Time: 12:00 - 13:00 (Tuesday, 4th February 2025).
Agenda: Introduction to topic and approving outline.
Attendance:
- Katie Arnold (27620935)
- William Fayers (27378661)
- Torin (26424071)
- Tom Ward (26479576)
- Daniel Morris (26700885)
- Alex Rushworth (27554937)
- Hayden Loyseau (27635146) - 9 mins late.
- Andrei Z…
Last Meeting | Next Meeting (planned Tuesday 14:00, 11th February 2025)
- Recommended to read the recommended reading (linked below as useful sources) - very comprehensive (source 2), although older so has table solutions (which are now obsolete).
- Use future supervisor meetings to ask specific questions.
- Discussed recurrence relations within Bessel functions (which only explain relationships between three functions, not what each function actually is - their existence is also not fully understood; they’re just embedded in the mathematics, even if you start with wrong values and work down then you can get better values, e.g. for significant precision).
- Discussed types (e.g. first and second type): and are some main types, but there are also spherical Bessel functions (sort of like siblings, relates to quantum physics also, like with Schrödinger equation) and others.
- Future plans is to look into Bessel functions, choose bits that are interesting, then research further into them (e.g. differential equations parts, properties, equations, etc.).
- We confirmed our outline, although derivation seems too much for one person (but we’ll see 🌝).
- Can see where we can add in plots, although they’re standard functions in places like Maple - but maybe we could re-create these anyway, or se alternative programs.
- INB3305 is a great room, but we can’t currently book it - Andrei’s looking into this (but for now we’ll just use it when empty).
- Refined outline and who’s contributing to each chapter:
- Derivation (Will, Hayden)
- Boundary Conditions (Katie)
- Types (Alex, Tom)
- Applications (Dan, Torin)
- just skim and cover interesting parts, like drum membranes.
- Note: also able to email to see Andrei at other times, or just drop in if the door is open.
Mentioned GIF demonstrating radial part of circular membrane.
Useful sources
[1] H. Jeffreys and B. Swirles, Methods of Mathematical Physics, Cambridge Univ. Press, 1956. [2] M. Abramowitz and I. Stegun, Handbook of Mathematical Functions, Martino Fine Books, 2014. [3] https://en.wikipedia.org/wiki/Bessel_function
Source 1 is more classic, source 2 is maybe more useful.
Source 2 PDF: M. Abramowitz and I. Stegun, Handbook of Mathematical Functions - BESSEL FUNCTIONS ONLY.pdf.