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jentschura u advanced classical electrodynamics 2017

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Textbook in PDF format Contents: Preface Integral and Differential Forms of the Maxwell Equations Relation of the Differential to the Integral Form Dirac δ Function Transverse and Longitudinal Components of a Vector Field Vector and Scalar Potentials Lorenz Gauge Coulomb Gauge Electric and Magnetic Field Energies Maxwell Stress Tensor Exercises Green Function of the Harmonic Oscillator Poisson and Laplace Equations in Electrostatics Laplace Equation in Spherical Coordinates Legendre Functions and Spherical Harmonics Expansion of the Green Function in Spherical Coordinates Multipole Expansion of Charge Distributions Addition Theorem for Spherical Harmonics Multipole Expansion in Cartesian Coordinates Multipole Expansion in an External Field Laplace Equation in Cylindrical Coordinates Cylindrical Coordinates and Bessel Functions Orthogonality Properties of Bessel Functions Expansion of the Green Function in Cylindrical Coordinates Eigenfunction Expansions for the Green Function Application to Electrostatics in Spherical Coordinates Summary: Green Function of Electrostatics Exercises Differential Equations of Electrostatics Boundary-Value Problems: One-Dimensional Analogy Green’s Theorem: Dirichlet and Neumann Green Functions Boundary-Value Problems and Laplace Equation Definition of the Functional Derivative Variational Principle and Euler–Lagrange Equations Variations with Constraints Second Functional Derivative and Hilbert Space Variational Calculation of the Capacitance of Plates Variational Calculation for Coaxial Cylinders Exact Integration of the Capacitance of Coaxial Cylinders Coordinate Systems and Special Functions Laplace Equation in a Rectangular Parallelepiped Laplace Equation in a Two-Dimensional Rectangle Boundary Conditions on the Finite Part of a Long Strip Cauchy’s Residue Theorem: A Small Digression Boundary Conditions on the Infinite Part of a Long Strip Cylinders and Zeros of Bessel Functions Dirichlet Green Function for Spherical Shells Boundary Condition of Dipole Symmetry Verification Using Series Expansion Sources and Fields in a Spherical Shell Induced Charge Distributions on the Boundaries .............................................. .............................................. Regularization and Renormalization Potential of a Uniformly Charged Plane Potential of a Uniformly Charged Long Wire Charged Structures in and Dimensions Abraham–Minkowski Controversy Relativistic Dynamics with Radiative Reaction Electrodynamics in General Relativity Exercises Bibliography Index

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Jentschura U. Advanced Classical Electrodynamics 2017.pdf 6.4 MB

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jentschura u advanced classical electrodynamics 2017