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# IB Maths Tripos

0.74MB. 0 audio & 954 images. Updated 2019-05-31.

The author has shared 1 other item(s).

## Description

## Sample (from 578 notes)

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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 |

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## Reviews

**on**

Good for me to learn about courses i did not go to

**on**

\forall \epsilon, | Neeliness - Cleanliness | < \epsilon

I don't think decks like this can be used "as is", though they certainly make a great base when creating your own deck.

I don't think decks like this can be used "as is", though they certainly make a great base when creating your own deck.

**on**

Neel = god