Numerical Analysis, 7/e

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

1. MATHEMATICAL PRELIMINARIES
Review of Calculus / Round-off Errors and Computer Arithmetic / Algorithms and C onvergence / Numerical Software
2. SOLUTIONS OF EQUATIONS IN ONE VARIABLE
The Bisection Method / Fixed-Point Iteration / The Newton's Method / Error Analy sis for Iterative Methods / Accelerating Convergence / Zeros of Polynomials and Muller's Method / Survey of Methods and Software
3. INTERPOLATION AND POLYNOMIAL APPROXIMATION
Interpolation and the LaGrange Polynomial / Divided Differences / Hermite Interp olation / Cubic Spline Interpolation / Parametric Curves / Survey of Methods and Software
4. NUMERICAL DIFFERENTIATION AND INTEGRATION
Numerical Differentiation / Richardson's Extrapolation / Elements of Numerical I ntegration / Composite Numerical Integration / Romberg Integration / Adaptive Qu adrature Methods / Gaussian Quadrature / Multiple Integrals / Improper Integrals / Survey of Methods and Software
5. INITIAL-VALUE PROBLEMS FOR ORDINARY DIFFERENTIAL EQUATIONS
The Elementary Theory of Initial-Value Problems / Euler's Method / Higher-Order Taylor Methods / Runge-Kutta Methods / Error Control and the Runge-Kutta-Fehlber g Method / Multi-Step Methods / Variable Step-Size Multi-Step Methods / Extrapol ation Methods / Higher-Order Equations and Systems of Differential Equations / S tability / Stiff Differential Equations / Survey of Methods and Software
6. DIRECT METHODS FOR SOLVING LINEAR SYSTEMS
Linear Systems of Equations / Pivoting Strategies / Linear Algebra and Matrix In version / The Determinant of a Matrix / Matrix Factorization / Special Types of Matrices / Survey of Methods and Software
7. ITERATIVE TECHNIQUES IN MATRIX ALGEBRA
Norms of Vectors and Matrices / Eigenvalues and Eigenvectors / Iterative Techniq ues for Solving Linear Systems / Error Bounds and Iterative Refinement / The Con jugate Gradient Method / Survey of Methods and Software
8. APPROXIMATION THEORY
Discrete Least Squares Approximation / Orthogonal Polynomials and Least Squares Approximation / Chebyshev Polynomials and Economization of Power Series / Ration al Function Approximation / Trigonometric Polynomial Approximation / Fast Fourie r Transforms / Survey of Methods and Software
9. APPROXIMATING EIGENVALUES
Linear Algebra and Eigenvalues / The Power Method / Householder's Method / The Q R Algorithm / Survey of Methods and Software
10. NUMERICAL SOLUTIONS OF NONLINEAR SYSTEMS OF EQUATIONS
Fixed Points for Functions of Several Variables / Newton's Method / Quasi-Newton Methods / Steepest Descent Techniques / Homotopy and Continuation Methods / Sur vey of Methods and Software
11. BOUNDARY-VALUE PROBLEMS FOR ORDINARY DIFFERENTIAL EQUATIONS
The Linear Shooting Method / The Shooting Method for Nonlinear Problems / Finite -Difference Methods for Linear Problems / Finite-Difference Methods for Nonlinea r Problems / The Rayleigh-Ritz Method / Survey of Methods and Software
12. NUMERICAL SOLUTIONS TO PARTIAL DIFFERENTIAL EQUATIONS
Elliptic Partial-Differential Equations / Parabolic Partial-Differential Equatio ns / Hyperbolic Partial-Differential Equations / An Introduction to the Finite-E lement Method / Survey of Methods and Software / BIBLIOGRAPHY / ANSWERS TO SELEC TED EXERCISES / INDEX