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Applied Numerical Analysis

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Synopses & Reviews

Publisher Comments:

The seventh edition of this classic text has retained the features that make it popular, while updating its treatment and inclusion of Computer Algebra Systems and Programming Languages. Interesting and timely applications motivate and enhance readers' understanding of methods and analysis of results. This text incorporates a balance of theory with techniques and applications, including optional theory-based sections in each chapter. The exercise sets include additional challenging problems and projects which show practical applications of the material. Also, sections which discuss the use of computer algebra systems such as Maple®, Mathematica®, and MATLAB®, facilitate the integration of technology in the course. Furthermore, the text incorporates programming material in both FORTRAN and C. The breadth of topics, such as partial differential equations, systems of nonlinear equations, and matrix algebra, provide comprehensive and flexible coverage of all aspects of numerical analysis.

 

Preliminaries; Solving Nonlinear Equations; Solving Sets of Equations; Interpolation and Curve Fitting; Approximation of Functions; Numerical Differentiation and Integration; Numerical Solution of Ordinary Differential Equations; Optimization; Partial Differential Equations; Finite Element Analysis

 

For all readers interested in applied numerical analysis.

Synopsis:

The seventh edition of this classic text has retained the features that make it popular, while updating its treatment and inclusion of Computer Algebra Systems and Programming Languages. Interesting and timely applications motivate and enhance readers' understanding of methods and analysis of results. This text incorporates a balance of theory with techniques and applications, including optional theory-based sections in each chapter. The exercise sets include additional challenging problems and projects which show practical applications of the material. Also, sections which discuss the use of computer algebra systems such as Maple®, Mathematica®, and MATLAB®, facilitate the integration of technology in the course. Furthermore, the text incorporates programming material in both FORTRAN and C. The breadth of topics, such as partial differential equations, systems of nonlinear equations, and matrix algebra, provide comprehensive and flexible coverage of all aspects of numerical analysis.

 

Preliminaries; Solving Nonlinear Equations; Solving Sets of Equations; Interpolation and Curve Fitting; Approximation of Functions; Numerical Differentiation and Integration; Numerical Solution of Ordinary Differential Equations; Optimization; Partial Differential Equations; Finite Element Analysis

 

For all readers interested in applied numerical analysis.

Table of Contents

0. Preliminaries.

Analysis versus Numerical Analysis.

Computers and Numerical Analysis.

An Illustrative Example.

Kinds of Errors in Numerical Procedures.

Interval Arithmetic.

Parallel and Distributed Computing.

Measuring the Efficiency of Procedures.

1. Solving Nonlinear Equations.

Interval Halving (Bisection).

Linear Interpolation Methods.

Newton's Method.

Muller's Method.

Fixed-Point Iteration.

Other Methods.

Nonlinear Systems.

2. Solving Sets of Equations.

Matrices and Vectors.

Elimination Methods.

The Inverse of a Matrix and Matrix Pathology.

Almost Singular Matrices - Condition Numbers.

Interactive Methods.

Parallel Processing.

3. Interpolation and Curve Fitting.

Interpolating Polynomials.

Divided Differences.

Spline Curves.

Bezier Curves and B-Splines.

Interpolating on a Surface.

Least Squares Approximations.

4. Approximation of Functions.

Chebyshev Polynomials and Chebyshev Series.

Rational Function Approximations.

Fourier Series.

5. Numerical Differentiation and Integration.

Differentiation with a Computer.

Numerical Integration - The Trapezoidal Rule.

Simpson's Rules.

An Application of Numerical Integration - Fourier Series and Fourier Transforms Adaptive Integration.

Gaussian Quadrature.

Multiple Integrals.

Applications of Cubic Splines.

6. Numerical Solution of Ordinary Differential Equations.

The Taylor Series Method.

The Euler Method and Its Modification.

Runge-Kutta Methods.

Multistep Methods.

Higher-Order Equations and Systems.

Stiff Equations.

Boundary-Value Problems.

Characteristic-Value Problems.

7. Optimization.

Finding the Minimum of y = f(x).

Minimizing a Function of Several Variables.

Linear Programming.

Nonlinear Programming.

Other Optimizations.

8. Partial Differential Equations.

Elliptic Equations.

Parabolic Equations.

Hyperbolic Equations.

9. Finite Element Analysis.

Mathematical Background.

Finite Elements for Ordinary Differential Equation.

Finite Elements for Partial Differential Equation.

Appendices.

A. Some Basic Information from Calculus.

B. Software Resources.

Answers to Selected Exercises.

References.

Index.

Product Details

ISBN:
9780321133045
Author:
Gerald, Curtis F.
Publisher:
Pearson
Author:
Green, Carol J.
Author:
Wheatley, Patrick O.
Location:
Boston
Subject:
Computer Science
Subject:
Applied
Subject:
Numerical analysis
Subject:
Mathematics-Applied
Copyright:
Edition Number:
7
Edition Description:
Trade paper
Series:
Featured Titles for Numerical Analysis
Series Volume:
v. 357, no. 1423
Publication Date:
July 2003
Binding:
TRADE PAPER
Grade Level:
College/higher education:
Language:
English
Illustrations:
Yes
Pages:
624
Dimensions:
9 x 7.5 x 1.4 in 1048 gr

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Computers and Internet » Computers Reference » General
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Science and Mathematics » Mathematics » Applied

Applied Numerical Analysis New Trade Paper
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Product details 624 pages Addison Wesley Publishing Company - English 9780321133045 Reviews:
"Synopsis" by ,

The seventh edition of this classic text has retained the features that make it popular, while updating its treatment and inclusion of Computer Algebra Systems and Programming Languages. Interesting and timely applications motivate and enhance readers' understanding of methods and analysis of results. This text incorporates a balance of theory with techniques and applications, including optional theory-based sections in each chapter. The exercise sets include additional challenging problems and projects which show practical applications of the material. Also, sections which discuss the use of computer algebra systems such as Maple®, Mathematica®, and MATLAB®, facilitate the integration of technology in the course. Furthermore, the text incorporates programming material in both FORTRAN and C. The breadth of topics, such as partial differential equations, systems of nonlinear equations, and matrix algebra, provide comprehensive and flexible coverage of all aspects of numerical analysis.

 

Preliminaries; Solving Nonlinear Equations; Solving Sets of Equations; Interpolation and Curve Fitting; Approximation of Functions; Numerical Differentiation and Integration; Numerical Solution of Ordinary Differential Equations; Optimization; Partial Differential Equations; Finite Element Analysis

 

For all readers interested in applied numerical analysis.

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