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  • Print publication year: 2006
  • Online publication date: March 2013

2 - Fourier theory

Summary

To be sung to the tune of Gilbert and Sullivan's Modern Major General:

I am the very model of a genius mathematical,

For I can do mechanics, both dynamical and statical,

Or integrate a function round a contour in the complex plane,

Yes, even if it goes off to infinity and back again;

Oh, I know when a detailed proof's required and when a guess'll do

I know about the functions of Laguerre and those of Bessel too,

I've finished every tripos question back to 1948;

There ain't a function you can name that I can't differentiate!

There ain't a function you can name that he can't differentiate [Tris]

I've read the text books and I can extremely quickly tell you where

To look to find Green's Theorem or the Principle of d'Alembert

Or I can work out Bayes' rule when the loss is not Quadratical

In short I am the model of a genius mathematical!

For he can work out Bayes' rule when the loss is not Quadratical

In short he is the model of a genius mathematical!

Oh, I can tell in seconds if a graph is Hamiltonian,

And I can tell you if a proof of 4CC's a phoney 'un

I read up all the journals and I'm ready with the latest news,

And very good advice about the Part II lectures you should choose.

Oh, I can do numerical analysis without a pause,

Or comment on the far-reaching significance of Newton's laws

I know when polynomials are soluble by radicals,

And I can reel off simple groups, especially sporadicals. […]

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