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Numerical Analysis,9780534382162

Numerical Analysis

by
Edition:
7th
ISBN13:

9780534382162

ISBN10:
0534382169
Format:
Paperback
Pub. Date:
12/29/2000
Publisher(s):
Brooks Cole
List Price: $144.66

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Summary

The new Seventh Edition of Burden and Faires' well-respected Numerical Analysis provides a foundation in modern numerical-approximation techniques. Explaining how, why, and when the techniques can be expected to work, the Seventh Edition places an even greater emphasis on building readers' intuition to help them understand why the techniques presented work in general, and why, in some situations, they fail. Applied problems from diverse areas, such as engineering and physical, computer, and biological sciences, are provided so readers can understand how numerical methods are used in real-life situations. The Seventh Edition has been updated and now addresses the evolving use of technology, incorporating it whenever appropriate.

Table of Contents

Mathematical Preliminaries
1(47)
Review of Calculus
2(16)
Roundoff Errors and Computer Arithmetic
18(13)
Algorithms and Convergence
31(9)
Numerical Software
40(7)
Solutions of Equations in One Variable
47(57)
The Bisection Method
48(7)
Fixed-Point Iteration
55(11)
Newton's Method
66(12)
Error Analysis for Iterative Methods
78(8)
Accelerating Convergence
86(5)
Zeros of Polynomials and Muller's Method
91(10)
Survey of Methods and Software
101(3)
Interpolation and Polynomial Approximation
104(62)
Interpolation and the Lagrange Polynomial
107(15)
Divided Differences
122(11)
Hermite Interpolation
133(8)
Cubic Spline Interpolation
141(15)
Parametric Curves
156(7)
Survey of Methods and Software
163(3)
Numerical Differentiation and Integration
166(83)
Numerical Differentiation
167(11)
Richardson's Extrapolation
178(8)
Elements of Numerical Integration
186(10)
Composite Numerical Integration
196(11)
Romberg Integration
207(6)
Adaptive Quadrature Methods
213(7)
Gaussian Quadrature
220(7)
Multiple Integrals
227(14)
Improper Integrals
241(6)
Survey of Methods and Software
247(2)
Initial-Value Problems for Ordinary Differential Equations
249(95)
The Elementary Theory of Initial-Value Problems
251(5)
Euler's Method
256(10)
Higher-Order Taylor Methods
266(6)
Runge-Kutta Methods
272(10)
Error Control and the Runge-Kutta-Fehlberg Method
282(7)
Multistep Methods
289(12)
Variable Step-Size Multistep Methods
301(6)
Extrapolation Methods
307(6)
Higher-Order Equations and Systems of Differential Equations
313(11)
Stability
324(10)
Stiff Differential Equations
334(8)
Survey of Methods and Software
342(2)
Direct Methods for Solving Linear Systems
344(73)
Linear Systems of Equations
345(14)
Pivoting Strategies
359(11)
Linear Algebra and Matrix Inversion
370(13)
The Determinant of a Matrix
383(5)
Matrix Factorization
388(10)
Special Types of Matrices
398(15)
Survey of Methods and Software
413(4)
Iterative Techniques in Matrix Algebra
417(66)
Norms of Vectors and Matrices
418(12)
Eigenvalues and Eigenvectors
430(7)
Iterative Techniques for Solving Linear Systems
437(17)
Error Bounds and Iterative Refinement
454(11)
The Conjugate Gradient Method
465(16)
Survey of Methods and Software
481(2)
Approximation Theory
483(67)
Discrete Least Squares Approximation
484(14)
Orthogonal Polynomials and Least Squares Approximation
498(9)
Chebyshev Polynomials and Economization of Power Series
507(10)
Rational Function Approximation
517(12)
Trigonometric Polynomial Approximation
529(8)
Fast Fourier Transforms
537(11)
Survey of Methods and Software
548(2)
Approximating Eigenvalues
550(50)
Linear Algebra and Eigenvalues
551(9)
The Power Method
560(17)
Householder's Method
577(8)
The QR Algorithm
585(12)
Survey of Methods and Software
597(3)
Numerical Solutions of Nonlinear Systems of Equations
600(45)
Fixed Points for Functions of Several Variables
602(9)
Newton's Method
611(9)
Quasi-Newton Methods
620(8)
Steepest Descent Techniques
628(7)
Homotopy and Continuation Methods
635(8)
Survey of Methods and Software
643(2)
Boundary-Value Problems for Ordinary Differential Equations
645(46)
The Linear Shooting Method
646(7)
The Shooting Method for Nonlinear Problems
653(7)
Finite-Difference Methods for Linear Problems
660(7)
Finite-Difference Methods for Nonlinear Problems
667(5)
The Rayleigh-Ritz Method
672(16)
Survey of Methods and Software
688(3)
Numerical Solutions to Partial Differential Equations
691(52)
Elliptic Partial Differential Equations
694(10)
Parabolic Partial Differential Equations
704(14)
Hyperbolic Partial Differential Equations
718(8)
An Introduction to the Finite-Element Method
726(15)
Survey of Methods and Software
741(2)
Bibliography 743(10)
Answers to Selected Exercises 753(78)
Index 831


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