| Preface | p. vii |
| Errata | p. xxi |
| Introduction and Overview | p. 1 |
| Structure of the Book | p. 3 |
| Modern Applications of Conformal Mapping | p. 7 |
| Electromagnetics | p. 8 |
| Vibrating Membranes & Acoustics | p. 8 |
| Transverse Vibrations & Buckling of Plates | p. 9 |
| Elasticity | p. 10 |
| Heat Transfer | p. 11 |
| Fluid Flow | p. 12 |
| Other Areas | p. 12 |
| Growth in Scope of Applications | p. 14 |
| Basic Mathematical Concepts | |
| Transformation of Coordinates | p. 16 |
| Transformation by Means of Complex Functions | p. 21 |
| Analytic Functions | p. 23 |
| Conformality and Uniqueness | p. 25 |
| A Selection of Mapping Functions | p. 33 |
| Elementary Transformations | p. 34 |
| Linear Transformation | p. 34 |
| Power Transformation | p. 36 |
| Inverse or Reciprocal Transformation | p. 40 |
| Logarithmic and Exponential Transformations | p. 43 |
| Hyperbolic Transformation | p. 45 |
| Interpretation of Elementary Transformation | p. 47 |
| Composite Transformations | p. 48 |
| Bilinear Transformation | p. 49 |
| Joukowski Transformation | p. 53 |
| Trigonometric and Hyperbolic Transformations | p. 57 |
| Maxwell's Transformation | p. 58 |
| Schwarz-Christoffel Transformation for Polygons | p. 60 |
| The Basic Method | p. 60 |
| Trigons | p. 68 |
| Maxwell's Transformation Revisited | p. 71 |
| Joukowski's Transformation Revisited | p. 76 |
| Mapping the Interior of a Rectangle | p. 77 |
| The Rectangle | p. 77 |
| The Square | p. 81 |
| Weierstrass Formulation for Rectangle and Triangle | p. 82 |
| Application | p. 83 |
| The Inverse and Further Notes | p. 84 |
| Mapping the Regions Exterior to Rectangles and Between Rectangles | p. 84 |
| Polygons with Rounded Corners | p. 88 |
| Exploiting Symmetry | p. 93 |
| Numerical Methods | p. 95 |
| Methods of Approximation | p. 95 |
| Series Approximations | p. 98 |
| Mapping the Interior of the Unit Circle | p. 99 |
| Method of Simultaneous Equations (Kantorovich) | p. 100 |
| Mapping Exterior Regions | p. 104 |
| Successive Approximations (Fornberg) | p. 104 |
| Variational Methods | p. 105 |
| Carrying out the Minimization | p. 108 |
| Orthogonalization | p. 111 |
| Minimizing the Perimeter, Orthogonal Polynomials | p. 113 |
| Example of Minimum Perimeter Method | p. 116 |
| Minimizing the Area, Comparison of Methods | p. 119 |
| Additional Extremum Principles | p. 119 |
| Additional Approximation Methods | p. 120 |
| Integral Equation Methods | p. 120 |
| Method of Lichtenstein and Gershgorin | p. 122 |
| Method of Theodorsen and Garrick | p. 128 |
| Method of Symm | p. 133 |
| Comments on Integral Equation Methods | p. 135 |
| Numerical Determination of Schwarz-Christoffel Transformation | p. 135 |
| The Parameter Problem | p. 137 |
| Averting Singularities at Infinity | p. 138 |
| Method of Trefethen | p. 139 |
| Method of Foster and Anderson | p. 141 |
| Doubly Connected Regions | p. 145 |
| General Observations | p. 146 |
| Symmetry and Circles | p. 148 |
| Symmetric Region with an Inner Circle | p. 150 |
| Symmetric Region with an Outer Circle | p. 152 |
| Other Configurations; Accuracy | p. 153 |
| Mathematical Models | p. 155 |
| Potential Fields and the Laplace Equation | p. 155 |
| The Laplace Equation under Conformal Mapping | p. 158 |
| Steady Current Flow, Electrostatics, Magnetostatics | p. 161 |
| Temperature Field | p. 165 |
| Fluid Flow Field | p. 166 |
