http://www.ptrinh.com/ 2026-05-14T23:23:14+00:00 http://www.ptrinh.com/ http://www.ptrinh.com/ttp://www.ptrinh.com/lib/tpl/white/images/favicon.ico text/html 2016-05-09T13:04:27+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/404?rev=1462799067&do=diff I think you're lost. text/html 2016-05-09T10:34:57+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/about?rev=1462790097&do=diff Temporary text/html 2024-09-02T09:55:56+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/aims-organisation?rev=1725270956&do=diff AIMS organisation links and details This is a temporary page to ensure that AIMS organisers have access to details. * Here is a link to the Google Spreadsheet for organising speakers. * AIMS mailing list organisation Sample invitation template Dear XXX, Insert personal message here are just below. We would love to invite you to give a seminar our Applied and Interdisciplinary Mathematics Seminar series ( text/html 2025-01-31T15:39:01+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/aims?rev=1738337941&do=diff Applied and Interdisciplinary Mathematics Seminars This page has been moved to <https://bath-aims.github.io/> text/html 2024-03-11T09:36:00+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/aims_2023?rev=1710149760&do=diff Zoom instructions In order to have the best experience, we have a strong preference to host the seminars in person. However, for accessibility, we also open it to online audiences as well. Please if you plan to join online, it is often helpful to let the organiser know in advance text/html 2024-09-02T14:33:02+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/aims_2024?rev=1725287582&do=diff Zoom instructions In order to have the best experience, we have a strong preference to host the seminars in person. However, for accessibility, we also open it to online audiences as well. Please if you plan to join online, it is often helpful to let the organiser know in advance text/html 2023-10-09T09:56:03+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/aims_unsubscribe?rev=1696845363&do=diff Unsubscribe Want to leave the mailing list? Send an email to sympa@lists.bath.ac.uk from the relevant account with the subject line: and leave the body blank. text/html 2019-10-30T09:14:21+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/altius?rev=1572426861&do=diff The Maths Department are delighted to offer you to opportunity to come and find about how ‘Big Data’ is being used to understand, model and predict business performance. On Friday 8th November, staff from Altius <https://www.altiusdata.com> will be giving a talk, from 12:15, followed by lunch, during which you will have the opportunity for informal discussions with the team. text/html 2021-03-22T17:06:46+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/ara-prob3?rev=1616432806&do=diff text/html 2021-03-26T11:29:42+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/ara-prob5?rev=1616758182&do=diff Monotonic shock solutions This is the caller code. You can call it 'KS_monotonic_caller.m'. Copy the below script and paste the code in and save it in an appropriate directory. The caller code will require 'KSode.m'. Save it and run it from the same directory. Make sure you name it with the correct upper and lower-case characters. text/html 2021-03-26T11:29:08+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/ara?rev=1616758148&do=diff Exponential asymptotics for physical applications This page will link some relevant information for the ARA Spring School session. We will be hosting four talks. * Exercises for tutorials and discussions: Overleaf * Outlines and references for talks: text/html 2025-12-01T19:32:57+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/bathhydrology2025?rev=1764617577&do=diff <https://commons.wikimedia.org/w/index.php?curid=35304322> A workshop between mathematical and flood risk communities We look forwards to welcoming you at this workshop in Bath on 3-4 December. The workshop will provide a forum for mathematicians and hydrological modellers to explore in depth how theoretical analysis can provide insights about the behaviour, calibration and robustness of rainfall-runoff models. The motivation for the workshop includes recognition that there is a vast array of… text/html 2025-12-05T10:43:19+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/bathhydrology2025questions?rev=1764931399&do=diff Mathematics and Hydrology Questions 2025 At the recent workshop between mathematical and flood risk communities, participants were asked early in the workshop to pose those questions they were interested in answering. Some of the responses are recorded below. We did some filtering of the questions into general subject areas (biased to maths). text/html 2019-03-16T19:57:01+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/blog?rev=1552766221&do=diff Blog text/html 2019-10-14T09:26:37+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/calendar?rev=1571045197&do=diff P.H. Trinh University of Bath Calendar text/html 2016-05-09T10:34:57+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/calendars?rev=1462790097&do=diff Michaelmas 2015 Calendars Physics Class of 2015 Maths Class of 2015 Maths Class of 2014 text/html 2023-11-17T15:19:00+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/chaos-circuits?rev=1700234340&do=diff Chaos in circuits Inductance meter with an arduino: <https://www.youtube.com/watch?v=BGjV5vUvGPc> Analog circuits <https://www.youtube.com/watch?v=DFKm0K5O7ak> Paul Horwitz: <http://seti.harvard.edu/unusual_stuff/misc/lorenz.htm> text/html 2020-09-11T11:20:34+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/chaos?rev=1599823234&do=diff MA30060 Dynamics and Chaos (2020-21') We use this website to largely keep track of supplementary videos and problem-set solutions for the course. The rest of the material, which includes the complete set of lecture notes, can be found on the Moodle site. text/html 2023-10-05T14:30:09+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/cnm?rev=1696516209&do=diff Centre for Nonlinear Mechanics October 2023-24: This is a temporary holding page for the Centre for Nonlinear Mechanics. text/html 2020-09-15T15:10:33+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/collaborators?rev=1600182633&do=diff Collaborators and co-authors Note to self: I am currently too busy to keep this page updated! Need to find a better mechanism...