Numerical Mathematics and Computing

by Cheney, E. Ward; Kincaid, David R.

• ISBN13: 9780495114758
• ISBN10: 0495114758
• Edition: 6th
• Format: Hardcover
• Copyright: 2007-08-03
• Publisher: Brooks Cole

Summary

Authors Ward Cheney and David Kincaid show students of science and engineering the potential computers have for solving numerical problems and give them ample opportunities to hone their skills in programming and problem solving. The text also helps students learn about errors that inevitably accompany scientific computations and arms them with methods for detecting, predicting, and controlling these errors. A more theoretical text with a different menu of topics is the authors' highly regarded NUMERICAL ANALYSIS: MATHEMATICS OF SCIENTIFIC COMPUTING, THIRD EDITION.

Table of Contents

Introduction

Preliminary Remarks

Review of Taylor Series

Floating-Point Representation And Errors

Floating-Point Representation

Loss of Significance

Locating Roots Of Equations

Bisection Method

Newton+s Method

Secant Method

Interpolation And Numerical Differentiation

Polynomial Interpolation

Errors in Polynomial Interpolation

Estimating Derivatives and Richardson Extrapolation

Numerical Integration

Lower and Upper Sums

Trapezoid Rule

Romberg Algorithm

Additional Topics On Numerical Integration

Simpson+s Rule and Adaptive Simpson+s Rule

Gaussian Quadrature Formulas

Systems Of Linear Equations

Naive Gaussian Elimination

Gaussian Elimination with Scaled Partial Pivoting

Tridiagonal and Banded Systems

Additional Topics Concerning Systems Of Linear Equations

Matrix Factorizations

Iterative Solutions of Linear Systems

Eigenvalues and Eigenvectors

Power Method

Approximation By Spline Functions

First-Degree and Second-Degree Splines

Natural Cubic Splines

B Splines: Interpolation and Approximation

Ordinary Differential Equations

Taylor Series Methods

Runge-Kutta Methods

Stability and Adaptive Runge-Kutta and Multistep Methods

Systems Of Ordinary Differential Equations

Methods for First-Order Systems

Higher-Order Equations and Systems

Adams-Bashforth-Moulton Methods

Smoothing Of Data And The Method Of Least Squares

Method of Least Squares

Orthogonal Systems and Chebyshev Polynomials

Other Examples of the Least-Squares Principle

Monte Carlo Methods And Simulation

Random Numbers

Estimation of Areas and Volumes by Monte Carlo Techniques

Simulation

Boundary-Value Problems For Ordinary Differential Equations

Shooting Method Shooting Method Algorithm

A Discretization Method

Partial Differential Equations

Parabolic Problems

Hyperbolic Problems

Elliptic Problems

Minimization Of Functions

One-Variable Case

Multivariate Case

Linear Programming

Standard Forms and Duality

Simplex Method

Approximate Solution of Inconsistent Linear Systems

Advice On Good Programming Practices

Programming Suggestions

Representation Of Numbers In Different Bases

Representation of Numbers in Different Bases

Additional Details On Ieee Floating-Point Arithmetic

More on IEEE Standard Floating-Point Arithmetic

Linear Algebra Concepts And Notation

Elementary Concepts

Abstract Vector Spaces

Answers For Selected Problems

Bibliography

Index

Table of Contents provided by Publisher. All Rights Reserved.