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Friendly Introduction to Numerical Analysis

ISBN-10: 0130130540
ISBN-13: 9780130130549
Edition: 2006
Authors: Brian Bradie
List price: $117.80
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Description: This student-friendly introduction to the fundamental concepts and techniques of numerical analysis and numerical methods aims to develop concepts and techniques in a clear, concise, easy-to-read manner, and features fully-worked examples.

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Book details

List price: $117.80
Copyright year: 2006
Publisher: Prentice Hall PTR
Publication date: 4/26/2005
Binding: Paperback
Pages: 976
Size: 7.50" wide x 9.75" long x 1.25" tall
Weight: 3.410
Language: English

This student-friendly introduction to the fundamental concepts and techniques of numerical analysis and numerical methods aims to develop concepts and techniques in a clear, concise, easy-to-read manner, and features fully-worked examples.

Getting Started
Algorithms
Convergence
Floating Point Numbers
Floating Point Arithmetic
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
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
Eigenvalues and Eigenvectors
The Power Method
The Inverse Power Method
Deflation
Reduction to Tridiagonal Form
Eigenvalues of Tridiagonal and Hessenberg Matrices
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
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
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
Second-Order One-Dimensional Two-Point Boundary Value Problems
Finite Difference Method
The Linear Problem with Dirichlet Boundary Conditions
Finite Difference Method
The Linear Problem with Non-Dirichlet Boundary Conditions
Finite Difference Method
Nonlinear Problems
The Shooting Method
Linear Boundary Value Problems
The Shooting Method
Nonlinear Boundary Value Problems
Finite Difference Method for Elliptic Partial Differential Equations
The Poisson Equation on a Rectangular Domain
Dirichlet Boundary Conditions
The Poisson Equation on a Rectangular Domain
Non-Dirichlet Boundary Conditions
Solving the Discrete Equations: Relaxation Schemes
Local Mode Analysis of Relaxation and the Multigrid Method
Irregular Domains
10
The Heat Equation with Dirichlet Boundary Conditions
Stability
More General Parabolic Equations
Non-Dirichlet Boundary Conditions
Polar Coordinates
Problems in Two Space Dimensions
Finite Difference Method for Hyperbolic Partial Differential Equations and the Convection-Diffusion Equation
Advection Equation
Upwind Differencing
Advection Equation
MacCormack Method
Convection-Diffusion Equation
The Wave Equation
Appendices
Important Theorems from Calculus
Algorithm for Solving a Tridiagonal System of Linear Equations
References
Index
Answers to Selected Problems

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