IB Maths Tripos

Decks for the IB Maths Tripos: All courses except Electromagnetism, Fluids and Optimisation Made by Neel Nanda. If you find this useful, I'd love to hear about it! And please message me with any errata. Disclaimer: These were entirely written to make sense to me, and according to how I think about maths. I hope they're useful! But some proportion are unlikely to make much sense to other people. To use these, there are Android (free), iOS (paid) apps, or you can download desktop software here https://apps.ankiweb.net/, you can't add shared decks directly through the website Categorised into subdecks by course, and into different note types: Define is definitions Recall is formulae/equation/fact recall Prove is bookwork, stating & proving theorems Archetype is the algorithm for a typical exam question Intuition is a mix of tricks, useful mindsets and high level understanding (note:[name of category] should sort for those) In descending order of how useful I expect them to be as flash cards and ascending order of how interesting I expect it to be to see another perspective on the course! Make a filtered deck if you want to do all the courses in a random order Complex Analysis v Methods was a bit of a fudge, if you're doing just one course sort by tag:CA or tag:CM (will be a bit of irrelevant stuff in methods)

Sample Data

Question	How to solve DEs with Laplace transforms? (ODEs vs PDEs, how to use bcs?)
Back	Transform wrt one variable, gets out an eqn if ODE, an ODE if PDE, each easy to solve.Bcs hopefully fall out of transform, if not then use the limit tricks to use them to constrain form of solution
Extra	Note that the reason this works is that we're converting to an eigenbasis, and in an eigenbasis each component is independent, we can consider each independently
Tags	CM

Definition	Connected Component
Back	Largest connected superset of a point x, ie union of all connected sets containing x. NOTE: Unrelated to closed and open with regards to the entire space, only care about connectedness of the subset, eg [$][0,1)[/$] would be included
Extra	Subtlety, to show it works must show that it's non empty because {x} works
Tags	MTS

Question	How to solve Laplace on the disk?
Back	1. Use FS to get bcs as [$]f(\theta)=\sum f_n e^{in\theta}[/$]2. [$]\phi(z, \bar z)=f_0+\sum (f_n z^n+f_{-n} \bar z^n)[/$]
Extra	[$]z,\bar z[/$] is a natural change of variables because Laplacian becomes nice
Tags	Methods