Enhanced descriptions from Syndetics:

Beside providing a foundation in modern numerical-approximation techniques, Burden and Faires' well-respected Numerical Analysis, Sixth Edition, explains how, why, and when the techniques can be expected to work. The authors use real-life problems from areas such as engineering, computer science, biology, and physics to show students how numerical methods are applied. more than 2,000 exercises are included, ranging from elementary applications of methods and algorithms to more rigorous generalizations and extensions of theory. Where appropriate, the text demonstrates how computer algebra systems can be of value in solving these problems. As with earlier editions, this text is designed to give students the preparation they need to pass the Actuaries' examination in Numerical Methods. To that end, the edition includes many more exercises of the type often found on the exam.

Table of contents provided by Syndetics

• 1 Mathematical preliminaries
• Review of Calculus
• Round-off Errors and Computer Arithmetic
• Algorithms and Convergence
• Numerical Software
• 2 Solutions of equations in one variable
• The Bisection Method. Fixed-Point Iteration
• The Newton's Method
• Error Analysis 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 Interpolation
• Cubic Spline Interpolation
• Parametric Curves
• Survey of Methods and Software
• 4 Numerical differentiation and integration
• Numerical Differentiation
• Richardson's Extrapolation
• Elements of Numerical Integration
• Composite Numerical Integration
• Romberg Integration
• Adaptive Quadrature 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-Fehlberg Method
• Multi-Step Methods
• Variable Step-Size Multi-Step Methods
• Extrapolation Methods
• Higher-Order Equations and Systems of Differential Equations
• Stability. 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 Inversion
• 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 Techniques for Solving Linear Systems
• Error Bounds and Iterative Refinement
• The Conjugate 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
• Rational Function Approximation
• Trigonometric Polynomial Approximation
• Fast Fourier Transforms
• Survey of Methods and Software
• 9 Approximating eigenvalues
• Linear Algebra and Eigenvalues
• The Power Method
• Householder's Method
• The QR 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
• Survey 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 Nonlinear Problems
• The Rayleigh-Ritz Method
• Survey of Methods and Software
• 12 Numerical solutions to partial differential equations
• Elliptic Partial-Differential Equations
• Parabolic Partial-Differential Equations
• Hyperbolic Partial-Differential Equations
• An Introduction to the Finite-Element Method
• Survey of Methods and Software
• Bibliography
• Answers to Selected Exercises
• Index