(Sept 2020) The world is filled with wonderful researchers. Here are a few of them. United Kingdom Prof. S. Jonathan Chapman text/html 2020-02-19T14:31:08+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/dropin?rev=1582122668&do=diff Bath applied maths weekly drop-in (2019-20') I've moved information from this to: bathmaths.com/dropin Please go there for the current schedule! Updated: 19 Feb 2020. text/html 2021-09-06T01:50:02+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/dynsys?rev=1630893002&do=diff The mathematics of patterns This image is produced by modeling the reaction and diffusion of two chemical concentrations, for which one is originally set to be highly concentrated in certain regions to produce the lettering shown. Dark areas correspond to high concentration of one of the species. Eventually, the dynamics of the two species are such that stripped patterns are seen. text/html 2023-08-04T11:02:43+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/espresso?rev=1691146963&do=diff Espresso notes These are a loose collection of notes about espresso brewing. Water treatment Water hardness is a function of two main components: calcium and magnesium. Hardness is typically measured in mg/L of equivalent calcium carbonate, which is found by adding together the concentration of calcium and magnesium ions with multipliers of 2.5 and 4.1, respectively. The formula is text/html 2026-01-23T16:15:36+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/flooding-new-directions?rev=1769184936&do=diff New directions for theoretical flooding research This page collects some ideas and material for new research directions on flooding at Bath, primarily motivated from some of the challenges proposed as part of the Integrative Think Tank 17 programme with the Environmental Agency and JBA Trust. text/html 2026-05-06T10:35:27+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/fun_movies?rev=1778063727&do=diff Movies I (used?) to love watching movies. At some point, I need to settle on a Top list. For the moment, I will add items to this list when I remember. I will shuffle the list when I feel like it. There is no real logic to the ranking. It is based simply on text/html 2019-09-20T04:28:22+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/gametheory?rev=1568953702&do=diff Game Theory Let's play prisoner's dilemma. * Group 1 text/html 2016-05-09T10:34:58+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/getinfo?rev=1462790098&do=diff Attempting to get info text/html 2026-05-03T09:01:24+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/graphics_tutorials?rev=1777798884&do=diff Tutorials Inkscape <https://www.youtube.com/watch?v=tFMqIsGcoIo> text/html 2026-03-09T11:18:22+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/group?rev=1773055102&do=diff Trinh research group at Bath Our research group focuses on the development of mathematical methodologies --- primarily asymptotic analysis and perturbation theory --- for applications in applied mathematics and real-world phenomena. If you are interested in my more recent work on flooding, there are some details here: text/html 2021-01-01T14:13:45+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/growpi?rev=1609510425&do=diff Raspberry Pi Grow Hello papi. For your Christmas present I prepared for you an automated watering kit. This kit is very customizable and uses a Raspberry Pi computer. If you learn how to program, you will be able to add many pumps to this kit and set up more advanced systems. text/html 2021-01-01T14:17:50+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/growpi_parts?rev=1609510670&do=diff Parts First, make sure that you have all the parts. You can click the links to see where I purchased the items. * Raspberry Pi 3 Model A+: this is the main computer * 1 x MicroSD card: I have plugged the micro SD card into the Raspberry Pi * Pimoroni grow LCD device: this “hat” plugs into the 40-pin header of the Raspberry Pi and allows the sensors to be connected text/html 2021-01-01T14:03:17+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/growpi_setupremote?rev=1609509797&do=diff Setting up remote login Hi papi. The next step is to setup remote login into the Raspberry Pi. It is likely the case that you will not want to access the Raspberry Pi by keyboard/mouse/monitor and instead you can login to the machine via your iPad or Desktop PC. text/html 2021-01-01T14:08:02+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/growpi_setuprpi?rev=1609510082&do=diff Navigation Home -> Current guide -> Next guide: setting up remote login Setting up the Raspberry Pi Hello papi. The first step is to set up the Raspberry Pi. I will call this the RPi. The Rpi is, itself, a desktop computer. You can read more about it on the product page. In terms of the desktop computer, it has these features: text/html 2021-01-01T14:05:05+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/growpi_testlcd?rev=1609509905&do=diff Test LCD screen Papi, it is now time to test the LCD screen. Attach the Grow Hat Mini to