| The Poisson Equation | p. 167 |
| The Two-Dimensional Wave Equation | p. 169 |
| The Two-Dimensional Diffusion Equation | p. 170 |
| Bending, Buckling, and Vibrations of Plates | p. 171 |
| Boundary Conditions | p. 173 |
| Sources and Sinks | p. 173 |
| Lines of Symmetry | p. 176 |
| Dirichlet and Neumann Conditions | p. 179 |
| Extracting the Results | p. 181 |
| Nonplanar Fields and Nonuniform Media | p. 183 |
| Nonplanar Fields | p. 183 |
| Description of Difficulties | p. 183 |
| Potential Fields with Rotational Symmetry | p. 188 |
| Symmetric Field in a Wedge-Shaped Region | p. 193 |
| General Coordinate Transofrmations in Three Dimensions | p. 198 |
| Cases with Rotational Symmetry Revisited | p. 201 |
| Transformation in Two Planes | p. 205 |
| Nonuniform Media | p. 209 |
| Field at Boundary Separating Different Media | p. 209 |
| Anisotropic Media | p. 214 |
| Quasiconformal Mappings | p. 220 |
| Static Fields in Electricity and Magnetism | p. 222 |
| Area-Networks and Hall Generators | p. 223 |
| Two-Terminal Devices | p. 223 |
| Three-Terminal Devices | p. 227 |
| Resistivity Measurement with Four Electrodes | p. 232 |
| Hall Effect Transducers | p. 235 |
| Nonuniform Resistivities | p. 237 |
| Electric Fields in Dielectrics | p. 238 |
| Electrode Shapes for Uniform Field Strength | p. 239 |
| Deflection Head for an Ink-Jet Printer | p. 241 |
| Magnetic Fields of Stationary Structures | p. 244 |
| Transformers | p. 244 |
| Magnetic Recording Heads | p. 251 |
| Perpendicular Field | p. 251 |
| Longitudinal Field | p. 254 |
| Magnetic Field of Rotating Machines | p. 259 |
| Field Analysis in Salient Pole Machines | p. 259 |
| Other Applications | p. 265 |
| Transmission Lines and Waveguides | p. 266 |
| The Basic Equations | p. 267 |
| Maxwell's Equations under Conformal Transformation | p. 269 |
| The Wave Equations | p. 270 |
| Transmission Lines | p. 273 |
| Two Basic Geometries | p. 273 |
| Wires within Parallel Plate Boundaries | p. 275 |
| Wire Inside a Square Revisited | p. 279 |
| Other Shapes | p. 283 |
| Transmission With Lossy Conductors | p. 284 |
| Pipe-Enclosed Cable | p. 288 |
| Single Wire Above Lossy Ground | p. 289 |
| Strip Lines | p. 290 |
| Homogeneous (Single Dielectric) Strip Lines | p. 290 |
| Inhomogeneities and Microstrip Lines | p. 301 |
| Anisotropic Striplines | p. 308 |
| Waveguides | p. 309 |
| Waveguide Characteristics | p. 310 |
| Conformal Mapping of the Transverse Section | p. 313 |
| Nonuniform Waveguides | p. 315 |
| Other Applications in Electromagnetics and Electrooptics | p. 318 |
| Vibrating Membranes and Acoustics | p. 320 |
| Membrane Vibrations | p. 320 |
| General Considerations | p. 320 |
| Upper Bound on Fundamental Frequency | p. 322 |
| Analysis of Free Vibrations | p. 324 |
| Applications | p. 326 |
| Other Solutions of Helmholtz Equation | p. 328 |
| Eigenvalues in Some Doubly Connected Regions | p. 332 |
| Optimization of Eigenvalues | p. 332 |
| Transverse Vibrations of Composite Membranes | p. 337 |
| Acoustic Wave Guides | p. 339 |
| Transverse Vibrations and Buckling of Plates | p. 341 |
| Approximate Determination of Fundamental Frequency | p. 342 |
| Examples | p. 344 |
| Plates of Arbitrary Shape Subjected to In-Plane Stress | p. 348 |
| Higher Frequencies of Vibration, Regular Polygons | p. 350 |
| Plates Carrying Concentrated Masses | p. 355 |
| Simply Supported Plates | p. 356 |
