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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 and source. Two-dimensional integration: iterated integrals, the example of the Gaussian curve.
Problem Sheet 2: ps, small ps, pdf, small pdf and source. Jacobians, spherical and polar coordinates, div and curl.
Problem Sheet 3: ps, small ps, pdf, small pdf and source. As for first two sheets and vector identities.
Solution for 1, 2 and 3: ps, small ps, pdf, small pdf and source.
Problem Sheet 4: ps, small ps, pdf, small pdf and source. Line integrals, conservative fields.
Problem Sheet 5: ps, small ps, pdf, small pdf and source. Surface integrals.
Problem Sheet 6: ps, small ps, pdf, small pdf and source. As for 4 and 5 plus Green's theorem.
Solution for 4, 5 and 6: ps, small ps, pdf, small pdf and source.
Problem Sheet 7: ps, pdf and source. Conservative forces, Gauss theorem.
Problem Sheet 8: ps, pdf and source. Vector potential, Hodge decomposition.
Problem Sheet 9: ps, pdf and source. As for 7 and 8 plus integrating scalars overs lines etc.
Solution for 7, 8 and 9: ps, small ps, pdf, small pdf and source.
Problem Sheet 10: ps, pdf and source. Fourier series.
Problem Sheet 11: ps, pdf and source. More Fourier series.
Problem Sheet 12: ps, small ps, pdf, small pdf and source. Still more Fourier series and Fourier transforms.
Solution for 10, 11 and 12: ps, small ps, pdf, small pdf and source.
Problem Sheet 13: ps, small ps, pdf, small pdf and source. Fourier transforms and the delta function.
Problem Sheet 14: ps, pdf and source. a multi-dimensional delta functions, an ode.
Problem Sheet 15: ps, small ps, pdf, small pdf and source. As for 13 and 14 plus ODEs.
Problem Sheet 16: ps, pdf and source. ODEs including Euler's equation.