the 40-pin connection on the Raspberry Pi. You do not need to shut off the computer when you do this. Video guide Navigation Home --> text/html 2021-01-19T04:26:59+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/growpi_testmoisture?rev=1611030419&do=diff OK papi, now try and run the moisture sensitivity test. Connect the three sensors to the Grow and run the code 01_test_moisture.py text/html 2023-10-19T12:35:38+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/guides?rev=1697718938&do=diff Student guides This is a misc. collection of guides for students, used at various points. * Hosting, networking, and attending seminars * Software text/html 2023-10-19T10:19:20+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/guides_seminars?rev=1697710760&do=diff Hosting seminars, networking, and asking the right questions This is a short to-do list and listing of discussion topics to cover during the Student Led Symposia at Bath in 2023. Hosting seminars As part of your journey as PhD students, you may have the opportunity to host and organise seminars. This can include departmental seminars, conference/workshop co-organising, postgraduate student seminars, and so forth. Here are some items to think about. text/html 2023-10-19T12:52:01+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/guides_software?rev=1697719921&do=diff Software Backup and cloud software: * Automatic backup schemes: rsync, Time Machine * It is crucially important to have a backup scheme * Cloud repository: Dropbox, Google Drive, OneDrive Referencing : * Search engines: Google Scholar mainly text/html 2016-05-16T23:38:06+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/interest?rev=1463441886&do=diff Things of interest * Roux text/html 2026-01-13T19:22:15+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/interesting?rev=1768332135&do=diff Interesting thoughts and tidbits It is a tradition for academics to collect interesting, and perhaps randomly sorted, tidbits which are shared via their personal website. In the era of AI slop and social media, perhaps this is ever more important. text/html 2025-06-03T20:11:38+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/it_bibliography?rev=1748981498&do=diff Tools for bibliography management bibiman: TUI for interacting with bibtex database <https://codeberg.org/lukeflo/bibiman> pdf2bib: extract bibtex direct from PDF <https://github.com/MicheleCotrufo/pdf2bib> bibmanager: bibtex manager; good for cleaning up: <https://github.com/pcubillos/bibmanager> papis uses yaml <https://github.com/papis/papis/?tab=readme-ov-file> papis neovim: <https://github.com/jghauser/papis.nvim> Instructions on using papis with zotero: text/html 2026-04-16T11:05:06+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/it_cas?rev=1776337506&do=diff Computer Algebra Systems (CAS) Computer algebra systems, such as Mathematica, Maple, SageMath, Matlab's Symbolic Math Toolbox, etc. are very useful for the following tasks (ranked in importance): * 1 = Deriving and manipulating exact closed-form quantities or special functions, including pattern recognition text/html 2024-03-23T23:43:22+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/it_cloudstorage?rev=1711237402&do=diff Using cloud storage I had previously made this video to get students used to sharing files on Cloud Storage. Our research group had been using Google Drive, but to be honest, we might prefer to move to OneDrive in the future since this space is provided by the University of Bath. text/html 2024-12-03T23:55:25+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/it_email?rev=1733270125&do=diff University email University blocks normal non-Outlook email options. Some info here to potentially bypass: <https://www.digitalocean.com/community/tutorials/how-to-setup-a-davmail-exchange-gateway-on-a-debian-7-vps> <https://github.com/LukeSmithxyz/mutt-wizard/issues/601> text/html 2025-04-08T13:00:45+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/it_firedrake?rev=1744117245&do=diff Firedrake notes Notes on installing firedrake via the guide: <https://www.firedrakeproject.org/firedrake/install.html> This worked on Homebreak on macOS. Note I operated on my home directory but probably a bad idea compared to operating within a distinct directory. Download the utility: Using the complex-variable version: text/html 2024-08-20T20:55:58+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/it_macos?rev=1724187358&do=diff MacOS setup and applications A little collection of tools used on MacOS. Tools for a better UI experience * Hidden Bar to declutter * Source Code Syntax Highlight and QLMarkdown to display code on the Quicklook. text/html 2025-05-02T18:40:41+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/it_matlab_figures?rev=1746211241&do=diff Generating nice images in Matlab Here are some brief details and tips for developing a good workflow for generating publication-quality images. 