fourier notes

(TODO) clean up this page and extract only relevant info

handwritten collection of notes: notes fourier.pdf

ana IV notes, ana IV sheet 10, ana IV sheet 11, ana IV sheet 12: corr 1.51 (fourier integrals + residues), par 2.4 (convolution defs), chap 3 (fourier) ana IV H10.2 (fourier convolution), 10.4 (fourier examples), 11.2 (fourier syms), 11.4 (diffusion equation with drift), 11.5 (wave equation), 12.2 (heisenberg uncertainty principle)

mmp chap 4: slide 9-10 (finite series approximation), slide 18-19 (gibbs phenomena), slide 25-29 (convolution thm, props, parseval thm), slide 42-25 (1d wave eq)
mmp chap 5: slide 3-6 (reprs of dirac delta), slide 10 (FS <-> FT), slide 19-25 (FT examples, link with residue thm), [repeat of ana IV, for sake of completion: slide 29-31 (convolution, parseval/plancherel, energy spectrum)], slide 34-46 (various examples of fun ODE's and PDE's)
mmp formulaire given for fun (careful about convention, mmp uses +ikx with sqrt(2pi) factor, instead of -ikx with unit factor)

plasma notes: chap 6.1.a math technique (FT in electromag), chap 6.5 general derivation of dispersion relation

phys IV : good recap on maxwell, dispersion, energy density

notebook: numerical fourier demo. see

• np.fft
• np.fft.rfftfreq
• np.fft.rfft

useful wikipedia links:

• fourier series
• plancherel theorem
• gibbs phenomenon

(laplace transform)[https://en.wikipedia.org/wiki/Laplace_transform], related to FT, useful in signal processing and also solving PDEs