Iterative Methods for Calculating Static Fields and Wave Scattering by Small Bodies
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1. Basic Problems.- 1. Statement of the Electrostatic Problems for Perfect Conductors.- 2. Statement of the Basic Problem for Dielectric Bodies.- 3. Reduction of the Basic Problems to Fredholm's Integral Equations of the Second Kind.- 4. Reduction of the Static Problems to Fredholm's Integral Equations of the First Kind.- 2. Iterative Processes6 for Solving Fredholm's Integral Equations for the Static Problems.- 1. An Iterative Process for Solving the Problem of Equilibrium Charge Distribution and Charge Distribution on a Conductor Placed in an Exterior Static Field.- 2. An Iterative Process for Solving the Problem of Dielectric Bodies in an Exterior Static Field.- 3. A Stable Iterative Process for Finding the Equilibrium Charge Distribution.- 4. An Iterative Process for Calculating the Equilibrium Charge Distribution on the Surface of a Screen.- 3. Calculating Electric Capacitance.- 1. Capacitance of Solid Conductors and Screens.- 2. Variational Principles and Two-Sided Estimates of Capacitance.- 3. Capacitance of Conductors in an Anisotropic and Nonhomogeneous Medium.- 4. Physical Analogues of Capacitance.- 5. Calculating the Potential Coefficients.- 4. Numerical Examples.- 1. Introduction.- 2. Capacitance of a Circular Cylinder.- 3. Capacitance of a Parallelepiped of Arbitrary Shape.- 4. Interaction Between Conductors.- 5. Calculating the Polarizability Tensor.- 1. Calculating the Polarizability Tensor of a Solid body.- 2. The Polarizability Tensor of a Thin Metallic Screen.- 3. The Polarizability Tensors of a Flaky-Homogeneous Body or a System of Bodies.- 4. Variational Principles for Polarizability.- 6. Iterative Methods of Solving some Integral Equations Basic in the Theory of Static Fields: Mathematical Results.- 1. Iterative Methods of Solving the Fredholm Equations of the Second Kind at a Characteristic Value.- 2. Iterative Processes for Solving Some Operator Equations.- 3. Iterative Processes for Solving the Exterior and Interior Boundary Value Problems.- 4. An Iterative Process for Solving the Fredholm Integral Equations of the First Kind with Pointwise Positive Kernel.- 7. Wave Scattering by Small Bodies.- 1. Introduction.- 2. Scalar Wave Scattering: The Single-Body Problem.- 3. Scalar Wave Scattering: The Many-Body Problem.- 4. Electromagnetic Wave Scattering.- 5. Radiation from Small Apertures and the Skin Effect for Thin Wires.- 6. The Inverse Problem of Radiation Theory.- Problems.- Bibliographical Notes.- List of Symbols.