2nd Edition

Numerical Analysis for Engineers Methods and Applications, Second Edition

By Bilal M. Ayyub, Richard H. McCuen Copyright 2016
    451 Pages 106 B/W Illustrations
    by Chapman & Hall

    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.

    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

    Biography

    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.