9780495114758

Numerical Mathematics and Computing

by ;
  • ISBN13:

    9780495114758

  • ISBN10:

    0495114758

  • Edition: 6th
  • Format: Hardcover
  • Copyright: 8/3/2007
  • Publisher: Brooks Cole
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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.

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