Applied Numerical Analysis Using MATLAB

ISBN-10: 0132397285

ISBN-13: 9780132397285

Edition: 2nd 2008

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Description: Uses introductory problems from particular applications that are easy to understand and show the reader that there is a need for a particular mathematical technique. Numerical techniques are explained from basics with an emphasis on why they work.Discusses the contexts and reasons for selection of each problem and solution method. Worked-out examples are very realistic and not contrived.

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Book details

List price: $117.80
Edition: 2nd
Copyright year: 2008
Publisher: Prentice Hall PTR
Publication date: 4/11/2007
Binding: Paperback
Pages: 688
Size: 7.00" wide x 9.10" long x 1.50" tall
Weight: 2.750

Preface
Foundations
Introductory Examples
Nonlinear Equations
Linear Systems
Numerical Integration
Useful Background
Results from Calculus
Results from Linear Algebra
A Little Information about Computers
Some Basic Issues
Error
Convergence
Getting Better Results
Using MATLAB
Command Window Computations
M-Files
Programming in MATLAB
Matrix Multiplication
Chapter Wrap-Up
Functions of One Variable
Bisection Method
Secant-Type Methods
Regula Falsi
Secant Method
Analysis
Newton's Method
Muller's Method
Minimization
Golden-Section Search
Brent's Method
Beyond the Basics
Using MATLAB's Functions
Laguerre's Method
Zeros of a Nonlinear Function
Chapter Wrap-Up
Solving Linear Systems: Direct Methods
Gaussian Elimination
Basic Method
Row Pivoting
Gauss-Jordan
Inverse of a Matrix
Tridiagonal Systems
Further Topics
MATLAB's Methods
Condition of a Matrix
Iterative Refinement
Chapter Wrap-Up
LU and QR Factorization
LU Factorization
Using Gaussian Elimination
Direct LU Factorization
Applications
Matrix Transformations
Householder Transformation
Givens Rotations
QR Factorization
Using Householder Transformations
Using Givens Rotations
Beyond the Basics
LU Factorization with Implicit Row Pivoting
Efficient Conversion to Hessenberg Form
Using MATLAB's Functions
Chapter Wrap-Up
Eigenvalues and Eigenvectors
Power Method
Basic Power Method
Rayleigh Quotient
Shifted Power Method
Accelerating Convergence
Inverse Power Method
General Inverse Power Method
Convergence
QR Method
Basic QR Method
Better QR Method
Finding Eigenvectors
Accelerating Convergence
Further Topics
Singular Value Decomposition
MATLAB's Methods
Chapter Wrap-Up
Solving Linear Systems: Iterative Methods
Jacobi Method
Gauss-Seidel Method
Successive Over-Relaxation
Beyond the Basics
MATLAB's Built-in Functions
Conjugate Gradient Methods
GMRES
Simplex Method
Chapter Wrap-Up
Nonlinear Functions of Several Variables
Nonlinear Systems
Newton's Method
Secant Methods
Fixed-Point Iteration
Minimization
Descent Methods
Quasi-Newton Methods
Further Topics
Levenberg-Marquardt Method
Nelder-Mead Simplex Search
Chapter Wrap-Up
Interpolation
Polynomial Interpolation
Lagrange Form
Newton Form
Difficulties
Hermite Interpolation
Piecewise Polynomial Interpolation
Piecewise Linear Interpolation
Piecewise Quadratic Interpolation
Piecewise Cubic Hermite Interpolation
Cubic Spline Interpolation
Beyond the Basics
Rational-Function Interpolation
Using MATLAB's Functions
Chapter Wrap-Up
Approximation
Least-Squares Approximation
Approximation by a Straight Line
Approximation by a Parabola
General Least-Squares Approximation
Approximation for Other Functional Forms
Continuous Least-Squares Approximation
Approximation Using Powers of x
Orthogonal Polynomials
Legendre Polynomials
Chebyshev Polynomials
Function Approximation at a Point
Pade Approximation
Taylor Approximation
Further Topics
Bezier Curves
Using MATLAB's Functions
Chapter Wrap-Up
Fourier Methods
Fourier Approximation and Interpolation
Derivation
Data on Other Intervals
Radix-2 Fourier Transforms
Discrete Fourier Transform
Fast Fourier Transform
Matrix Form of FFT
Algebraic Form of FFT
Mixed-Radix FFT
Using MATLAB's Functions
Chapter Wrap-Up
Numerical Differentiation and Integration
Differentiation
First Derivatives
Higher Derivatives
Partial Derivatives
Richardson Extrapolation
Numerical Integration
Trapezoid Rule
Simpson's Rule
Newton-Cotes Open Formulas
Extrapolation Methods
Quadrature
Gaussian Quadrature
Other Gauss-Type Quadratures
MATLAB's Methods
Differentiation
Integration
Chapter Wrap-Up
Ordinary Differential Equations: Fundamentals
Euler's Method
Geometric Introduction
Approximating the Derivative
Approximating the Integral
Using Taylor Series
Runge-Kutta Methods
Second-Order Runge-Kutta Methods
Third-Order Runge-Kutta Methods
Classic Runge-Kutta Method
Fourth-Order Runge-Kutta Methods
Fifth-Order Runge-Kutta Methods
Runge-Kutta-Fehlberg Methods
Multistep Methods
Adams-Bashforth Methods
Adams-Moulton Methods
Adams Predictor-Corrector Methods
Other Predictor-Corrector Methods
Further Topics
MATLAB's Methods
Consistency and Convergence
Chapter Wrap-Up
ODE: Systems, Stiffness, Stability
Systems
Systems of Two ODE
Euler's Method for Systems
Runge-Kutta Methods for Systems
Multistep Methods for Systems
Second-Order ODE
Stiff ODE
BDF Methods
Implicit Runge-Kutta Methods
Stability
A-Stable and Stiffly Stable Methods
Stability in the Limit
Further Topics
MATLAB's Methods for Stiff ODE
Extrapolation Methods
Rosenbrock Methods
Multivalue Methods
Chapter Wrap-Up
ODE: Boundary-Value Problems
Shooting Method
Linear ODE
Nonlinear ODE
Finite-Difference Method
Linear ODE
Nonlinear ODE
Function Space Methods
Collocation
Rayleigh-Ritz
Chapter Wrap-Up
Partial Differential Equations
Heat Equation: Parabolic PDE
Explicit Method
Implicit Method
Crank-Nicolson Method
Insulated Boundary
Wave Equation: Hyperbolic PDE
Explicit Method
Implicit Method
Poisson Equation: Elliptic PDE
Finite-Element Method for Elliptic PDE
Defining the Subregions
Defining the Basis Functions
Computing the Coefficients
Using MATLAB
Chapter Wrap-Up
Bibliography
Answers
Index
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