Elementary Numerical Analysis

ISBN-10: 0471433373
ISBN-13: 9780471433378
Edition: 3rd 2004 (Revised)
List price: $241.95 Buy it from $55.99 Rent it from $30.51
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Description: Offering a clear, precise, and accessible presentation, complete with MATLAB programs, this new Third Edition of Elementary Numerical Analysis gives students the support they need to master basic numerical analysis and scientific computing. Now  More...

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Book details

List price: $241.95
Edition: 3rd
Copyright year: 2004
Publisher: John Wiley & Sons, Incorporated
Publication date: 10/27/2003
Binding: Hardcover
Pages: 576
Size: 7.50" wide x 9.25" long x 1.25" tall
Weight: 2.508
Language: English

Offering a clear, precise, and accessible presentation, complete with MATLAB programs, this new Third Edition of Elementary Numerical Analysis gives students the support they need to master basic numerical analysis and scientific computing. Now updated and revised, this significant revision features reorganized and rewritten content, as well as some new additional examples and problems. The text introduces core areas of numerical analysis and scientific computing along with basic themes of numerical analysis such as the approximation of problems by simpler methods, the construction of algorithms, iteration methods, error analysis, stability, asymptotic error formulas, and the effects of machine arithmetic.

Kendall E. Atkinson, PhD, is Professor Emeritus in the Departments of Mathematics and Computer Science at the University of Iowa. He has authored books and journal articles in his areas of research interest, which include the numerical solution of integral equations and boundary integral equation methods. Weimin Han, PhD, is Professor in the Department of Mathematics at the University of Iowa, where he is also Director of the interdisciplinary PhD Program in Applied Mathematical and Computational Science. Dr. Han currently focuses his research on the numerical solution of partial differential equations. David E. Stewart, PhD, is Professor and Associate Chair in the Department of Mathematics at the University of Iowa, where he is also the departmental Director of Undergraduate Studies. Dr. Stewart's research interests include numerical analysis, computational models of mechanics, scientific computing, and optimization.

Taylor Polynomials
The Taylor Polynomial
The Error in Taylor's Polynomials
Infinite Series
Polynomial Evaluation
An Example Program
Error and Computer Arithmetic
Floating-Point Numbers
Accuracy of Floating-Point Representation
Rounding and Chopping
Consequences for Programming of Floating-Point Arithmetic
Errors: Definitions, Sources, and Examples
Sources of Error
Loss-of-Significance Errors
Noise in Function Evaluation
Underflow and Overflow Errors
Propagation of Error
Propagated Error in Function Evaluation
Summation
Rounding versus Chopping
A Loop Error
Calculation of Inner Products
Rootfinding
The Bisection Method
Error Bounds
Newton's Method
Error Analysis
Error Estimation
Secant Method
Error Analysis
Comparison of Newton and Secant Methods
The MATLAB Function
Fixed Point Iteration
Aitken Error Estimation and Extrapolation
Higher-Order Iteration Formulas
Ill-Behaving Rootfinding Problems
Stability of Roots
Interpolation and Approximation
Polynomial Interpolation
Linear Interpolation
Quadratic Interpolation
Higher-Degree Interpolation
Divided Differences
Properties of Divided Differences
Newton's Divided Difference Interpolation
Error in Polynomial Interpolation
Another Error Formula
Behavior of the Error
Interpolation Using Spline Functions
Spline Interpolation
Construction of the Interpolating Natural Cubic Spline
Other Interpolating Spline Functions
The MATLAB Program spline
The Best Approximation Problem
Accuracy of the Minimax Approximation
Chebyshev Polynomials
The Triple Recursion Relation
The Minimum Size Property
A Near-Minimax Approximation Method
Odd and Even Functions
Least Squares Approximation
Legendre Polynomials
Solving for the Least Squares Approximation
Generalizations of Least Squares Approximation
Numerical Integration and Differentiation
The Trapezoidal and Simpson Rules
Simpson's Rule
Error Formulas
An Asymptotic Estimate of the Trapezoidal Error
Error Formulas for Simpson's Rule
Richardson Extrapolation
Periodic Integrands
Gaussian Numerical Integration
Weighted Gaussian Quadrature
Numerical Differentiation
Differentiation Using Interpolation
The Method of Undetermined Coefficients
Effects of Error in Function Values
Solution of Systems of Linear Equations
Systems of Linear Equations
Matrix Arithmetic
Arithmetic Operations
Elementary Row Operations
The Matrix Inverse
Matrix Algebra Rules
Solvability Theory of Linear Systems
Gaussian Elimination
Partial Pivoting
Calculation of Inverse Matrices
Operations Count
The LU Factorization
Compact Variants of Gaussian Elimination
Tridiagonal Systems
Matlab Built-in Functions for Solving Linear Systems
Error in solving Linear Systems
The Residual Correction Method
Stability in Solving Linear Systems
Iteration Methods
Jacobi Method and Gauss-Seidel Method
General Schema
The Residual Correction Method
Numerical Linear Algebra: Advanced Topics
Least Squares Data Fitting
The Linear Least Squares Approximation
Polynomial Least Squares Approximation
The Eigenvalue Problem
The Characteristic Polynomial
Eigenvalues for Symmetric Matrices
The Nonsymmetric Eigenvalue Problem
The Power Method
Convergence of the Power Method
Matlab Eigenvalue Calculations
Nonlinear Systems
Newton's Method
The General Newton Method
A Modified Newton's Method
Ordinary Differential Equations
Theory of Differential Equations: An Introduction
General Solvability Theory
Stability of the Initial Value Problem
Direction Fields
Euler's Method
Convergence Analysis of Euler's Method
Asymptotic Error Analysis
Richardson Extrapolation
Numerical Stability, Implicit Methods
The Backward Euler Method
The Trapezoidal Method
Taylor and Runge-Kutta Methods
Runge-Kutta Methods
Error Prediction and Control
Matlab Built-in Functions
Multistep Methods
Systems of Differential Equations
Higher-Order Differential Equations
Numerical Methods for Systems
Finite Difference Method for Two-Point Boundary Value Problems
Finite Difference Method for PDEs
The Poisson Equation
One-Dimensional Heat Equation
Semidiscretization
Explicit Full Discretization
Implicit Full Discretization
One-Dimensional Wave Equation
Mean Value Theorems
Mathematical Formulas
Algebra
Geometry
Trigonometry
Calculus
Numerical Analysis Software Packages
Commercial Packages
Public Domain Packages
Interactive Numerical Computation Environments
Symbolic Computation Environments
Literature of Mathematical Software
Matlab: An Introduction
The Binary Number System
Conversion from Decimal to Binary
Hexadecimal Numbers
Answers to Selected Problems
Bibliography
Index

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