Title:
Numerical analysis
Personal Author:
Edition:
5th ed.
Publication Information:
Boston : PWS Pubs. Co., 1993
ISBN:
9780534932190
Subject Term:
Added Author:
Available:*
Library | Item Barcode | Call Number | Material Type | Item Category 1 | Status |
|---|---|---|---|---|---|
Searching... | 30000002224180 | QA297 B84 1993 | Open Access Book | Book | Searching... |
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Summary
Summary
* For math majors rather than engineering majors..* New survey of methods and software sections included in chapters 2-12 to cover the latest technology in the field..* Outstanding examples relate tothe routine exercises in the text so students can see the similarities..* Exercises are varied to include basic drill, interesting applicaitons, and deeper theoretical extensions.
Table of Contents
| 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 |
