Numerical Methods

ISBN-10: 0495114766
ISBN-13: 9780495114765
Edition: 4th 2013
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Description: NUMERICAL METHODS, Fourth Edition emphasizes the intelligent application of approximation techniques to the type of problems that commonly occur in engineering and the physical sciences. Readers learn why the numerical methods work, what kinds of  More...

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Book details

Edition: 4th
Copyright year: 2013
Publisher: Cengage Learning
Binding: Hardcover
Pages: 608
Size: 8.50" wide x 10.25" long x 1.00" tall
Weight: 3.014
Language: English

NUMERICAL METHODS, Fourth Edition emphasizes the intelligent application of approximation techniques to the type of problems that commonly occur in engineering and the physical sciences. Readers learn why the numerical methods work, what kinds of errors to expect, and when an application might lead to difficulties. The authors also provide information about the availability of high-quality software for numerical approximation routines. The techniques are the same as those covered in the authors' top-selling Numerical Analysis text, but this text provides an overview for students who need to know the methods without having to perform the analysis. This concise approach still includes mathematical justifications, but only when they are necessary to understand the methods. The emphasis is placed on describing each technique from an implementation standpoint, and on convincing the reader that the method is reasonable both mathematically and computationally.

Richard L. Burden is Emeritus Professor of Mathematics at Youngstown State University. His master's degree in mathematics and doctoral degree in mathematics, with a specialization in numerical analysis, were both awarded by Case Western Reserve University. He also earned a masters degree in computer science from the University of Pittsburgh. His mathematical interests include numerical analysis, numerical linear algebra, and mathematical statistics. Dr. Burden has been named a distinguished professor for teaching and service three times at Youngstown State University. He was also named a distinguished chair as the chair of the Department of Mathematical and Computer Sciences. He wrote the Actuarial Examinations in Numerical Analysis from 1990 until 1999.

J. Douglas Faires, late of Youngstown State University, pursued mathematical interests in analysis, numerical analysis, mathematics history, and problem solving. Dr. Faires won numerous awards, including the Outstanding College-University Teacher of Mathematics by the Ohio Section of MAA and five Distinguished Faculty awards from Youngstown State University, which also awarded him an Honorary Doctor of Science award in 2006.

Mathematical Preliminaries And Error Analysis
Introduction
Review of Calculus
Round-off Error and Computer Arithmetic
Errors in Scientific Computation
Computer Software
Solutions Of Equations Of One Variable
Introduction
The Bisection Method
The Secant Method
Newton's Method
Error Analysis and Accelerating Convergence
M ller's Method
Survey of Methods and Software
Interpolation And Polynomial Approximation
Introduction
Lagrange Polynomials
Divided Differences
Hermite Interpolation
Spline Interpolation
Parametric Curves
Survey of Methods and Software
Numerical Integration And Differentiation
Introduction
Basic Quadrature Rules
Composite Quadrature Rules
Romberg Integration
Gaussian Quadrature
Adaptive Quadrature
Multiple Integrals
Improper Integrals
Numerical Differentiation
Survey of Methods and Software
Numerical Solution Of Initial-Value Problems
Introduction
Taylor Methods
Runge-Kutta Methods
Predictor-Corrector Methods
Extrapolation Methods
Adaptive Techniques
Methods for Systems of Equations
Stiff Differentials Equations
Survey of Methods and Software
Direct Methods For Solving Linear Systems
Introduction
Gaussian Elimination
Pivoting Strategies
Linear Algebra and Matrix Inversion
Matrix Factorization
Techniques for Special Matrices
Survey of Methods and Software
Iterative Methods For Solving Linear Systems
Introduction
Convergence of Vectors
Eigenvalues and Eigenvectors
Conjugate Gradient Methods
The Jacobi and Gauss-Seidel Methods
The SOR Method
Error Bounds and Iterative Refinement
Survey of Methods and Software
Approximation Theory
Introduction
Discrete Least Squares Approximation
Continuous Least Squares Approximation
Chebyshev Polynomials
Rational Function Approximation
Trigonometric Polynomial Approximation
Fast Fourier Transforms
Survey of Methods and Software
Approximating Eigenvalues
Introduction
Isolating Eigenvalues
The Power Method
Householder's Method
The QR Method
Survey of Methods and Software
Solutions Of Systems Of Nonlinear Equations
Introduction
Newton's Methods for Systems
Quasi-Newton Methods
The Steepest Descent Method
Survey of Methods and Software
Homotopy and Continuation Methods
Boundary-Value Problems For Ordinary Differential Equations
Introduction
The Linear Shooting Method
Linear Finite Difference Methods
The Nonlinear Shooting Method
Nonlinear Finite-Difference Methods
Variational Techniques
Survey of Methods and Software
Numerical Methods For Partial Differential Equations
Introduction
Finite-Difference Methods for Elliptic Problems
Finite-Difference Methods for Parabolic Problems
Finite-Difference Methods for Hyperbolic Problems
Introduction to the Finite-Element Method
Survey of Methods and Software.

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