Magnificent Marvel Supersale

Special Offers see all

Enter to WIN a $100 Credit

Subscribe to
for a chance to win.
Privacy Policy

Visit our stores

    Recently Viewed clear list

    The Powell's Playlist | March 13, 2015

    Kent Russell: IMG Kent Russell's Playlist for I Am Sorry to Think I Have Raised a Timid Son

    I don't listen to music while I write. Frankly, I don't see how anyone can. Since all style is rhythm, and since I cannot write anything that's as... Continue »

Qualifying orders ship free.
New Trade Paper
Ships in 1 to 3 days
Add to Wishlist
Available for In-store Pickup
in 7 to 12 days
Qty Store Section
1 Remote Warehouse Mathematics- Calculus
1 Remote Warehouse Mathematics- Analysis General

More copies of this ISBN

Introduction To Numerical Analysis 2ND Edition


Introduction To Numerical Analysis 2ND Edition Cover


Synopses & Reviews

Publisher Comments:

The ultimate aim of the field of numerical analysis is to provide convenient methods for obtaining useful solutions to mathematical problems and for extracting useful information from available solutions which are not expressed in tractable forms. This well-known, highly respected volume provides an introduction to the fundamental processes of numerical analysis, including substantial grounding in the basic operations of computation, approximation, interpolation, numerical differentiation and integration, and the numerical solution of equations, as well as in applications to such processes as the smoothing of data, the numerical summation of series, and the numerical solution of ordinary differential equations.

Chapter headings include:

l. Introduction

2. Interpolation with Divided Differences

3. Lagrangian Methods

4. Finite-Difference Interpolation

5. Operations with Finite Differences

6. Numerical Solution of Differential Equations

7. Least-Squares Polynomial Approximation

In this revised and updated second edition, Professor Hildebrand (Emeritus, Mathematics, MIT) made a special effort to include more recent significant developments in the field, increasing the focus on concepts and procedures associated with computers. This new material includes discussions of machine errors and recursive calculation, increased emphasis on the midpoint rule and the consideration of Romberg integration and the classical Filon integration; a modified treatment of prediction-correction methods and the addition of Hamming's method, and numerous other important topics.

In addition, reference lists have been expanded and updated, and more than 150 new problems have been added. Widely considered the classic book in the field, Hildebrand's Introduction to Numerical Analysis is aimed at advanced undergraduate and graduate students, or the general reader in search of a strong, clear introduction to the theory and analysis of numbers.


Well-known, respected introduction, updated to integrate concepts and procedures associated with computers. Computation, approximation, interpolation, numerical differentiation and integration, smoothing of data, more. Includes 150 additional problems in this edition.

