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 and source. Two-dimensional integration: iterated integrals.
Problem Sheet 2: ps, pdf and source. Two-dimensional integration: iterated integrals, change of coordinates, the Gaussian trick, three-d integration.
Problem Sheet 3: ps, pdf, short pdf and source. Two and three dimensional integration: iterated integrals, change of coordinates, grad.
Solution Sheet 1, 2 and 3: ps, pdf, short pdf and source.
Problem Sheet 4: ps, pdf and source. Grad and div.
Problem Sheet 5: ps, pdf, short pdf and source. Curl, line integrals.
Problem Sheet 6: ps, pdf, short pdf and source. Curl, line integrals, conservative forces.
Solution Sheet 4, 5 and 6: ps, pdf, short pdf and source.
Problem Sheet 7: ps, pdf, short pdf and source. Surface integrals, the Stokes and Greens Theorems.
Problem Sheet 8: ps, pdf, short pdf and source. More Stokes and Greens.
Problem Sheet 9: ps, pdf and source. Gauss, vector potentials and the Hodge decomposition.
Solution Sheet 7, 8 and 9: ps, pdf, short pdf and source.
Problem Sheet 10: ps, pdf, short pdf and source. Fourier series.
Problem Sheet 11: ps, pdf, short pdf and source. Fourier series, complex series, Parceval's theorem
Problem Sheet 12: ps, pdf, short pdf and source. Fourier series, Parceval's theorem, Fourier integrals.
Solution Sheet 10, 11 and 12: ps, pdf, short pdf and source.
Problem Sheet 13: ps, pdf, short pdf and source. Fourier integrals. Delta functions.
Problem Sheet 14: ps, pdf, and source. Delta functions in more than one dimension.
Problem Sheet 15: ps, pdf, short pdf and source. Delta functions, ODEs
Solution Sheet 13, 14 and 15: ps, pdf, short pdf and source.
Problem Sheet 16: ps, pdf, short pdf and source. ODEs: forced damped harmonic oscillator.
Problem Sheet 17: ps, pdf, short pdf and source. ODEs: Euler's Eqn.
Problem Sheet 18: ps, pdf, short pdf and source. Series solution, Froebenius.
Solution Sheet 13, 14 and 15: ps, pdf, short pdf and source. Uncorrected draft
Solution 18 question 4: ps, pdf, short pdf and source.
Problem Sheet 19: ps, pdf, short pdf and source. Froebenius, Legendre.
Problem Sheet 20: ps, pdf. and source. PDEs: existence theorems.
Problem Sheet 21: ps, pdf. and source. PDEs: seperation of variables.