1. A workflow for saving images As you become a more experienced researcher, you will learn the value of developing a workflow where images can be easily re-generated. This means that you can easily replot the images when you are finalising the presentation. `startup.m``open brewermap` text/html 2024-03-23T23:40:42+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/it_matlab_startup?rev=1711237242&do=diff Matlab startup file Use a similar startup.m script below to set figure defaults. This ensures that axis labels are appropriately sized. Run this command to open the startup file Once you have run the above, the relevant startup file should appear. You can copy and paste the below as a starter. Comment in or out the relevant scripts. text/html 2024-11-28T10:32:05+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/it_python?rev=1732789925&do=diff Notes in getting start with Python Python can be complicated to set up, particularly if using virtual environments. Virtual environments and choosing a distribution I used to setup Python via Miniconda in order to have virtual python environments (see text/html 2023-11-20T10:18:24+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/it_thunderbird?rev=1700475504&do=diff Thunderbird settings You may be interested in how to get plain text emails using Thunderbird with universities that use Office 365. FIrst off, you need to use Owl for Exchange (paid add-on). * Main OWL account: change the main setting for composing to plain text under text/html 2025-01-28T09:11:56+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/it_typesetting?rev=1738055516&do=diff Typesetting This is a current repository of information related to academic typesetting. Quarto Currently, I use Quarto to typeset my lecture notes, providing facility between HTML and LaTeX outputs. * Cameron Patrick on generating a thesis with Quarto: text/html 2024-09-12T14:38:55+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/it_webpages?rev=1726151935&do=diff Webpages You can create your own webpage at Bath. Go here: <https://people.bath.ac.uk/> Login to your Linux server: ssh linux.bath.ac.uk Note you can set up authorized keys via: <https://alvinalexander.com/linux-unix/how-use-scp-without-password-backups-copy/> text/html 2024-07-28T00:48:38+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/it_windows?rev=1722127718&do=diff Windows setup Windows absolutely drives me crazy, but there may be good reasons why it should be used as an alternative to Linux and MacOS. Some notes here on setup. Interface * X-Mouse Button Control is an app to provide customisation on mice control. * Mouse Wheel accelerator provides the kind of inertia scrolling you get on Macs. text/html 2024-02-14T22:18:37+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/it_wsl?rev=1707949117&do=diff Setting up Ubuntu with WSL On Windows 11: * Enable virtualization on your motherboard (if required) * Install WSL: <https://learn.microsoft.com/en-us/windows/wsl/install> * text/html 2024-07-04T22:54:36+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/it_xdrive?rev=1720133676&do=diff Accessing XDrive or OneDrive at Bath Two ways. then Alternatively (on Linux) * Ensure you are connected to the University VPN. * Open Files and select Other Locations from the list on the left. * Enter the server address smb:campus.bath.ac.uk/files of the network drive in text field in the bottom right. - Click Connect - Select Connect As: Registered User - Put in your University username and password and set the Domain field to CAMPUS. - Click Connect. - Now the X drive sho… text/html 2024-06-08T21:45:34+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/itt20?rev=1717883134&do=diff ITT20 with BeZero and RR Here is a dump of references. * Course notes from MA40255 Viscous Fluid Dynamics by JD Evans * Above notes are closely related to: @book{ockendon1995viscous, title={Viscous flow}, author={Ockendon, Hilary and Ockendon, John R}, volume={13}, year={1995}, publisher={Cambridge University Press} text/html 2025-01-05T01:04:02+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/latex?rev=1736039042&do=diff Coding in LaTeX I currently code using neovim and vimtex. I wouldn't recommend it given the rather extreme difficulty. Nevertheless here are some resources for my own use: <https://jdhao.github.io/2019/03/26/nvim_latex_write_preview/> <https://github.com/jdhao/nvim-config/blob/master/README.md#ctags> Use of makefiles and latexmk <http://paulklemm.com/blog/2016-03-06-watch-latex-documents-using-latexmk/> Use of sty and cls and font files I put all my style and cls files into a folder accessi… text/html 2024-02-15T13:39:30+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/ma30287?rev=1708004370&do=diff MA30287 Maths of Planet Earth Key links: * Moodle: <https://moodle.bath.ac.uk/course/view.php?id=60108> * Github lecture notes: <https://github.com/trinh/MA30287> * Github codes folder: <https://github.com/trinh/ma30287-codes> * Lecture notes: <https://trinh.github.io/MA30287/> Noteable instructions * Go to Noteable via the Moodle link * Run the +Gitrepo tool with: <https://github.com/trinh/ma30287-codes.git> text/html 2022-12-06T10:09:08+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/meeting-hosting-academics?rev=1670321348&do=diff Meeting and hosting academics This page is intended for PhD students and postdocs who are learning to meet or host academics (e.g. for seminars). Why Academia and mathematics is a terribly small world. As evidenced by the Mathematics Geneology project, almost everybody is connected in a very immediate way. By meeting with academics or helping to host visitors or speakers, you're working towards extending your professional network. This might give you opportunities through: text/html 2020-02-15T11:35:12+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/misc?rev=1581766512&do=diff Miscellaneous collection Statistics * A very nice illustration of frequentist and bayesian conclusions text/html 2021-11-07T03:42:54+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/news_2021-10-04?rev=1636256574&do=diff Group report (October 2021) As we enter the start of the 2021-22 academic term, it is time to bring our summer to a close, to celebrate the various comings and goings, and to look forwards to all sorts of new things. MMath success First, we congratulate our MMath and BSc project students for completing their dissertations in such a difficult year. Ana Cassaniga Simmons did hers on text/html 