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| Preface | |
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| Errata | |
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| Introduction and Overview | |
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| Structure of the Book | |
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| Modern Applications of Conformal Mapping | |
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| Electromagnetics | |
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| Vibrating Membranes & Acoustics | |
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| Transverse Vibrations & Buckling of Plates | |
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| Elasticity | |
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| Heat Transfer | |
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| Fluid Flow | |
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| Other Areas | |
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| Growth in Scope of Applications | |
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| Basic Mathematical Concepts | |
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| Transformation of Coordinates | |
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| Transformation by Means of Complex Functions | |
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| Analytic Functions | |
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| Conformality and Uniqueness | |
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| A Selection of Mapping Functions | |
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| Elementary Transformations | |
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| Linear Transformation | |
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| Power Transformation | |
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| Inverse or Reciprocal Transformation | |
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| Logarithmic and Exponential Transformations | |
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| Hyperbolic Transformation | |
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| Interpretation of Elementary Transformation | |
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| Composite Transformations | |
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| Bilinear Transformation | |
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| Joukowski Transformation | |
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| Trigonometric and Hyperbolic Transformations | |
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| Maxwell's Transformation | |
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| Schwarz-Christoffel Transformation for Polygons | |
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| The Basic Method | |
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| Trigons | |
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| Maxwell's Transformation Revisited | |
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| Joukowski's Transformation Revisited | |
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| Mapping the Interior of a Rectangle | |
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| The Rectangle | |
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| The Square | |
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| Weierstrass Formulation for Rectangle and Triangle | |
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| Application | |
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| The Inverse and Further Notes | |
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| Mapping the Regions Exterior to Rectangles and Between Rectangles | |
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| Polygons with Rounded Corners | |
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| Exploiting Symmetry | |
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| Numerical Methods | |
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| Methods of Approximation | |
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| Series Approximations | |
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| Mapping the Interior of the Unit Circle | |
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| Method of Simultaneous Equations (Kantorovich) | |
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| Mapping Exterior Regions | |
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| Successive Approximations (Fornberg) | |
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| Variational Methods | |
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| Carrying out the Minimization | |
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| Orthogonalization | |
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| Minimizing the Perimeter, Orthogonal Polynomials | |
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| Example of Minimum Perimeter Method | |
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| Minimizing the Area, Comparison of Methods | |
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| Additional Extremum Principles | |
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| Additional Approximation Methods | |
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| Integral Equation Methods | |
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| Method of Lichtenstein and Gershgorin | |
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| Method of Theodorsen and Garrick | |
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| Method of Symm | |
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| Comments on Integral Equation Methods | |
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| Numerical Determination of Schwarz-Christoffel Transformation | |
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| The Parameter Problem | |
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| Averting Singularities at Infinity | |
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| Method of Trefethen | |
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| Method of Foster and Anderson | |
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| Doubly Connected Regions | |
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| General Observations | |
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| Symmetry and Circles | |
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| Symmetric Region with an Inner Circle | |
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| Symmetric Region with an Outer Circle | |
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| Other Configurations; Accuracy | |
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| Mathematical Models | |
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| Potential Fields and the Laplace Equation | |
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| The Laplace Equation under Conformal Mapping | |
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| Steady Current Flow, Electrostatics, Magnetostatics | |
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| Temperature Field | |
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| Fluid Flow Field | |
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| The Poisson Equation | |
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| The Two-Dimensional Wave Equation | |
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| The Two-Dimensional Diffusion Equation | |
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| Bending, Buckling, and Vibrations of Plates | |
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| Boundary Conditions | |
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| Sources and Sinks | |
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| Lines of Symmetry | |
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| Dirichlet and Neumann Conditions | |
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| Extracting the Results | |
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| Nonplanar Fields and Nonuniform Media | |
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| Nonplanar Fields | |
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| Description of Difficulties | |
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| Potential Fields with Rotational Symmetry | |
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| Symmetric Field in a Wedge-Shaped Region | |
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| General Coordinate Transofrmations in Three Dimensions | |
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| Cases with Rotational Symmetry Revisited | |
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| Transformation in Two Planes | |
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| Nonuniform Media | |
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| Field at Boundary Separating Different Media | |
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| Anisotropic Media | |
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| Quasiconformal Mappings | |
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| Static Fields in Electricity and Magnetism | |
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| Area-Networks and Hall Generators | |
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| Two-Terminal Devices | |
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| Three-Terminal Devices | |
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| Resistivity Measurement with Four Electrodes | |
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| Hall Effect Transducers | |
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| Nonuniform Resistivities | |
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| Electric Fields in Dielectrics | |
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| Electrode Shapes for Uniform Field Strength | |
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| Deflection Head for an Ink-Jet Printer | |
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| Magnetic Fields of Stationary Structures | |
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| Transformers | |
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| Magnetic Recording Heads | |
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| Perpendicular Field | |
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| Longitudinal Field | |
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| Magnetic Field of Rotating Machines | |
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| Field Analysis in Salient Pole Machines | |
