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Mathematical concepts II


  • Vector analysis
    • Scalar and vector fields in electrodynamics
    • Divergence
    • Curl
  • Vector analysis in orthogonal curvilinear coordinates
    • Line, surface, and volume element
    • Differential operators in orthogonal curvilinear coordinates
  • Complex numbers and complex analysis
    • Complex numbers
    • Cauchy-Riemann conditions
    • Analytic functions
    • Integration in the complex plane
    • Residue theorem
  • Expansion in systems of orthogonal functions
    • Motivation
    • Fourier series
    • Fourier transformation
    • Delta function
    • Solution of linear differential equations by means of Fourier transformation
    • Legendre polynomials
  • Partial Differential equations
    • Examples and classification
    • Solution by separation of variables
      • Cartesian coordinates
      • Spherical coordinates