Numerical Analysis for Engineers: Methods and Applications, Second Edition, 2nd Edition (Hardback) book cover

Numerical Analysis for Engineers

Methods and Applications, Second Edition, 2nd Edition

By Bilal Ayyub, Richard H. McCuen

Chapman and Hall/CRC

431 pages | 106 B/W Illus.

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Description

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, and potentials.

Each chapter contains many computational examples, as well as a section on applications that contain additional engineering examples. Each chapter also includes a set of exercise problems.

The problems are designed to meet the needs of instructors in assigning homework and to help students with practicing the fundamental concepts. Although the book was developed with emphasis on engineering and technological problems, the numerical methods can also be used to solve problems in other fields of science.

Table of Contents

Introduction

Numerical Analysis in Engineering

Analytical versus Numerical Analysis

Taylor Series Expansion

Applications

Problems

Matrices

Introduction

Vectors

Determinants

Rank of a Matrix

Applications

Problems

Introduction to Numerical Methods

Introduction

Accuracy, Precision, and Bias

Significant Figures

Analysis of Numerical Errors

Advantages and Disadvantages of Numerical Methods

Applications

Problems

Roots of Equations

Introduction

Eigenvalue Analysis

Direct-Search Method

Bisection Method

Newton–Raphson Iteration

Secant Method

Polynomial Reduction

Synthetic Division

Multiple Roots

Systems of Nonlinear Equations

Applications

Problems

Simultaneous Linear Equations

Introduction

Gaussian Elimination

Gauss–Jordan Elimination

Additional Considerations for Elimination Procedures

LU Decomposition

Iterative Equation-Solving Methods

Use of Determinants

Matrix Inversion

Applications

Problems

Numerical Interpolation

Introduction

Method of Undetermined Coefficients

Gregory–Newton Interpolation Method

Finite-Difference Interpolation

Newton’s Method

Lagrange Polynomials

Interpolation Using Splines

Guidelines for Choice of Interpolation Method

Multidimensional Interpolation

Applications

Problems

Differentiation and Integration

Numerical Differentiation

Numerical Integration

Applications

Problems

Differential Equations

Introduction

Taylor Series Expansion

Euler’s Method

Modified Euler’s Method

Runge–Kutta Methods

Predictor–Corrector Methods

Least-Squares Method

Galerkin Method

Higher Order Differential Equations

Boundary-Value Problems

Integral Equations

Applications

Problems

Data Description and Treatment

Introduction

Classification of Data

Graphical Description of Data

Histograms and Frequency Diagrams

Descriptive Measures

Applications

Problems

Curve Fitting and Regression Analysis

Introduction

Correlation Analysis

Introduction to Regression

Principle of Least Squares

Reliability of the Regression Equation

Correlation versus Regression

Applications of Bivariate Regression Analysis

Multiple Regression Analysis

Regression Analysis of Nonlinear Models

Applications

Problems

Numerical Optimization

Introduction

The Response Surface Analysis

Numerical Least Squares

Steepest Descent Method

Illustrating Applications

Applications

Concluding Remarks

Problems

About the Authors

Bilal Ayyub, PhD, is a professor of civil and environmental engineering at the University of Maryland, College Park, and the director of the Center for Technology and Systems Management at the A. James Clark School of Engineering. Dr. Ayyub is a fellow of the American Society of Civil Engineers, the American Society of Mechanical Engineers, the Society of Naval Architects and Marine Engineers, and the Society for Risk Analysis, and is also a senior member of the Institute of Electrical and Electronics Engineers (IEEE). He has completed many research and development projects for many governmental and private entities. Dr. Ayyub has received numerous awards and is the author or coauthor of more than 600 publications in journals, conference proceedings, and reports including 8 textbooks and 14 edited books.

Richard H. McCuen, PhD, is the Ben Dyer Professor of civil and environmental engineering at the University of Maryland, College Park. Dr. McCuen earned degrees from Carnegie Mellon University and the Georgia Institute of Technology. Topics in statistical hydrology and stormwater management are his primary research interests. He received numerous awards and is the author of 26 books and over 250 professional papers.

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Subject Categories

BISAC Subject Codes/Headings:
MAT000000
MATHEMATICS / General
MAT021000
MATHEMATICS / Number Systems
TEC009070
TECHNOLOGY & ENGINEERING / Mechanical