Research Methods and Statistics Arena

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• Price: $119.95 $107.96
• Hardback: 648 pages
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• Published: April 2009
• ISBN: 978-1-4200630-9-7
• Publisher: CRC Press
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Continuing in the bestselling tradition of the first edition, this edition demonstrates how to pose, numerically analyze, and solve electromagnetic problems (EM). Significant updates include the transition of all FORTRAN code into the more widely used MATLAB® format as well as improvements made to the standard algorithm for the finite difference time domain (FDTD) method and the treatment of absorbing boundary conditions in FDTD, the finite element method, and the transmission-line-matrix method. In addition to updated examples and new homework problems throughout, the second edition adds a chapter on the method of lines. An appendix covers use of MATLAB code. A solution manual is available for qualifying instructors

Table of Contents

Fundamental Concepts

Introduction

Review of Electromagnetic Theory

Classification of EM Problems

Some Important Theorems

Analytical Methods

Introduction

Separation of Variables

Separation of Variables in Rectangular Coordinates

Separation of Variables in Cylindrical Coordinates

Separation of Variables in Spherical Coordinates

Some Useful Orthogonal Functions

Series Expansion

Practical Applications

Attenuation Due to Raindrops

Concluding Remarks

Finite Difference Methods

Introduction

Finite Difference Schemes

Finite Differencing of Parabolic PDEs

Finite Differencing of Hyperbolic PDEs

Finite Differencing of Elliptic PDEs

Accuracy and Stability of FD Solutions

Practical Applications I — Guided Structures

Practical Applications II — Wave Scattering (FDTD)

Absorbing Boundary Conditions for FDTD

Finite Differencing for Nonrectangular Systems

Numerical Integration

Concluding Remarks

Variational Methods

Introduction

Operators in Linear Spaces

Calculus of Variations

Construction of Functionals from PDEs

Rayleigh–Ritz Method

Weighted Residual Method

Eigenvalue Problems

Practical Applications

Concluding Remarks

Moment Methods

Introduction

Integral Equations

Green’s Functions

Applications I — Quasi-Static Problems

Applications II — Scattering Problems

Applications III— Radiation Problems

Applications IV — EM Absorption in the Human Body

Concluding Remarks

Finite Element Method

Introduction

Solution of Laplace’s Equation

Solution of Poisson’s Equation

Solution of the Wave Equation

Automatic Mesh Generation I — Rectangular Domains

Automatic Mesh Generation II — Arbitrary Domains

Bandwidth Reduction

Higher Order Elements

Three-Dimensional Elements

Finite Element Methods for Exterior Problems

Finite-Element Time-Domain Method

Concluding Remarks

Transmission-line-matrix Method

Introduction

Transmission-line Equations

Solution of Diffusion Equation

Solution of Wave Equations

Inhomogeneous and Lossy Media in TLM

Three-Dimensional TLM Mesh

Error Sources and Correction

Absorbing Boundary Conditions

Concluding Remarks

Monte Carlo Methods

Introduction

Generation of Random Numbers and Variables

Evaluation of Error

Numerical Integration

Solution of Potential Problems

Regional Monte Carlo Methods

Time-Dependent Problems

Concluding Remarks

Method of Lines

Introduction

Solution of Laplace’s Equation

Solution of Wave Equation

Time-Domain Solution

Concluding Remarks

References

Problems

　

APPENDICES

Vector Relations

Vector Identities

Vector Theorems

Orthogonal Coordinates

Programming in MATLAB

MATLAB Fundamentals

Using MATLAB to Plot

Programming with MATLAB

Functions

Solving Equations

Programming Hints

Other Useful MATLAB Commands

Solution of Simultaneous Equations

Elimination Methods

Iterative Methods

Matrix Inversion

Eigenvalue Problems

Answers to Odd-Numbered Problems