2023-08-24T14:08:07+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/nimbus?rev=1692886087&do=diff Running on nimbus General links * Introduction class: <https://research-software-skills-bath.github.io/intro_nimbus_hpc/00_schedule.html> Launching an interactive node for Matlab Here is the command that allows you to run an interactive Matlab sesson salloc --account=EB-MA3194M-0XX --partition=spot-fsv2-1 --qos=spot-fsv2-1 --nodes=1 --cpus-per-task=1 --time=23:00:00 text/html 2023-08-14T09:09:06+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/oist?rev=1692004146&do=diff Links for OIST workshop Big Google document of organisational info, including participants list: <https://docs.google.com/spreadsheets/d/1Ir6FqcXZknx6gaMq16ieLca9LAPSmx9vnAn4SdcrajE/edit#gid=837195478> Google document for symposium planning: <https://docs.google.com/document/d/1GYC5RAHz1K6KxTs_sWdiqQfef52hRu4zTTP08tpCogM/edit> Spreadsheet for symposium <https://docs.google.com/spreadsheets/d/1WjoN3CJuegk3efL8VorMK5-zH3Oxu56sio_XCoEn6n0/edit?usp=sharing> text/html 2023-09-04T05:07:06+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/oist_chairing?rev=1693804026&do=diff Chairing sessions Thank you for helping to chair the sessions! Here is a to-do checklist: * Consult with the organisers before the start of the first session if there are any special announcements. * Warn the speakers that you will raise a finger/hand if they are over time and apologise for rudeness. text/html 2020-03-18T12:35:06+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/onlinemeetings?rev=1584534906&do=diff Online research and teaching meetings I'm currently experimenting with using Zoom instead of Skype. This seems to be advantageous on a few fronts: * It has less overhead in terms of signups, verifications, etc. * It seems much simpler in terms of conducting meetings between multiple people text/html 2016-05-09T10:34:58+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/playground?rev=1462790098&do=diff <texit info> author=MySelf title=MyTitle </texit> Playground Testing testing testing. text/html 2020-04-15T10:22:26+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/projects?rev=1586946146&do=diff Bath BSc and MMath projects Hello! This is a temporary page that I will fill with additional details about projects I am offering to University of Bath students for their BSc project or MMath dissertation. 2020-21 projects This year, I decided to offer a really interesting project on non-photorealistic rendering that I'm hoping the right student will pick up! text/html 2020-04-10T13:11:11+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/projects_divergentphysics?rev=1586524271&do=diff MMath project 2020-21' Divergent series and quantum physics In the study of quantum theories (like quantum mechanics and quantum field theory), one of the key questions is how to grapple with the interpretation of divergent series. As a simple example, you have learned how to solve the regular Schrodinger harmonic oscillator, where the potential function looks like a quadratic, $$ V(x) = \frac{1}{2} x^2. $$$E_n = (n + 1/2)$$$ V(x) = \frac{1}{2} x^2 + \lambda x^4. $$$$ E_n = \left(n + \frac{1}… text/html 2020-04-10T13:55:48+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/projects_flooding?rev=1586526948&do=diff MMath projects Mathematical modelling of flooding Examine the present news releases on the issue of flooding in the UK and this will tell you all about the pressing need to develop accurate and reliable predictive theories for flooding. A typical question that concerns us is how flooding can be predicted in sites where there is limited data. In this case, mathematical models can be used to anticipate the chance of flooding. text/html 2020-04-15T00:57:06+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/projects_music?rev=1586912226&do=diff MMath projects Can you hear the shape of a drum? If you took the second-year MA20223 Vectors & PDEs course, you might remember discussing the applications of Fourier series to studying music (or more generally signal processing). There are a lot of beautiful applications of spectral and harmonic analysis to sound and music, and this project will delve into those applications. text/html 2020-05-03T09:32:34+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/projects_npr?rev=1588498354&do=diff MMath project for 2020-21 Non-photorealistic rendering of Riemann surfaces The ability to create visualisations of mathematical surfaces or diagrams is an immensely important skill that has been rarely addressed in your studies at Bath. This is a project about the visualisation of maths. text/html 2020-04-01T13:18:27+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/ramp?rev=1585747107&do=diff If you're here, then you're helping to edit the spreadsheet to add your name to the list of people who want to contribute to the RAMP covid-19 application. Editable link to the spreadsheet text/html 2023-10-19T13:33:57+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/random?rev=1697722437&do=diff Here is a page text/html 2024-11-29T10:35:56+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/references-request?rev=1732876556&do=diff Student/Postdoc references Hi! You are on this page because you've asked me for a reference letter. Previously, I used to write letters from scratch, following discussions with the requester. However, more recently, I have developed a new workflow for writing references, and I have found it to be very useful, and ensures a strong reference that captures the right details. text/html 2016-05-09T10:34:58+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/reports?rev=1462790098&do=diff text/html 2025-04-14T08:58:26+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/research?rev=1744621106&do=diff