Mathematics

• Integration
  • General Case
  • Special Cases
  • Motivation
  • Example
• Residue Theorem
  • Computation of Residues
  • Useful Formulas
  • Complex Substitution
• Fourier Transform
• Discrete Fourier Transform
• Laplace Transform
• Periodic Functions
• Polar Coordinates
  • Example
• Spherical Coordinates
  • Example I
  • Example II
• Argument function, atan2
• Multiple Argument Formulas
  • sin(a x)
  • cos(a x)
• Delta Function
• Distributions
• Variations and Functional Derivatives
  • Functions of One Variable
  • Functions of several variables
  • Functionals
  • Examples
• Dirac Notation
• Homogeneous functions
  • Example 1
  • Example 2
• Green Functions
  • Introduction
  • Boundary Conditions
  • Symmetry
  • Examples
• Binomial Coefficients
• Double Sums
• Triangle Inequality
• Gamma Function
• Incomplete Gamma Function
  • Example
• Factorial
• Double Factorial
  • Example
• Legendre Polynomials
  • Example I
  • Example II
  • Example III
  • Example IV
• Spherical Harmonics
  • Examples
• Gaunt Coefficients
  • Example I
  • Example II
  • Example III
  • Example IV
  • Example V
  • Example VI
• Wigner 3j Symbols
  • Examples
• Multipole Expansion
• Hypergeometric Functions
  • Convergence Conditions
  • Elementary and Special Functions
  • Example I
  • Example II
  • Example III
• Feynman Parameters
  • Example 1
  • Example 2
• Groups
  • Theory
  • Crystallographic Point Groups
  • Applications of finite groups
  • Continuous Groups
  • Literature
• Wigner D Function
  • Derivation
• Ordinary Differential Equations
  • Finite Difference Formulas
  • Integrating ODE
  • Radial Poisson Equation
• Linear Algebra
  • Scalar Product
  • Projections
• Differential Geometry
  • Manifolds
  • Examples
• Operators
  • Introduction
  • Spectrum
  • Derivative Operator
  • Sturm–Liouville Operator
  • Angular Momentum Operator