Always Learning

Numerical Analysis and Scientific Computation
Jeffery J. Leader, Rose-Hulman Institute of Technology

ISBN-10: 0201734990
ISBN-13:  9780201734997

Publisher:  Pearson
Copyright:  2005
Format:  Paper; 608 pp
Published:  02/05/2004
Status: Instock


Customers outside the U.S., click here.


Print this content

In this section:


Description

This text is intended for a first course in Numerical Analysis taken by students majoring in mathematics, engineering, computer science, and the sciences. This text emphasizes the mathematical ideas behind the methods and the idea of mixing methods for robustness. The optional use of MATLAB is incorporated throughout the text.


Features

  • Quick introduction to numerical methods, with round-off error and computer arithmetic deferred until students have had experience with real algorithms.
  • Modern approach to numerical linear algebra.
  • Explanation of numerical techniques from MATLAB and other programs and subroutine libraries.
  • Appropriate mix of numerical analysis theory and practical scientific computation principles.
  • Greater than usual emphasis on optimization.
  • Extensive numerical experiments so students can gain experience.
  • Efficient and unobtrusive introduction to MATLAB.


Table of Contents



1. Nonlinear Equations.

Biscetion and Inverse Linear Interpolation.

Newton's Method.

The Fixed Point Theorem.

Quadratic Convergence of Newton's Method.

Variants of Newton's Method.

Brent's Method.

Effects of Finite Precision Arithmetic.

Newton's Method for Systems.

Broyden's Method.



2. Linear Systems.

Gaussian Elimination with Partial Pivoting.

The LU Decomposition.

The LU Decomposition with Pivoting.

The Cholesky Decomposition.

Condition Numbers.

The QR Decomposition.

Householder Triangularization and the QR Decomposition.

Gram-Schmidt Orthogonalization and the QR Decomposition.

The Singular Value Decomposition.



3. Iterative Methods.

Jacobi and Gauss-Seidel Iteration.

Sparsity.

Iterative Refinement.

Preconditioning.

Krylov Space Methods.

Numerical Eigenproblems.



4. Polynomial Interpolation.

Lagrange Interpolating Polynomials.

Piecewise Linear Interpolation.

Cubic Splines.

Computation of the Cubic Spline Coefficients.



5. Numerical Integration.

Closed Newton-Cotes Formulas.

Open Newton-Cotes Formulas and Undetermined Coeffients.

Gaussian Quadrature.

Gauss-Chebyshev Quadrature.

Radau and Lobatto Quadrature.

Adaptivity and Automatic Integration.

Romberg Integration.



6. Differential Equations.

Numerical Differentiation.

Euler's Method.

Improved Euler's Method.

Analysis of Explicit One-Step Methods.

Taylor and Runge-Kutta Methods.

Adaptivity and Stiffness.

Multi-Step Methods.



7. Nonlinear Optimization.

One-Dimensional Searches.

The Method of Steepest Descent.

Newton Methods for Nonlinear Optimization.

Multiple Random Start Methods.

Direct Search Methods.

The Nelder-Mead Method.

Conjugate Direction Methods.



8. Approximation Methods.

Linear and Nonlinear Least Squares.

The Best Approximation Problem.

Best Uniform Approximation.

Applications of the Chebyshev Polynomials.



Afterword.


Bibliography.


Answers.


Index.



Back to top

Print this content

In this section:

Instructor's Solutions Manual
Brown & Haynes
©2005  |  Pearson  |  Electronic Supplement; 320 pp  |  Available
ISBN-10: 0321257324  |  ISBN-13: 9780321257321

Show Downloadable Files
 | More Info

Back to top


Websites and online courses

Student Solutions Manual (Download only) for Numerical Analysis and Scientific Computation
Brown & Haynes
©2005  |  Pearson  |  On-line Supplement; 208 pp  |  Live
ISBN-10: 0321257332  |  ISBN-13: 9780321257338


For the Mathematics Discipline

Allied Health Study Card, 2/E
Forshier
©2006  |  Pearson  |  Study Card  |  Instock
ISBN-10: 0321394747  |  ISBN-13: 9780321394743
More Info

Basic Math Review Card, 2/E
Addison Wesley Higher Education
©2006  |  Pearson  |  Study Card; 6 pp  |  Instock
ISBN-10: 0321394763  |  ISBN-13: 9780321394767
More Info

Center for Excellence Sticker
Addison Wesley Higher Education Group
©2000  |  Pearson  |  Unknown / Other  |  Instock
ISBN-10: 0201716275  |  ISBN-13: 9780201716276
More Info

Concept Videos: Algebra
Addison Wesley Higher Education
©2008  |  Pearson  |  Multiple Media Package  |  Instock
ISBN-10: 0321517199  |  ISBN-13: 9780321517197
More Info

Concept Videos: Basic Math & Prealgebra
Addison Wesley Higher Education
©2008  |  Pearson  |  Multiple Media Package  |  Instock
ISBN-10: 032151758X  |  ISBN-13: 9780321517586
More Info

Discovering Algebra: Examples with Keystrokes on the TI-83/TI-82 and TI-85/TI-86, A Laboratory Approach
Pirich & Bigliani
©1997  |  Pearson  |  Paper; 195 pp  |  Instock
ISBN-10: 0136492037  |  ISBN-13: 9780136492030
More Info

Graphing Calculator Tutorial CD
Addison Wesley Higher Education
©2006  |  Pearson  |  CD-ROM Only  |  Instock
ISBN-10: 0321357744  |  ISBN-13: 9780321357748
More Info

Overcoming Math Anxiety, 2/E
Davidson & Levitov
©2000  |  Pearson  |  Paper  |  Instock
ISBN-10: 0321069188  |  ISBN-13: 9780321069184
More Info

Prealgebra Review Workbook
Wheel
©2006  |  Pearson  |  Paper; 300 pp  |  Instock
ISBN-10: 0321473329  |  ISBN-13: 9780321473325
More Info

Review of Algebra, A
Howard
©2002  |  Pearson  |  Paper; 224 pp  |  Instock
ISBN-10: 0201773473  |  ISBN-13: 9780201773477
More Info

Spanish Basic Math Study Card
Leonarte
©2007  |  Pearson  |  Study Card  |  Instock
ISBN-10: 0321438582  |  ISBN-13: 9780321438584
More Info

TestGen All-in-One 2005 Package
Addison Wesley Higher Education
©2005  |  Pearson  |  CD-ROM Only  |  Instock
ISBN-10: 0321334469  |  ISBN-13: 9780321334466
More Info


Back to top

close

Sign in to the Instructor Resource Center

Cancel

Print this content

Pearson Higher Education offers special pricing when you choose to package your text with other student resources. If you're interested in creating a cost-saving package for your students contact your Pearson Higher Education representative.

Back to top