Numerical analysis for engineers : methods and applications

書誌事項

Numerical analysis for engineers : methods and applications

Bilal Ayyub, Richard H. McCuen

(Textbooks in mathematics)

CRC Press, c2016

2nd ed

  • : hardback

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注記

"A Chapman & Hall Book"

Includes index

内容説明・目次

内容説明

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.

目次

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

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