3. Mathematics¶
- 3.1. Integration
- 3.2. Complex Numbers
- 3.3. Residue Theorem
- 3.4. Fourier Transform
- 3.5. Fourier Transform of a Periodic Function (e.g. in a Crystal)
- 3.6. Discrete Fourier Transform
- 3.7. Fast Fourier Transform (FFT)
- 3.8. Laplace Transform
- 3.9. Hilbert Transform
- 3.10. Periodic Functions
- 3.11. Polar Coordinates
- 3.12. Spherical Coordinates
- 3.13. Argument function, atan2
- 3.14. Multiple Argument Formulas
- 3.15. Delta Function
- 3.16. Distributions
- 3.17. Variations and Functional Derivatives
- 3.18. Dirac Notation
- 3.19. Homogeneous Functions (Euler’s Theorem)
- 3.20. Green Functions
- 3.21. Binomial Coefficients
- 3.22. Double Sums
- 3.23. Triangle Inequality
- 3.24. Gamma Function
- 3.25. Incomplete Gamma Function
- 3.26. Factorial
- 3.27. Double Factorial
- 3.28. Fermi-Dirac Integral
- 3.29. Legendre Polynomials
- 3.30. Spherical Harmonics
- 3.31. Gaunt Coefficients
- 3.32. Wigner 3j Symbols
- 3.33. Multipole Expansion
- 3.34. Hypergeometric Functions
- 3.35. Feynman Parameters
- 3.36. Groups
- 3.37. Wigner D Function
- 3.38. Ordinary Differential Equations
- 3.39. Linear Algebra
- 3.40. Differential Geometry
- 3.41. Operators
- 3.42. Variational Formulation of PDEs