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Numerical Analysis,9780534392000
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Numerical Analysis

by
Edition:
8th
ISBN13:

9780534392000

ISBN10:
0534392008
Media:
Hardcover
Pub. Date:
12/10/2004
Publisher(s):
Brooks Cole
List Price: $301.99

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Questions About This Book?

What version or edition is this?
This is the 8th edition with a publication date of 12/10/2004.
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  • The Used copy of this book is not guaranteed to inclue any supplemental materials. Typically, only the book itself is included.

Summary

This well-respected text gives an introduction to the modern approximation techniques and explains how, why, and when the techniques can be expected to work. The authors focus on building students' intuition to help them understand why the techniques presented work in general, and why, in some situations, they fail. With a wealth of examples and exercises, the text demonstrates the relevance of numerical analysis to a variety of disciplines and provides ample practice for students. The applications chosen demonstrate concisely how numerical methods can be, and often must be, applied in real-life situations. In this edition, the presentation has been fine-tuned to make the book even more useful to the instructor and more interesting to the reader. Overall, students gain a theoretical understanding of, and a firm basis for future study of, numerical analysis and scientific computing. A more applied text with a different menu of topics is the authors' highly regarded NUMERICAL METHODS, Third Edition.

Table of Contents

Mathematical Preliminaries and Error Analysis
1(44)
Review of Calculus
2(15)
Round-off Errors and Computer Arithmetic
17(13)
Algorithms and Convergence
30(8)
Numerical Software
38(7)
Solutions of Equations in One Variable
45(56)
The Bisection Method
46(7)
Fixed-Point Iteration
53(10)
Newton's Method
63(12)
Error Analysis for Iterative Methods
75(8)
Accelerating Convergence
83(4)
Zeros of Polynomials and Muller's Method
87(10)
Survey of Methods and Software
97(4)
Interpolation and Polynomial Approximation
101(66)
Interpolation and the Lagrange Polynomial
104(15)
Divided Differences
119(11)
Hermite Interpolation
130(7)
Cubic Spline Interpolation
137(20)
Parametric Curves
157(7)
Survey of Methods and Software
164(3)
Numerical Differentiation and Integration
167(82)
Numerical Differentiation
168(11)
Richardson's Extrapolation
179(8)
Elements of Numerical Integration
187(9)
Composite Numerical Integration
196(11)
Romberg Integration
207(5)
Adaptive Quadrature Methods
212(8)
Gaussian Quadrature
220(6)
Multiple Integrals
226(15)
Improper Integrals
241(5)
Survey of Methods and Software
246(3)
Initial-Value Problems for Ordinary Differential Equations
249(96)
The Elementary Theory of Initial-Value Problems
250(6)
Euler's Method
256(10)
Higher-Order Taylor Methods
266(7)
Runge-Kutta Methods
273(10)
Error Control and the The Runge-Kutta-Fehlberg Method
283(8)
Multistep Methods
291(11)
Variable Step-Size Multistep Methods
302(6)
Extrapolation Methods
308(5)
Higher-Order Equations and Systems of Differential Equations
313(12)
Stability
325(10)
Stiff Differential Equations
335(7)
Survey of Methods and Software
342(3)
Direct Methods for Solving Linear Systems
345(72)
Linear Systems of Equations
346(14)
Pivoting Strategies
360(10)
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(64)
Norms of Vectors and Matrices
418(11)
Eigenvalues and Eigenvectors
429(7)
Iterative Techniques for Solving Linear Systems
436(18)
Error Bounds and Iterative Refinement
454(10)
The Conjugate Gradient Method
464(15)
Survey of Methods and Software
479(2)
Approximation Theory
481(66)
Discrete Least Squares Approximation
482(12)
Orthogonal Polynomials and Least Squares Approximation
494(9)
Chebyshev Polynomials and Economization of Power Series
503(9)
Rational Function Approximation
512(11)
Trigonometric Polynomial Approximation
523(9)
Fast Fourier Transforms
532(12)
Survey of Methods and Software
544(3)
Approximating Eigenvalues
547(50)
Linear Algebra and Eigenvalues
548(9)
The Power Method
557(17)
Householder's Method
574(8)
The QR Algorithm
582(12)
Survey of Methods and Software
594(3)
Numerical Solutions of Nonlinear Systems of Equations
597(44)
Fixed Points for Functions of Several Variables
598(9)
Newton's Method
607(10)
Quasi-Newton Methods
617(7)
Steepest Descent Techniques
624(7)
Homotopy and Continuation Methods
631(8)
Survey of Methods and Software
639(2)
Boundary-Value Problems for Ordinary Differential Equations
641(46)
The Linear Shooting Method
642(7)
The Shooting Method for Nonlinear Problems
649(7)
Finite-Difference Methods for Linear Problems
656(6)
Finite-Difference Methods for Nonlinear Problems
662(6)
The Rayleigh--Ritz Method
668(16)
Survey of Methods and Software
684(3)
Numerical Solutions to Partial Differential Equations
687(50)
Elliptic Partial Differential Equations
690(9)
Parabolic Partial Differential Equations
699(14)
Hyperbolic Partial Differential Equations
713(8)
An Introduction to the Finite-Element Method
721(14)
Survey of Methods and Software
735(2)
Bibliography 737(10)
Answers to Selected Exercises 747(90)
Index 837


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