Numerical Analysis

by Burden, Richard L.; Faires, J. Douglas

• ISBN13: 9780534382162
• ISBN10: 0534382169
• Edition: CD
• Format: Hardcover
• Copyright: 2000-12-29
• Publisher: Brooks Cole

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