Research You will be able to find a mostly-complete list of my publications on Google Scholar. A good way to learn about what I do is to examine my PhD student talks! Here are a few that have been recorded over the last little while. * Piotr Morawiecki gives a talk on mathematical models of flooding * Josh Shelton gives a talk on parasitic gravity-capillary waves * Yyanis Johnson-Llambias gives a talk on water waves due to flows past smoothed bodies For researchers who are interested … text/html 2024-01-18T07:08:25+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/research_flooding?rev=1705561705&do=diff Asymptotics for intermodel comparisons of flood-estimation models [Burton Fleming floods at Christmas time. (CC BY-SA 2.0) by Phillip Andrew Carl Taylor] One of the key problems in flood estimation is to predict the flow in the river after an intensive rainfall. Hydrologists use a variety of methods for such predictions, ranging from physical (PDE) to conceptual to statistical models. These models are often based on different assumptions; such assumptions may be subtle and hidden, and perhaps … text/html 2025-06-14T09:31:26+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/research_pdmcode?rev=1749893486&do=diff An example of a conceptual rainfall-runoff model Here is an example implementation of the Probability Distributed Model. text/html 2022-05-03T08:17:55+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/ripples?rev=1651565875&do=diff Capillary ripples on steep gravity waves Placeholder to host Josh's videos. text/html 2019-10-04T11:05:49+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/samba-events?rev=1570187149&do=diff SAMBa events calendar Here lies the SAMBa events calendar. The public link can be accessed here. Integrating the calendar You can integrate the calendar in a variety of ways: * Add it to your Google Calendar via the calendar ID * Access via the public text/html 2023-03-31T14:37:02+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/siamposter?rev=1680273422&do=diff text/html 2024-12-03T23:56:46+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/sidebar?rev=1733270206&do=diff * Home * Research * Teaching * Research group * AIMS seminars text/html 2026-01-23T16:14:29+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/start?rev=1769184869&do=diff Hello! Welcome to my homepage. Please access links to the left by clicking the button with the four horizontal lines. For information on the Bath Hydrology workshop in Dec 2025 see here. During the 2025-26 year, I am pleased to announce that I will be working with JBA Trust as a Knowledge Exchange Catalyst fellow for the text/html 2020-09-27T16:24:32+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/stream?rev=1601223872&do=diff Live stream page All meetings are recorded and will be uploaded for you afterwards in case you cannot attend. You may want to log in a few minutes ahead of time: www.twitch.tv/ptrinh It may be useful for you to download the app or create an account (in order to chat). text/html 2024-03-23T23:41:47+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/student-research-guide?rev=1711237307&do=diff Student researcher guide This is a currently-written and updated guide providing some tips to students and researchers on aspects related to research. Writing reports * LaTeX referencing Coding * Notes on getting started with Python * Using a Matlab startup file * Generating nice images in Matlab * Using cloud storage text/html 2025-02-10T14:22:43+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/students_meetingemails?rev=1739197363&do=diff Meeting emails Hello! It is really helpful when doing research, to try and initiate the research meeting with a short progress update and set of questions. I find that this can help students better track where they are currently in their research, and also help to articulate questions or points of discussion. $F$ text/html 2025-08-01T10:01:11+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/talks?rev=1754042471&do=diff Talks archive 2025 text/html 2025-08-01T10:08:53+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/talks_2025-lms-careers?rev=1754042933&do=diff LMS Summer School at Bath Careers Talk This was a one-hour talk given to talented summer school students at the 2025 LMS Summer Undergraduate Mathematics School hosted at the University of Bath. [LMS Careers talk] Short summary: * Slide 2: I started with a short introduction to who I was and my background. I mentioned that PhD and post-PhD experiences are highly variable so you have to take my advice for what it is. text/html 2024-09-26T09:42:20+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/teaching?rev=1727343740&do=diff Teaching This used to be a somewhat active portion where I would list all sorts of interesting items about mathematics teaching. However, these days universities (including Bath) have moved towards having central repository systems for courses, which means that all teaching material is uploaded there and only granted to Bath students. At some point, I will have to decide what to do with this page, but for the moment, I shall list my courses at Bath. text/html 2024-12-02T13:18:31+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/teaching_eaforscience?rev=1733145511&do=diff Exponential asymptotics for the physical sciences This will be a course page for the Autumn 2024 Taught Centre Course Live stream This course will be live streamed on Mondays and Wednesdays at 3pm on Twitch via <https://www.twitch.tv/ptrinh> <https://www.twitch.tv/ptrinh> Video archives The videos can be found either on Twitch or on a separate text/html 2016-05-09T10:34:59+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/teachingcv?rev=1462790099&do=diff