Outlines of Muhammadan Law

Name: Outlines of Muhammadan Law
Price: 48.74 USD
Availability: InStock
ISBN: 9780195603750

ISBN-10: 0195603753

ISBN-13: 9780195603750

Edition: 4th 1974 (Revised)

Authors: Asaf A.A. Fyzee

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The fourth edition of this classic textbook incorporates changes in the law through 1980 including changes in English law in relation to Muslim immigrants as well as new laws resulting from the formation of Bangladesh. This edition also includes the complete text of the Pakistan Orders of 1979 which have had far-reaching implications in the introduction of Islamic law in Pakistan.

Book details

List price: $24.00
Edition: 4th
Copyright year: 1974
Publisher: Oxford University Press, Incorporated
Publication date: 8/19/1993
Binding: Hardcover
Pages: 540
Size: 5.75" wide x 8.75" long x 1.22" tall
Weight: 1.650
Language: English



Preface



Background to Numerical Methods


Introduction


Number Systems and their Conversions


Representation of Negative Numbers


Addition and Subtraction Rules


Binary Multiplication and Division


Fixed-point Representation


Floating-point Representation


Actual Computer Number System



Scope of Mathematical and Numerical Methods


Introduction


Numerical Methods


Mathematical Formula and Numerical Computation


Stability of Numerical Solution


Safeguard For Wrong Use of Mathematical Results


Practical Guidelines For Numerical Computation


Remarks



Errors and their Propagation


Introduction


Basic Sources of Errors


Errors in Measurement


Absolute, Relative, and Percentage Errors


Errors in Infinite-precision Representation


Error Propagation


Process Graphs for Propagated Errors


Extended Additions and Multiplications


Error Analysis


Truncation Error


Error Bounds in Number Approximation


A Complete Computational Problem



Programming Tools and Techniques


Introduction


Algorithms


Flow Chart


Basic


Fortran


Pascal


C


Matlab


Mathematica


C, Pascal, and Fortran Constructs


Example 1


Example 2



Solutions of Algebraic and Transcendental Equations


Introduction


Initial Work and First Approximation


Method of Bisection


Regula falsi (Method of False Position)


