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Applied Numerical Analysis

Edition: 
7
Publisher: 
Addison Wesley
Number of Pages: 
624
Price: 
124.00
ISBN: 
978-0321133045
Date Received: 
Wednesday, January 17, 2007
Reviewable: 
Yes
Include In BLL Rating: 
Yes
Curtis F. Gerald and Patrick O. Wheatley
Publication Date: 
2003
Format: 
Hardcover
Audience: 
Category: 
Textbook
BLL
07/15/2009
BLL Rating: 

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.

Publish Book: 
Modify Date: 
Wednesday, July 15, 2009

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