| Clamped Plates | p. 360 |
| Stepped Thickness over a Concentric Circular Region | p. 366 |
| Buckling under In-Plane Compression | p. 371 |
| Optimization of the Calculated Eigenvalues | p. 373 |
| Stresses and Strains in an Elastic Medium | p. 375 |
| Stresses in a Plane | p. 375 |
| Torsion and Crack Problems | p. 385 |
| Steady State Heat Conduction in Doubly Connected Regions | p. 389 |
| Shape Factors for Circular Bars with Polygonal Perforations | p. 389 |
| Analysis of Certain Composite Configurations | p. 393 |
| Temperatures in Composite Rod with Heat Generation in a Circular Core | p. 399 |
| Heat Transfer in Internally Cooled Fuel Elements | p. 407 |
| A Case Study | p. 408 |
| A Sampling of Other Problems | p. 422 |
| Mixed Boundary Value Problems | p. 422 |
| Buried Cables | p. 423 |
| Porous Region with Curved Boundary | p. 424 |
| Heat Flow in Conjunction with Other Fields | p. 425 |
| Transient Heat Transfer in Isotropic and Anisotropic Media | p. 426 |
| Isotropic Configurations | p. 426 |
| Orthotropic Configurations | p. 434 |
| Numerical Results | p. 438 |
| Effect of Changing the Orientation of the Axes of Orthotropy | p. 443 |
| Orthotropic Plates with Complicated Initial Conditions | p. 447 |
| Long Rods with Complicated Initial Conditions, Adiabatic Boundaries | p. 455 |
| Combined Fluid Flow and Heat Transfer | p. 458 |
| Optimized Rayleigh-Ritz Approach | p. 460 |
| Fluid Flow | p. 464 |
| Potential Flow | p. 464 |
| Simple Cases of Two-Dimensional Potential Flow | p. 465 |
| Flow Around Circular Cylinder | p. 467 |
| Presence of Circulation | p. 468 |
| Air Foils | p. 470 |
| Ship Hulls | p. 473 |
| Free Streamline Flow: The Hodograph | p. 474 |
| Unsteady Flow and Waves | p. 477 |
| Porous Media, Diffusion, Flow Normal to Boundaries | p. 479 |
| Seepage Underneath a Dam | p. 479 |
| Discharge Wells | p. 481 |
| Slotted Well Casing | p. 483 |
| Measurement of Diffusion Constant | p. 484 |
| Vortices and Flow Normal to Boundaries | p. 485 |
| Hydrostatic Bearing | p. 486 |
| Other Applications | |
| Conformal Mapping and Other Methods | p. 491 |
| Methods of Solution | p. 492 |
| Analytical Methods | p. 493 |
| Green's Function | p. 493 |
| Conformal Mapping | p. 495 |
| Numerical Methods | p. 496 |
| Interior Methods | p. 497 |
| Finite Differences | p. 497 |
| Finite Elements | p. 497 |
| Boundary Methods | p. 499 |
| Source Simulation | p. 499 |
| Matching or Collocation | p. 500 |
| Boundary Elements | p. 500 |
| Moments | p. 500 |
| Galerkin | p. 500 |
| Monte Carlo Method | p. 501 |
| Analogs and Graphical Methods | p. 501 |
| Conductive Sheet Analog | p. 502 |
| Graphical Field Plotting | p. 504 |
| Comparison and Combination of Methods | p. 505 |
| Conformal Mapping Coupled With Other Methods | p. 505 |
| Emphasis/Deemphasis of Regions | p. 505 |
| Infinite Boundaries | p. 506 |
| Boundary Simplification | p. 507 |
| Boundary Fitted Coordinates | p. 507 |
| Mesh Generation | p. 508 |
| Anisotropic Media | p. 508 |
| Inverse Problem | p. 509 |
| Comparison of Numerical and Analog Methods | p. 509 |
| Concluding Remarks | p. 511 |
| Appendices | |
| List of Symbols | p. 513 |
| Index of Transformations | p. 516 |
| |
| Selected Bibliography | p. 522 |
| Additional References | p. 568 |
| Name and Author Index | p. 570 |
| Subject Index | p. 577 |
| Table of Contents provided by Ingram. All Rights Reserved. |