Table of Contents


1 Introduction

  1.1 Numerical Analysis

  1.2 Approximation

  1.3 Errors

  1.4 Significant Figures

  1.5 Determinacy of Functions. Error Control

  1.6 Machine Errors

  1.7 Random Errors

  1.8 Recursive Computation

  1.9 Mathematical Preliminaries

  1.10 Supplementary References


2 Interpolation with Divided Differences

  2.1 Introduction

  2.2 Linear Interpolation

  2.3 Divided Differences

  2.4 Second-Degree Interpolation

  2.5 Newton's Fundamental Formula

  2.6 Error Formulas

  2.7 Iterated Interpolation

  2.8 Inverse Interpolation

  2.9 Supplementary References


3 Lagrangian Methods

  3.1 Introduction

  3.2 Lagrange's Interpolation Formula

  3.3 Numerical Differentiation and Integration

  3.4 Uniform-spacing Interpolation

  3.5 Newton-Cotes Integration Formulas

  3.6 Composite Integration Formulas

  3.7 Use of Integration Formulas

  3.8 Richardson Extrapolation. Romberg Integration

  3.9 Asympotic Behavior of Newton-Cotes Formulas

  3.10 Weighting Functions. Filon Integration

  3.11 Differentiation Formulas

  3.12 Supplementary References


4 Finite-Difference Interpolation

  4.1 Introduction

  4.2 Difference Notations

  4.3 Newton Forward- and Backward-difference Formulas

  4.4 Gaussian Formulas

  4.5 Stirling's Formula

  4.6 Bessel's Formula

  4.7 Everett's Formulas

  4.8 Use of Interpolation Formulas

  4.9 Propogation of Inherent Errors

  4.10 Throwback Techniques

  4.11 Interpolation Series

  4.12 Tables of Interpolation Coefficients

  4.13 Supplementary References


5 Operations with Finite Differences

  5.1 Introduction

  5.2 Difference Operators

  5.3 Differentiation Formulas

  5.4 Newtonian Integration Formulas

  5.5 Newtonian Formulas for Repeated Integration

  5.6 Central-Difference Integration Formulas

  5.7 Subtabulation

  5.8 Summation and Integration. The Euler-Maclaurin Sum Formula

  5.9 Approximate Summation

  5.10 Error Terms in Integration Formulas

  5.11 Other Representations of Error Terms

  5.12 Supplementary References


6 Numerical Solution of Differential Equations

  6.1 Introduction

  6.2 Formulas of Open Type

  6.3 Formulas of Closed Type

  6.4 Start of Solution

  6.5 Methods Based on Open-Type Formulas

  6.6 Methods Based on Closed-Type Formulas. Prediction-Correction Methods

  6.7 The Special Case F = Ay

  6.8 Propagated-Error Bounds

  6.9 Application to Equations of Higher Order. Sets of Equations

  6.10 Special Second-order Equations

  6.11 Change of Interval

  6.12 Use of Higher Derivatives

  6.13 A Simple Runge-Kutta Method

  6.14 Runge-Kutta Methods of Higher Order

  6.15 Boundary-Value Problems

  6.16 Linear Characteristic-value Problems

  6.17 Selection of a Method

  6.18 Supplementary References


7 Least-Squares Polynomial Approximation

  7.1 Introduction

  7.2 The Principle of Least Squares

  7.3 Least-Squares Approximation over Discrete Sets of Points

  7.4 Error Estimation

  7.5 Orthogonal Polynomials

  7.6 Legendre Approximation

  7.7 Laguerre Approximation

  7.8 Hermite Approximation

  7.9 Chebsyshev Approximation

  7.10 Properties of Orthoogonal Polynomials. Recursive Computation

  7.11 Factorial Power Functions and Summation Formulas

  7.12 Polynomials Orthogonal over Discrete Sets of Points

  7.13 Gram Approximation

  7.14 Example: Five-Point Least-Squares Approximation

  7.15 Smoothing Formulas

  7.16 Recursive Computation of Orthogonal Polynomials on Discrete Set of Points

  7.17 Supplementary References


8 Gaussian Quadrature and Related Topics

  8.1 Introduction

  8.2 Hermite Interpolation

  8.3 Hermite Quadrature

  8.4 Gaussian Quadrature

  8.5 Legendre-Gauss Quadrature

  8.6 Laguerre-Gauss Quadrature

  8.7 Hermite-Gauss Quadrature

  8.8 Chebyshev-Gauss Quadrature

  8.9 Jacobi-Gauss Quadrature

  8.10 Formulas with Assigned Abscissas

  8.11 Radau Quadrature

  8.12 Lobatto Quadrature

  8.13 Convergence of Gaussian-quadrature Sequences

  8.14 Chebyshev Quadrature

  8.15 Algebraic Derivations

  8.16 Application to Trigonometric Integrals

  8.17 Supplementary References


9 Approximations of Various Types

  9.1 Introduction

  9.2 Fourier Approximation: Continuous Domain

  9.3 Fourier Approximation: Discrete Domain

  9.4 Exponential Approximation

  9.5 Determination of Constituent Periodicities

  9.6 Optimum Polynomial Interpolation with Selected Abscissas

  9.7 Chebyshev Interpolation

  9.8 Economization of Polynomial Approximations

  9.9 Uniform (Minimax) Polynomial Approximation

  9.10 Spline Approximation

  9.11 Splines with Uniform Spacing

  9.12 Spline Error Estimates

  9.13 A Special Class of Splines

  9.14 Approximation by Continued Fractions

  9.15 Rational Approximations and Continued Fractions

  9.16 Determination of Convergents of Continued Fractions

  9.17 Thiele's Continued-Fraction Approxmations

  9.18 Uniformization of Rational Approximations

  9.19 Supplementary References


10 Numerical Solution of Equations

  10.1 Introduction

  10.2 Sets of Linear Equations

  10.3 The Gauss Reduction

  10.4 The Crout Reduction

  10.5 Intermediate Roudoff Errors

  10.6 Determination of the Inverse Matrix

  10.7 Inherent Errors

  10.8 Tridiagonal Sets of Equations

  10.9 Iterative Methods and Relaxation

  10.10 Iterative Methods for Nonlinear Equations

  10.11 The Newton-Raphson Method

  10.12 Iterative Methods of Higher Order

  10.13 Sets of Nonlinear Equations

  10.14 Iterated Synthetic Division of Polynomials. Lin's Method

  10.15 Determinacy of Zeros of Polynomials

  10.16 Bernoulli's Iteration

  10.17 Graeffe's Root-squaring Technique

  10.18 Quadratic Factors. Lin's Quadratic Method

  10.19 Bairstow Iteration

  10.20 Supplementary References



A Justification of the Crout Reduction

B Bibliography

C Directory of Methods


Product Details

Hildebrand, F. B.
Hildebrand, Francis Begnaud
Hildebrand, F. B.
Dover Publications
New York :
Mathematical Analysis
Numerical analysis
General Mathematics
Edition Number:
Edition Description:
Second Edition
Dover Books on Mathematics
Series Volume:
Publication Date:
8.5 x 5.38 in 1.66 lb

Other books you might like

  1. Analysis of Numerical Methods Used Hardcover $7.95
  2. The Finite Element Method: Linear... Used Trade Paper $17.00
  3. Methods of Applied Mathematics 2ND... New Trade Paper $17.95
  4. Calculus with Analytic Geometry Used Hardcover $4.95
  5. Geometry of Complex Numbers: Circle... New Trade Paper $16.95
  6. Calculus Used Trade Paper $1.75

Related Subjects

Science and Mathematics » Mathematics » Advanced
Science and Mathematics » Mathematics » Analysis General
Science and Mathematics » Mathematics » Calculus » General
Science and Mathematics » Mathematics » General
Science and Mathematics » Mathematics » Numeric Analysis
Science and Mathematics » Physics » General

Introduction To Numerical Analysis 2ND Edition New Trade Paper
0 stars - 0 reviews
$28.95 In Stock
Product details 704 pages Dover Publications - English 9780486653631 Reviews:
"Synopsis" by ,
Well-known, respected introduction, updated to integrate concepts and procedures associated with computers. Computation, approximation, interpolation, numerical differentiation and integration, smoothing of data, more. Includes 150 additional problems in this edition.
  • back to top


Powell's City of Books is an independent bookstore in Portland, Oregon, that fills a whole city block with more than a million new, used, and out of print books. Shop those shelves — plus literally millions more books, DVDs, and gifts — here at