Bisection Method vs Regula Falsi Method


Ridders' Method


General Iterative Methods


Linear Iterative Method


Aitken's-$$ Method


Newton-Raphson Method


Secant Method


Kizner's Method


Brent's Method


Polynomial Equations


Iterative Methods for Polynomial Equations


Laguerre's Method


Mï¿½ller's Method


Bairstow-Hitchcock Method for Complex Roots


Bernoulli's Method


Graeffe's Root-squaring Method


Quotient-Difference (QD) Algorithm


Comments and Discussions With Examples


Applications



Numerical Solutions of Linear Equations: Direct Methods


Introduction


Gaussian Elimination and Triangular Systems


Gauss-Jordan Method


Error and Sensitivity Analysis


Iterative Refinement with Gaussian Elimination


Wilkinson Algorithm


Cholesky Factorization


Complex System of Linear Equations



Numerical Solutions for Matrix Inversion


Introduction


Two-array Method


Gauss-Jordan Two-array Method with Pivoting


Inverse in Place without Pivoting


Inverse in Place with Pivoting


Inverse of Triangular Matrices


Inverse of Complex Matrices


Iterative Procedure



Numerical Solutions of Linear Systems of Equations: Iterative Methods


Introduction


Nature of Iterative Methods for Linear Equations


Point Iterative Methods


Computational Techniques for Point Iterative Methods


Block Iterative Methods



Linear Least-Squares Problem


Introduction


Existence of Solution: Normal Equations


Solution of Normal Equations


Orthogonalization Process


Solution of Linear Least-squares Problem


Recursive Least-square Problem



Numerical Solutions of Systems of Non-linear Equations


Introduction


The Problem


Generalized Linear Iterative Method


Newton's Method


Generalized Linear Methods


Steepest Descentor Gradient Method



Eigenvalues and Eigenvectors


Introduction


The Problem


Polynomial Method


Danilevsky Method


Power and Inverse Power Methods


Eigenvalues and Eigenvectors of Symmetric Matrices


Eigenpair from Tri-diagonal Matrix


Eigenvalues by QL Method


Eigenvalues by QR Method


Eigenvalues and Eigenvectors by LU Method


Generalized Eigenvalue Problem


Methods for Non-symmetric Matrices



Interpolation and Extrapolation


Introduction


Linear Method of Interpolation


Lagrangian Method of Interpolation


Iterated Linear Interpolation


Newton's Divided Difference Interpolation


Difference Operators


Equal Interval Finite Difference Methods


Different Finite Difference Interpolation Formulae


Correction of Tabular Values


Inverse Interpolation


Osculating Polynomials


Chebyshev Interpolation


Multi-dimensional Interpolation


Piecewise Polynomial Interpolation



Numerical Differentiation


Introduction


Differentiation


Differentiation Formulae for Numerical Computation


Computational Problems


Extrapolation in Derivative Computation


Application to Solving Differential Equation



Numerical Integration


Quadrature Formula


Methods Based on Difference Polynomials


Computers in Numerical Integration


Error Analysis in Trapezoidal Rule


Romberg Integration


Adaptive Quadrature


Gaussian Quadrature


Orthogonal Polynomials


Lagrangian Interpolating Polynomials


Gaussian Quadrature Problem


Use of Gaussian Quadrature


Comparison of Integration Formulae


Spline Integration


Integrals Within Finite Range of Integration


Singular Integrals


Multiple Integration


Application of Quadrature Rules


Numerical Integration Using Monte Carlo Method



Numerical Solutions of Ordinary Differential Equations: Initial Value Problem


Introduction


First-order Differential Equation


Intuitive Meaning of Solution to Differential Equation


Theoretical Results


Semi-numeric Method


Simple Difference Methods


Single-step Methods


Runge-Kutta (RK) Methods


Multi-step Methods


Predictor-Corrector (PC) Methods


Multi-valued Methods


Choosing a Method


System of First-order Ordinary Differential Equations



Numerical Solutions of Ordinary Differential Equations: Boundary Value Problems


Introduction


Problem


Shooting Methods


Finite Difference Methods


Finite Elements Methods


Relaxation Methods



Numerical Solutions of Partial Differential Equations


Introduction


Definitions and Terminology


Classification of Partial Differential Equations


Some Standard Partial Differential Equations


Methodology to Solve Partial Differential Equations



Numerical Solutions of Parabolic Partial Differential Equations


Introduction


Heat Equation


Why Numerical Methods?


Explicit Methods


Implicit Method


Unified Explicit and Implicit Scheme


Iterative Methods


Improves Patial Accuracy


Generalization


Non-linear Parabolic Partial Differential Equations


Parabolic Partial Differential Equation in 2D or 3D


Alternating Direction Implicit (ADI) Method



Numerical Solutions of Hyperbolic Partial Differential Equations


Introduction


Derivation of Wave Equation


Simple Finite Difference Methods


Second-order Hyperbolic Equations


Method of Characteristics for Hyperbolic Partial Differential Equations


Hyperbolic Differential Equations in 2D or 3D



Numerical Solutions of Elliptic Partial Differential Equations


Introduction


Direct Method


Finite Difference Methods


ADI Method


Relaxation Methods


Finite Element Methods



Advances in Numerical Methods Using Parallel Computing Paradigm


Introduction


Parallel Computing


Parallel Programming


Basic Numerical Operations in Parallel Computing


Root of One-dimensional Non-linear Equation


Interpolation


Integration


System of Linear Equations


Differential Equations



Numerical Methods Using Neural Networks


Introduction


Biological Neural Network


Artificial Neural Network


Network Architecture


Learning


Multi-layer Perceptron (MLP)


Radial Basis Function (RBF) Neural Network


Hopfield Network


Function Approximation Using MLP


Numerical Differentiation Using RBF


Numerical Integration Using MLP


Solution of Non-linear Equations Using Neural Networks


Matrix Inversion Using Hopfield Network


System of Linear Equations


Eigenvalues and Eigenvectors Computation


Interpolation Using Neural Networks


Extrapolation Using Neural Networks


Neural Networks for Differential Equations



Numerical Solutions of Difference Equations


Introduction


Difference Equations


Computational Problems


Second-order Boundary Value Problem


Answers


Bibliography


Index