## Overview

The availability of inexpensive high-speed computing power makes the numerical solution of even complex engineering problems economically feasible. In the face of ever-increasing demands on the engineering profession to perform better, students preparing to face the challenges of the twenty-first century should learn not only the theory behind the numerical methods, but also acquire the skills needed to implement the methods for computer solution. In addition, students should be aware of the many commercial software systems available and their appropriate uses in the solution of engineering problems. The student should be in a position to intelligently select and use suitable numerical methods and software systems as the need arises in practice. He or she should solve a given problem using different approaches with a variety of software systems and experiment with the various parameters of the problem. This book is intended for courses on numerical methods at the junior/senior level as well as at the beginning graduate level. The book also serves as a reference for numerical methods in engineering.

**Special Features:**

- In derivations and developments, steps needed for continuity of understanding have been included to aid the reader at the introductory level.
- A variety of engineering applications are presented. More than 800 problems are included.
- Review questions are given to help students in reviewing and testing their understanding of the text material. These include multiple choice questions, questions with brief answers, true(false questions, questions involving matching of related descriptions, and fill-in-the-blank type questions.
- Several open-ended project- and design-type problems are included at the end of each chapter.
- Examples and problems based on MATLAB, Maple, and Mathcad are included in each chapter.
- Representative Fortran 90 and C programs are given in the book and several additional programs can be found at the course website.
- Helpful appendices describing the basics of Fortran 90, C Language, MATLAB, Maple, Mathcad, and matrix algebra are included.
- Brief biographical information and photographs of scientists and mathematicians who contributed to the development of numerical methods are given in the book.

## Table of contents

*Each chapter concludes with References and Bibliography, Review Questions, and Problems.*)

**1. Introduction to Numerical Methods.**

**2. Solution of Nonlinear Equations.**

**3. Solution of Simultaneous Linear Algebraic Equations.**

*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.**

**5. Curve Fitting and Interpolation.**

**6. Statistical Methods.**

**7. Numerical Differentiation.**

**8. Numerical Integration.**

**9. Ordinary Differential Equations: Initial-Value Problems.**

**10. Ordinary Differential Equations: Boundary-Value Problems.**

*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.**

**12. Optimization.**

**13. Finite-Element Method.**

**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.**

## For teachers

All the material you need to teach your courses.

Discover teaching material