1. Minutiae (Password Protected Page)
2. Overview of Sturm-Liouville theory: the maths behind quantum mechanics
3. Maple code for quantum scattering from an Eckart potential
4. The p-adic number field as a completion of the rationals
5. Topological equivalence of the 2-sphere and the extended complex plane
6. Pythagorean triples in a stereographic projection
7. Gauss’s flux theorem for gravity, Poisson’s equation and Newton’s law
8. Brownian motion and fractional Brownian motion: self-similar processes
9. Applying Chebyshev’s inequality and Borel-Cantelli lemma to Brownian motion
10. A variant of Einstein’s partial differential equation for Brownian motion
11. A division algorithm for converting prime reciprocals into ternary numbers
12. A note on the quaternion rotation operator
13. Different branch cuts for the principal argument, log and square root functions
14. On classifying singularities, with a quick look at a Schwarzschild black hole
15. Matrix calculus approach to changing variables in Laplace’s equation
16. Changing variables in the square of the angular momentum operator
17. Variational setups yielding Newton’s second law and Schrödinger’s equation
18. Alternative approaches to formulating geodesic equations on manifolds
20. Invariance under rotations in space and conservation of angular momentum
21. Dirichlet character tables up to mod 11
22. Overview of the Lie theory of rotations
23. Solving Schrödinger’s equation by B-spline collocation
24. Proving the relativistic rotation paradox
25. Decomposition of Lorentz transformations using orthogonal matrices
26. Classical and quantum harmonic oscillators
27. A scale-free probability distribution must be a power law
28. A simple Yule-Simon process and Zipf’s law
29. Approximating logarithms of large numbers
30. From random walk to Brownian motion with drift
31. Strange notations in mathematical probability
32. A couple of results involving the beta function
33. Useful methods in Laplace transform theory
34. Quick way to explain the concept of a solid angle
35. Some mathematics relating to phonons
36. Free particle in a ring with a periodic boundary condition
37. Bra-ket formalism of quantum mechanical measurement
38. Differentiating a double integral with respect to its upper limits
39. Markov’s inequality and the Cramér-Chernoff bounding method
40. The role of the Legendre transform in large deviation theory
41. Two versions of the exponential cumulant generating function
42. Inverse Fourier transform of a characteristic function
43. Applying the Bromwich integral to a cumulant generating function
44. Using an asymptotic approximation to obtain a closed form solution
45. Using Lagrange’s interpolation formula to prove complicated sum/product identities
46. A Phys. Rev. Letter by M Wilkinson on large deviation analysis of rapid-onset rainfall
47. Accurate analytical approximation formulae for large-deviation analysis of rainfall
48. A note on mathematics in Latin
49. Monomer injections leading to oscillatory behaviour in a model of rain formation
50. Study of a Lagrangian function approach to analysing raindrop growth
51. A spline approximation scheme for large deviation theory problems
52. Derivation and manipulation of a generalised Erlang distribution
53. Royal Holloway lectures (Quantitative Methods in Economics II)
54. Quick memo on five basic types of first-order differential equation
55. Integrating integer powers of a sine function via a hypergeometric function
56. Electronics (Password Protected Page)
57. Surface charge density of a conducting disk from that of a conducting ellipsoid
58. Useful formula for integrating integer powers of a sine function over a period
59. Equivalent integral formulae for Bessel functions of the first kind, order zero
60. A note on a Fourier sine series solution to a heat flow problem
61. Legendre-transforming a Lagrangian mechanics problem into a Hamiltonian one
62. Overview of mathematical modelling ideas in single particle quantum mechanics
63. A note on Singular Value Decomposition and Principal Components
64. Boolean array indexing and finding multiple zeros of a function at once
65. Fast Fourier Transform by hand
66. Quadratic B-Spline interpolation of points on a modulus function
67. A note on an unusual system of two masses connected by a spring
68. Using wxdrawdf in MAXIMA to plot a phase portrait with a stable limit cycle
69. Canonical derivation of the mean and variance of the binomial distribution
70. From simple random walk to Wiener process and diffusion equation
71. Ornstein-Uhlenbeck process: derivation and simulation of its pdf and moments
72. Fourier transform of a function that is scaled and translated in either order
73. Zero-field singularity of magnetic susceptibility in a 4-D Ising model
74. Boltzmann distribution, Gibbs-Shannon entropy and Helmholtz free energy
75. Using the Python library NetworkX to find all Hamiltonian cycles in a graph
76. A max-flow/min-cut network problem solved both manually and with Python
77. Using Prüfer sequences to count and classify irreducible labelled 10-node trees
78. Why we can omit the modulus symbol in ln(|x|) in the integrating factor method
Dr Christian P. H. Salas 