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A Friendly Introduction to Numerical Analysis

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Synopses & Reviews

Publisher Comments:

This reader-friendly introduction to the fundamental concepts and techniques of numerical analysis/numerical methods develops concepts and techniques in a clear, concise, easy-to- read manner, followed by fully-worked examples. Application problems drawn from the literature of many different fields prepares readers to use the techniques covered to solve a wide variety of practical problems. Rootfinding. Systems of Equations. Eigenvalues and Eigenvectors. Interpolation and Curve Fitting. Numerical Differentiation and Integration. Numerical Methods for Initial Value Problems of Ordinary Differential Equations. Second-Order One-Dimensional Two-Point Boundary Value Problems. Finite Difference Method for Elliptic Partial Differential Equations. Finite Difference Method for Parabolic Partial Differential Equations. Finite Difference Method for Hyperbolic Partial Differential Equations and the Convection-Diffusion Equation. For anyone interested in numerical analysis/methods and their applications in many fields

Table of Contents

(NOTE: Each chapter begins with An Overview.)

1. Getting Started.

Algorithms. Convergence. Floating Point Numbers. Floating Point Arithmetic.

2. Rootfinding.

Bisection Method. Method of False Position. Fixed Point Iteration. Newton's Method. The Secant Method and Muller's Method. Accelerating Convergence. Roots of Polynomials.

3. Systems of Equations.

Gaussian Elimination. Pivoting Strategies. Norms. Error Estimates. LU Decomposition. Direct Factorization. Special Matrices. Iterative Techniques for Linear Systems: Basic Concepts and Methods. Iterative Techniques for Linear Systems: Conjugate-Gradient Method. Nonlinear Systems.

4. Eigenvalues and Eigenvectors.

The Power Method. The Inverse Power Method. Deflation. Reduction to Tridiagonal Form. Eigenvalues of Tridiagonal and Hessenberg Matrices.

5. Interpolation and Curve Fitting.

Lagrange Form of the Interpolating Polynomial. Neville's Algorithm. The Newton Form of the Interpolating Polynomial and Divided Differences. Optimal Interpolating Points. Piecewise Linear Interpolation. Hermite and Hermite Cubic Interpolation. Regression.

6. Numerical Differentiation and Integration.

Continuous Theory and Key Numerical Concepts. Euler's Method. Higher-Order One-Step Methods. Multistep Methods. Convergence Analysis. Error Control and Variable Step Size Algorithms. Systems of Equations and Higher-Order Equations. Absolute Stability and Stiff Equations.

7. Numerical Methods for Initial Value Problems of Ordinary Differential Equations.

Continuous Theory and Key Numerical Concepts. Euler's Method. Higher-Order One-Step Methods. Multistep Methods. Convergence Analysis. Error Control and Variable Step Size Algorithms. Systems of Equations and Higher-Order Equations. Absolute Stability and Stiff Equations.

8. Second-Order One-Dimensional Two-Point Boundary Value Problems.

Finite Difference Method, Part I: The Linear Problem with Dirichlet Boundary Conditions. Finite Difference Method, Part II: The Linear Problem with Non-Dirichlet Boundary Conditions. Finite Difference Method, Part III: Nonlinear Problems. The Shooting Method, Part I: Linear Boundary Value Problems. The Shooting Method, Part II: Nonlinear Boundary Value Problems.

9. Finite Difference Method for Elliptic Partial Differential Equations.

The Poisson Equation on a Rectangular Domain, I: Dirichlet Boundary Conditions. The Poisson Equation on a Rectangular Domain, II: Non-Dirichlet Boundary Conditions. Solving the Discrete Equations: Relaxation Schemes. Local Mode Analysis of Relaxation and the Multigrid Method. Irregular Domains.

10. Finite Difference Method for Parabolic Partial Differential Equations.

The Heat Equation with Dirichlet Boundary Conditions. Stability. More General Parabolic Equations. Non-Dirichlet Boundary Conditions. Polar Coordinates. Problems in Two Space Dimensions.

11. Finite Difference Method for Hyperbolic Partial Differential Equations and the Convection-Diffusion Equation.

Advection Equation, I: Upwind Differencing. Advection Equation, II: MacCormack Method. Convection-Diffusion Equation. The Wave Equation.

Appendices.

Appendix A. Important Theorems from Calculus. Appendix B. Algorithm for Solving a Tridiagonal System of Linear Equations.

References.

Index.

Answers to Selected Problems.

Product Details

ISBN:
9780130130549
Other:
Bradie, Brian
Publisher:
Pearson
Other:
Bradie, Brian
Author:
Bradie, Brian
Subject:
General
Subject:
Computer Science
Subject:
Mathematics - General
Copyright:
Edition Description:
Trade paper
Series:
Featured Titles for Numerical Analysis
Publication Date:
April 2005
Binding:
TRADE PAPER
Grade Level:
College/higher education:
Language:
English
Illustrations:
Y
Pages:
976
Dimensions:
9 x 7 x 2 in 1479 gr

Related Subjects

Computers and Internet » Computers Reference » General
Computers and Internet » Personal Computers » General
Science and Mathematics » Mathematics » Advanced
Science and Mathematics » Mathematics » General
Science and Mathematics » Mathematics » Number Theory
Science and Mathematics » Mathematics » Numeric Analysis

A Friendly Introduction to Numerical Analysis New Trade Paper
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