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| Other Applications | |
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| Transmission Lines and Waveguides | |
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| The Basic Equations | |
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| Maxwell's Equations under Conformal Transformation | |
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| The Wave Equations | |
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| Transmission Lines | |
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| Two Basic Geometries | |
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| Wires within Parallel Plate Boundaries | |
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| Wire Inside a Square Revisited | |
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| Other Shapes | |
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| Transmission With Lossy Conductors | |
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| Pipe-Enclosed Cable | |
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| Single Wire Above Lossy Ground | |
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| Strip Lines | |
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| Homogeneous (Single Dielectric) Strip Lines | |
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| Inhomogeneities and Microstrip Lines | |
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| Anisotropic Striplines | |
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| Waveguides | |
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| Waveguide Characteristics | |
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| Conformal Mapping of the Transverse Section | |
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| Nonuniform Waveguides | |
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| Other Applications in Electromagnetics and Electrooptics | |
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| Vibrating Membranes and Acoustics | |
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| Membrane Vibrations | |
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| General Considerations | |
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| Upper Bound on Fundamental Frequency | |
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| Analysis of Free Vibrations | |
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| Applications | |
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| Other Solutions of Helmholtz Equation | |
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| Eigenvalues in Some Doubly Connected Regions | |
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| Optimization of Eigenvalues | |
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| Transverse Vibrations of Composite Membranes | |
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| Acoustic Wave Guides | |
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| Transverse Vibrations and Buckling of Plates | |
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| Approximate Determination of Fundamental Frequency | |
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| Examples | |
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| Plates of Arbitrary Shape Subjected to In-Plane Stress | |
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| Higher Frequencies of Vibration, Regular Polygons | |
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| Plates Carrying Concentrated Masses | |
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| Simply Supported Plates | |
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| Clamped Plates | |
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| Stepped Thickness over a Concentric Circular Region | |
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| Buckling under In-Plane Compression | |
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| Optimization of the Calculated Eigenvalues | |
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| Stresses and Strains in an Elastic Medium | |
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| Stresses in a Plane | |
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| Torsion and Crack Problems | |
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| Steady State Heat Conduction in Doubly Connected Regions | |
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| Shape Factors for Circular Bars with Polygonal Perforations | |
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| Analysis of Certain Composite Configurations | |
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| Temperatures in Composite Rod with Heat Generation in a Circular Core | |
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| Heat Transfer in Internally Cooled Fuel Elements | |
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| A Case Study | |
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| A Sampling of Other Problems | |
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| Mixed Boundary Value Problems | |
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| Buried Cables | |
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| Porous Region with Curved Boundary | |
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| Heat Flow in Conjunction with Other Fields | |
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| Transient Heat Transfer in Isotropic and Anisotropic Media | |
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| Isotropic Configurations | |
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| Orthotropic Configurations | |
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| Numerical Results | |
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| Effect of Changing the Orientation of the Axes of Orthotropy | |
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| Orthotropic Plates with Complicated Initial Conditions | |
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| Long Rods with Complicated Initial Conditions, Adiabatic Boundaries | |
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| Combined Fluid Flow and Heat Transfer | |
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| Optimized Rayleigh-Ritz Approach | |
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| Fluid Flow | |
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| Potential Flow | |
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| Simple Cases of Two-Dimensional Potential Flow | |
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| Flow Around Circular Cylinder | |
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| Presence of Circulation | |
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| Air Foils | |
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| Ship Hulls | |
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| Free Streamline Flow: The Hodograph | |
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| Unsteady Flow and Waves | |
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| Porous Media, Diffusion, Flow Normal to Boundaries | |
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| Seepage Underneath a Dam | |
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| Discharge Wells | |
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| Slotted Well Casing | |
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| Measurement of Diffusion Constant | |
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| Vortices and Flow Normal to Boundaries | |
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| Hydrostatic Bearing | |
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| Other Applications | |
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| Conformal Mapping and Other Methods | |
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| Methods of Solution | |
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| Analytical Methods | |
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| Green's Function | |
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| Conformal Mapping | |
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| Numerical Methods | |
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| Interior Methods | |
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| Finite Differences | |
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| Finite Elements | |
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| Boundary Methods | |
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| Source Simulation | |
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| Matching or Collocation | |
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| Boundary Elements | |
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| Moments | |
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| Galerkin | |
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| Monte Carlo Method | |
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| Analogs and Graphical Methods | |
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| Conductive Sheet Analog | |
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| Graphical Field Plotting | |
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| Comparison and Combination of Methods | |
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| Conformal Mapping Coupled With Other Methods | |
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| Emphasis/Deemphasis of Regions | |
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| Infinite Boundaries | |
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| Boundary Simplification | |
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| Boundary Fitted Coordinates | |
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| Mesh Generation | |
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| Anisotropic Media | |
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| Inverse Problem | |
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| Comparison of Numerical and Analog Methods | |
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| Concluding Remarks | |
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| Appendices | |
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| List of Symbols | |
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| Index of Transformations | |
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| Selected Bibliography | |
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| Additional References | |
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| Name and Author Index | |
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| Subject Index | |