Numerical Analysis for Engineers

Methods and Applications, Second Edition

Bilal Ayyub, Richard H. McCuen

• Publisher: Chapman and Hall/CRC
• Year: 2015
• ISBN:
  9781482250381
• Edition: 2
• Topic: Mathematics
• Subtopic: Mathematics General
• Index: Mathematics

Numerical Analysis for Engineers: Methods and Applications demonstrates the power of numerical methods in the context of solving complex engineering and scientific problems. The book helps to prepare future engineers and assists practicing engineers in understanding the fundamentals of numerical methods, especially their applications, limitations,

1

Introduction

1.1 Numerical Analysis in Engineering

The advancement of computer technology and its availability to practicing engineers has affected engineering education in many aspects. To prepare engineering students and practicing engineers for current and future challenges, an introduction to and sometimes emphasis on computer-based methods are needed. Currently, practical engineering problems demand the use of computers to obtain solutions in a timely manner and with acceptable accuracy.

The solutions of engineering problems can be obtained using analytical methods or numerical methods. The complexity of many practical engineering problems makes it necessary to use numerical methods; that is, very often analytical solutions cannot be obtained. For example, engineering students learn analytical differentiation and integration of mathematical functions within the first two years of their college education. However, analytical differentiation and integration provide a closed-form derivative and integral, respectively, only for simple functions. As the problems take on greater reality and the complexity of these functions increases, our ability to use analytical differentiation or integration diminishes until the point where analytical solutions are not possible. Also, it is common in engineering to require the use of functions that cannot be expressed in closed form for which derivatives or integrals are needed. In such cases, analytical methods of differentiation and integration cannot be used. Therefore, there is a need for another class of solution methods. Numerical methods belong to this second class of solution tools that can be used where analytical methods are not capable of or practical for providing solutions.

The objective of this book is to introduce numerical methods to students of engineering and science and practicing engineers. The practical aspects of the use of these methods are emphasized throughout the book, with sections in each chapter where practical applications are provided. Although the book was developed with emphasis on engineering and technological problems, numerical methods can be used to solve problems in many other fields. Numerical methods are provided with varying levels of detail and emphasis. A critical presentation of these methods is provided to enhance the readers’ understanding.

The numerical methods can be solved by hand or with a computer. The importance of numerical methods in engineering can be effectively demonstrated in cases dealing with complex problems for which ...

Table of contents

• Cover
• Half Title
• Series Page
• Title Page
• Copyright Page
• Dedication Page
• Table of Contents
• Preface
• Acknowledgments
• Authors
• Chapter 1 Introduction
• Chapter 2 Matrices
• Chapter 3 Introduction to Numerical Methods
• Chapter 4 Roots of Equations
• Chapter 5 Simultaneous Linear Equations
• Chapter 6 Numerical Interpolation
• Chapter 7 Differentiation and Integration
• Chapter 8 Differential Equations
• Chapter 9 Data Description and Treatment
• Chapter 10 Curve Fitting and Regression Analysis
• Chapter 11 Numerical Optimization
• Index