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Mathematical Foundations for Electromagnetic Theory

  • Linear Analysis
    • Introduction
    • Linear Space
    • Inner Product Space
    • Normed Linear Space
    • Hilbert Space
    • Best Approximation
      • eqn(1.56), eqn(1.57),
      • Example 1.21
      • Example 1.22
      • Example 1.23
        • eqn(1.70)
    • Operators in Hilbert Space
      • eqn(1.76), eqn(1.77)
      • Example 1.23
        • eqn(1.80)
      • Example 1.25
        • eqn(1.81), eqn(1.83) to eqn(1.93)
    • Method of Moments
      • eqn(1.106) to eqn(1.128)***
    • Appendix-Proof of Projection Theorem
      • eqn(A.1) to eqn(A.10)
    • Problems 1.1 to Prob. 1.31
  • The Green’s Function Method
    • Introduction
    • Delta Function
    • Sturm-Liouville Operator Theory
    • Sturm-Liouville Problem of the First Kind
    • Sturm-Liouville Problem of the Second Kind
    • Sturm-Liouville Problem of the Third Kind
  • The Spectral Representation Method
    • Introduction
    • Eigenfunctions and Eigenvalues
    • Spectral Representations for SLPI and SLP2
    • Spectral Representations for SLP3
    • Green’s Functions and Spectral Representations
    • Problems
  • Electromagnetic Sources
    • Introduction
    • Delta Function Transformations
    • Time-Harmonic Representations
    • The Electromagnetic Model
    • The Sheet Current Source
    • The Line Source
    • The Cylindrical Shell Source
    • The Ring Source
    • The Point Source
    • Problems
  • Electromagnetic Boundary Value Problems
    • Introduction
    • SLPI Extension to Three Dimensions
    • SLPI in Two Dimensions
    • SLP2 and SLP3 Extension to Three Dimensions
    • The Parallel Plate Waveguide
    • Iris in Parallel Plate Waveguide
    • Aperture Diffraction
    • Scattering by a Perfectly Conducting Cylinder
    • Perfectly Conducting Circular Cylinder
    • Dyadic Green’s Functions
    • Problems