# Applied Numerical Methods for Engineers and Scientists

## Singiresu Rao

Oct 2001, Hardback, 880 pagesISBN13: 9780130894809

ISBN10: 013089480X

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## Description

- Table of Contents
- Features

For courses in Numerical Methods at junior/senior level as well as beginning graduate level. The book also serves as a reference for numerical methods in engineering.

- Description
## Table of Contents

- Features

(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.**

- Description
- Table of Contents
## Features

**A variety of engineering applications at the beginning of each chapter**—Illustrate the practicality of the methods considered in that chapter.

**Software and programming methods are discussed in every chapter.**Illustrative examples in MATLAB, MathCAD, MAPLE, Fortran, and C are given. A section in every chapter discusses the trade-offs of each of these tools and how to choose the most effective tool for a problem type.

**Over 800 problems including open ended, project type and design problems at the end of chapters**—With guidelines for their solution in Instructor's Manual.

**Review question sections in each chapter which are separate from end-of-chapter problems**—Includes multiple choice questions, questions with brief answers, true-false questions, questions involving matching of related description, and fill-in-the-blank type questions. Answers are provided to students on the book's website.Helps students in reviewing and testing their understanding of the text material.