Teaching history text/html 2025-04-29T11:50:36+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/thesis-writing?rev=1745927436&do=diff Student BSc/MMath writeup Some notes to help students write up. LaTeX Use the prepared thesis format. You may prefer to tweak this to your satisfaction (e.g. you may prefer a report-style rather than a book-style). This documentclass uses the memoir package and you can look up the memoir documentation. text/html 2023-11-10T11:30:54+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/visiting-bath-maths?rev=1699615854&do=diff Visiting Mathematical Sciences at Bath Most people will be arriving at Bath Spa station. From there, you can either take a taxi or a bus. Both are quite convenient and are similar in time. * Taxis are best taken directly outside of the Bath Spa Station front doors. Alternatively if you are coming from somewhere else, we would suggest Abbey V Cars tel:01225464646 text/html 2020-04-23T07:33:27+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/vpde?rev=1587627207&do=diff MA20223 Vectors and PDEs (2019-20') Welcome to the off-Moodle website. Exam study guide * 2019-20' topic study guide * [What is on the exam (2019-20')?] * Solutions for 2018-19 exam found on the Moodle site. Important links * Tutor details * Moodle site Special COVID-19 links * How we will proceed with cancellation of face-to-face lectures * Discussion board for questions * Live stream page Course diary * MA20223 2019-20' diary * text/html 2020-03-14T15:41:39+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/vpde_2019-20-diary?rev=1584200499&do=diff MA20223 2019-20' diary Week 1 Lecture 1 (4 Feb 2020) * Introductions and preliminaries (course structure; problem sets; hand-ins) * Why are you here and why should you take this course? * A mathematical model of transport * A review of multivariable calculus (Chap. 2) text/html 2020-03-18T13:13:06+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/vpde_covid19?rev=1584537186&do=diff MA20223 COVID-19 Edition As you will have heard, due to the recent coronavirus situation, we will be taking our learning online (see University of Bath announcement). This means that your face-to-face lectures and tutorials will be cancelled from Wednesday 17 March to (currently) the end of Easter. text/html 2020-04-30T20:43:14+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/vpde_errata?rev=1588279394&do=diff Errata for the 2019-20' MA20223 materials Typed notes * The Corollary 8.4 on convex sets should specify that “if every straight line (that includes a point on the interior of $\Omega$) intersects $\partial\Omega$ at two points at most”. * There were some typos in the derivation of the wave equation in Chap. 10. It should instead look like this:$x\in[0, L]$$x\in[0, \pi]$$0 < x < \pi$$0 < x < 2$$\lambda^2$$\lambda$$G$$u(x, 0) = f(x)$$u_t(x, 0) = g(x)$$\partial \phi$$\nabla \phi$$dx$$dy$$\si… text/html 2020-03-20T19:19:38+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/vpde_lecture20?rev=1584731978&do=diff MA20223 Lecture 20 Fourier convergence theorem We will first start by reviewing Lecture 19 and our introduction of the Fourier convergence theorem. This involves Theorem 12.5 in the notes. In particular, the theorem states that if $f$ is a $2\pi$-periodic function with $f$$f'$$(-\pi, \pi)$$f$$x$$$ \frac{1}{2}[f(x_-) + f(x_+)] = \frac{a_0}{2} + \sum_{1}^\infty [a_n \cos(nx) + b_n \sin(nx)] $$$2\pi$$[-\pi, \pi]$$[-L, L]$$2L$$f$$2L$$$ f(x) \sim \frac{a_0}{2} + \sum_{n=1}^\infty \left[ a_n \cos\… text/html 2020-03-20T21:22:18+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/vpde_lecture21?rev=1584739338&do=diff MA20223 Lecture 21 Example 1 We finished the example from lecture 18, which was to calculate the Fourier series of the $2\pi$-periodic extension of the function $f(x) = x^2$ defined on $[0, 2\pi]$. The Fourier series is given by $$ f(x) \sim \frac{a_0}{2} + \sum_{n=1}^\infty [a_n \cos(nx) + b_n\sin(nx)] $$ where we showed that $$ a_0 = \frac{1}{\pi}\frac{(2\pi)^3}{3}, \qquad a_n = \frac{4}{n^2}, \ n \geq 1 $$ and $$ b_n = -\frac{4\pi}{n}. $$ We then used a Matlab code to plot it. $2\pi$$f(x… text/html 2020-03-26T13:42:08+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/vpde_lecture22?rev=1585230128&do=diff MA20223 Lecture 22 This lecture is about terminology but it is important not to be bogged down by terminology. You will practice by doing! This lecture covered part of Chapter 15. An example We're now going to return to partial differential equations (which motivated Fourier series). We will mainly study $$ \begin{gathered} u_t = \kappa u_{xx}, \quad x\in[0, L], t \geq 0 \\ u(0, t) = 0 = u(L, t) \\ u(x, 0) = f(x). \end{gathered} $$$x = 0$$x = L$$f(x)$$u(x,t)$$v(x, t)$$u + v$$u(\mathbf{x}, … text/html 2020-03-26T17:05:06+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/vpde_lecture23?rev=1585242306&do=diff MA20223 Lecture 23 The 1D heat equation with zero Dirichlet conditions We will complete our determination of the Fourier series solution of the heat equation as presented in the previous lecture. This was the problem of: $$ \begin{gathered} u_t = \kappa u_{xx}, \quad x\in[0, \pi], t \geq 0 \\ u(0, t) = 0 = u(\pi, t) \\ u(x, 0) = f(x) = 1. \end{gathered} $$ $$ u(x, t) \sim \sum_1^\infty \left[b_n \sin\left(\frac{n\pi x}{L}\right)\right]. $$ where $b_n$ will be the Fourier sine coefficien… text/html 2020-04-04T22:00:55+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/vpde_lecture24?rev=1586037655&do=diff Lecture 24: Computation of the heat equation III Example 15.4: Solution of the inhomogeneous Dirichlet problem This lecture starts off with Example 15.4 from the notes, where we look to solve $$ \begin{gathered} u_t = u_{xx} \\ u(0, t) = 2, \qquad u(\pi, t) = 1 \\ u(x, 0) = 0. \end{gathered} $$ We show that the solution is given by $$ u(x, t) = U(x) + \sum_{n=1}^\infty B_n \sin(nx) \mathrm{e}^{-n^2 t} $$ where we have found the steady-state solution $$ U(x) = 2 - \frac{x}{\pi}, $$$$ B_… text/html 2020-04-04T21:33:45+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/vpde_lecture25?rev=1586036025&do=diff Lecture 25: Wave equation I This lecture will do apply separation of variables and Fourier series in order to solve for the wave equation on a finite interval. Definition 16.1 (1D wave equation with homogeneous Dirichlet BCs We look to solve $$ \begin{gathered} u_{tt} = c^2 u_{xx} \\ u(0, t) = 0 = u(L, t) \\ u(x, 0) = u_0(x), \\ u_t(x, 0) = v_0(x), \end{gathered} $$ $L$$$ u(x, t) = X(t) T(t), $$$T(t)$$X$$T$$$ u_n(x, t) = \sin\left(\frac{n\pi x}{L}\right) \left[ A_n \cos\left(\frac{n\p… text/html 2020-04-04T21:46:36+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/vpde_lecture26?rev=1586036796&do=diff Lecture 26: Computation of the wave equation II Theorem 16.3 (Solution of the zero-Dirichlet wave equation) At the start of the lecture, we continue deriving the Fourier coefficients for the problem of zero Dirichlet conditions on the wave equation. We show that $$ u(x, t) = \sum_{n=0}^\infty \sin\left(\frac{n\pi x}{L}\right) \left[ A_n \cos\left(\frac{n\pi ct}{L}\right) + B_n \sin\left(\frac{n\pi ct}{L}\right)\right] $$$$ A_n = \frac{2}{L} \int_0^L u_0(x) \sin\left(\frac{n\pi x}{L}\right) \… text/html 2020-04-04T21:09:56+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/vpde_lecture27?rev=1586034596&do=diff Lecture 27: Problem set 8 and solutions of the wave equation This lecture follows along for [problem set 8] and its [solutions]. We managed to get through Q1, Q3, and made a start on the (exhausting) Q4---or rather this was at the point I was exhausted (to pick up Q4 in another video!) text/html 2020-04-20T11:07:38+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/vpde_lecture28?rev=1587380858&do=diff Lecture 28: Solving the heat equation text/html 2020-04-20T11:07:02+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/vpde_lecture29?rev=1587380822&do=diff Lecture 29: d'Alembert's solution of the wave equation text/html 2020-04-20T11:06:19+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/vpde_lecture30?rev=1587380779&do=diff Lecture 30: d'Alembert's solution of the wave equation text/html 2020-04-16T08:31:59+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/vpde_lecture31?rev=1587025919&do=diff Lecture 31: d'Alembert's solution III This lecture will do d'Alembert's solution of the wave equation text/html 2020-04-16T12:34:56+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/vpde_lecture32?rev=1587040496&do=diff Lecture 33: Uniqueness of solutions I In this lecture, we'll prove uniqueness for two variants of the heat equation. The different variants you should consider as as follows (all posed on $x\in[0, L]$): $$ \begin{aligned} u_t &= \kappa u_{xx}, \\ u(x, 0) &= 0, \end{aligned} $$ with either Dirichlet conditions [D] $$ \begin{aligned} u &= T_0 \quad (x = 0), \\ u(L, t) &= T_1\quad (x = L), \end{aligned} $$ or Neumann conditions [N] $$ \begin{aligned} u_x &= G_0 \quad (x = 0), \\ u_x &= G_1\quad… text/html 2020-04-20T11:05:21+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/vpde_lecture33?rev=1587380721&do=diff Lecture 33: Uniqueness of the wave equation text/html 2020-04-23T08:16:22+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/vpde_lecture34?rev=1587629782&do=diff Lecture 34: The maths of music I The Fourier spectra The techniques of Fourier analysis that you've learned in this are remarkable for a few reasons, but one reason is that it sets up a correspondence between understanding real space and Fourier space.$$ f(x) \sim \sum_{k=1}^\infty b_k \sin(\lambda_k x) $$$\lambda_k = k$$b_k = 4/(k\pi)$$k$$k$$(x, f(x))$$(k, b_k)$$(k, b_k)$$k$$f(x)$$f(t)$$f(t)$$$ f(t) = \sin(2\pi f t) \qquad 0 \leq t \leq t_f. $$$f$$s^{-1}$$2\pi/(2\pi f) = 1/f$$f = 100Hz$$F_… text/html 2020-04-27T17:40:36+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/vpde_lecture35?rev=1588009236&do=diff Lecture 35: Maths of music II I don't want to dwell on the details of how the fft command works but it is enough to talk about analogies. Suppose we give you an $N$ vector $f_n$ with elements $n = 0, 1, 2, \ldots N-1$ that represents the signal we want to process. Think instead of a function $f(n)$$[0, 2L] = [0, N]$$L = N/2$$N$$$ f(n) = \sum_{k=0}^{N-1} \left[a_k \cos\left(\frac{k\pi n}{L}\right) + b_k \sin\left(\frac{k\pi n}{L}\right)\right] $$$$ f(n) = \sum_{k=0}^{N-1} F_k \exp\left(i\frac… text/html 2020-04-27T17:39:52+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/vpde_lecture36?rev=1588009192&do=diff Lecture 36: Problem set 10 text/html 2020-02-20T13:57:29+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/vpde_solutionsrequest?rev=1582207049&do=diff MA20223 Solutions Request I have been informed, and am fully aware that obtaining the solutions before I have tried my best to complete the problem sets may have a detrimental effect on my own study. Below you must type the following to access the link to the solutions: text/html 2020-02-22T14:50:08+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/vpdesolution201920garden-belgium-reached-race?rev=1582383008&do=diff Solutions page Welcome to the solutions page for students who want to see solutions ahead of schedule. Use at your own risk. * * * * * * * * * text/html 2024-03-23T23:39:23+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ptrinh.com/writing_bibtex?rev=1711237163&do=diff LaTeX referencing Here is a brief YouTube guide I made on how to use bibtex for referencing.