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Problem Sheets
Everything below is available both as Postscript and pdf. If you are using a Unix machine, Postscript will probably open faster and look better on the screen, otherwise, you should click on the pdf version.
- Problem Sheet 1: ps, pdf, short pdf and source. Solutions: ps, pdf, short pdf and source. Orthogonality of the sines and cosines. Oddness and evenness. Fourier series.
- Problem Sheet 2: ps, pdf, short pdf and source. Solutions: ps, pdf, short pdf and source. Periods. The Fourier series. The Complex Fourier series.
- Problem Sheet 3: ps, pdf and source. Solutions: ps, pdf, short pdf and source. The Complex Fourier series, the Fourier transform.
- Problem Sheet 4: ps, pdf and source. Solutions: ps, pdf, short pdf and source. The Fourier transform, the Dirac delta function.
- Fourier Work Sheet: pdf and source. Solutions to q1-3: pdf, short pdf and source. Solutions to q4-5: pdf and source. Solutions to q6-9: pdf, short pdf and source. Some hardish Fourier questions for revision and review purposes. (Note, in the solutions I use the notation "!=" to mean "not equals", the same thing that is more commonly denoted by an = with a line through it, sorry for any confusion this might cause.)
- Problem Sheet 5: ps, pdf and source. Solutions: ps, pdf, short pdf and source. The Fourier series and transform, the Dirac delta function.
- Problem Sheet 6: ps, pdf and source. Solutions: ps, pdf, short pdf and source. First order linear odes, second order homogenous linear odes with constant coefficients.
- Problem Sheet 7: ps, pdf and source. Solutions: ps, pdf, short pdf and source. Second order homogenous linear odes with constant coefficients, homogeneous and inhomogeneous.
- Problem Sheet 8: ps, pdf and source. Solutions: ps, pdf, short pdf and source. Euler equations, series solutions.
- ODE Work Sheet: pdf and source. Solutions to q1-3: pdf and source. Solutions to q4-7: pdf short pdf and source. Solutions to q8-9: pdf short pdf and source. Solutions to q10-11: pdf short pdf and source. Lots of ODE questions for revision and review purposes.
The source is the original LaTeX file used to produce the file along with any figures in xfig, ps and xmaple, multiple files are tarred and gzipped.