic Polynomial Equations. Jacobi Method. Given's Method. Householder's Method. Eigenvalues of a Tridiagonal Matrix. Eigenvectors of a Tridiagonal Matrix. Power Method. Choice of Method. Use of Software Packages. Computer Programs.

5. Curve Fitting and Interpolation.

Introduction. Engineering Applications. Collocation-Polynomial Fit. Interpolation. Lagrange Interpolation Formula. Newton's Divided-Difference Interpolating Polynomials. Interpolation Using Chebysev Polynomials. Interpolation Using Splines. Least-Squares Regression. Curve Fitting with Multiple Variables. Choice of Method. Use of Software Packages. Computer Programs.

6. Statistical Methods.

Introduction. Engineering Applications. Basic Definitions. Histogram and Probability Density Function. Statistical Characteristics. Normal Distributions. Statistical Tests. Chi-Square Test for Distribution. Choice of Method. Use of Software Packages. Computer Programs.

7. Numerical Differentiation.

Introduction. Engineering Applications. Definition of the Derivative. Basic Finite-Difference Approximations. Using Taylor's Series Expansions. Using Difference Operators. Approximation of Derivatives Using Difference Operators. Using Differentiation of Interpolating Polynomials. Finite-Difference Approximations for Partial Derivatives. Choice of Method. Use of Software Packages. Computer Programs.

8. Numerical Integration.

Introduction. Engineering Applications. Newton-Cotes Formulas. Simpson's Rule. General Newton-Cotes Formulas. Richardson's Extrapolation. Romberg Integration. Gauss Quadrature. Integration with Unequal Segments. Numerical Integration of Improper Integrals. Numerical Integration in Two- and Three-Dimensional Domains. Choice of Method. Use of Software Packages. Computer Programs.

9. Ordinary Differential Equations: Initial-Value Problems.

Introduction. Engineering Applications. Simultaneous Differential Equations. Solution Concept. Euler's Method. Improvements and Modifications of Euler's Method. Runge-Kutta Methods. Multistep Methods. Adams Methods. Predictor-Corrector Methods. Simultaneous Differential Equations. Stiff Equations. Choice of Method. Use of Software Packages. Computer Programs.

10. Ordinary Differential Equations: Boundary-Value Problems.

Introduction. Engineering Applications. Shooting Methods. Generalization to n Equations. Finite-Difference Methods. Solution of Nonlinear Boundary-Value Problems. Solution of Eigenvalue Problems. Choice of Method. Use of Software Packages. Computer Programs.

11. Partial Differential Equations.

Introduction. Engineering Applications. Initial and Boundary Conditions. Elliptic Partial Differential Equations. Parabolic Partial Differential Equations. Crank-Nicholson Method. Method of Lines. Two-Dimensional Parabolic Problems. Hyperbolic Partial Differential Equations. Method of Characteristics. Finite-Difference Formulas in Polar Coordinate System. Choice of Method. Use of Software Packages. Computer Programs.

12. Optimization.

Introduction. Types of Optimization Problems. Engineering Applications. Optimization Methods from Differential Calculus. Linear-Programming Problem. Simplex Method. Search Methods for Nonlinear Optimization. Optimization of a Function of a Single Variable. Unconstrained Minimization of a Function of Several Variables. Constrained Minimization of a Function of Several Variables. Choice of Method. Use of Software Packages. Computer Programs.

13. Finite-Element Method.

Introduction. Engineering Applications. Discretization of the Domain. Interpolation Functions. Derivation of Element Characteristic Matrices and Vectors. Assemblage of Element Characteristics Matrices and Vectors. Solution of System Equations. Choice of Method. Use of Software Packages. Computer Programs.

Appendix A: Basics of Fortran 90.

Appendix B: Basics of C Language.

Appendix C: Basics of MAPLE.

Appendix D: Basics of MATLAB.

Appendix E: Basics of MathCAD.

Appendix F: Review of Matrix Algebra.

Appendix G: Statistical Tables.

Index.

Customer Reviews

Average Review:

Write a Review

and post it to your social network

     

Most Helpful Customer Reviews

See all customer reviews >