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Mathematical methods in physics


  • Vector analysis
    • General remarks on vectors
    • Scalar product
    • Component representation in cartesian coordinates
    • Non-orthogonal coordinate systems
    • Rotation of the coordinate system
    • Cross product
    • Dyadic procuct
  • Calculus
    • Reminder on differentiation
    • Integral calculus
  • Complex analysis
    • Complex numbers
    • Cauchy-Riemann differential equation
    • Analytic functions
    • Complex integration
    • Residue theorem
  • Vector calculus
    • Vector functions and spatial curves
    • Gradient
    • Divergence and Gauss' theorem
    • Curl and Stokes' theorem
    • Important relations in vector calculus
  • Curvilinear coordinate systems
    • Polar coordinates
    • Cylindric coordinates
    • Spherical coordinates
  • Decomposition in a function basis
    • Fourier series
    • Fourier transformation
    • Delta function
    • Orthogonal polynomials
  • Differential equations
    • Homogeneous differential equations of first order
    • Systems of homogeneous differential equations of first order and differential equations of higher order
    • Inhomogeneous linear differential equations
    • Green function method
    • Solving differential equations by Fourier transformation