1. K. F. Riley, M. P. Hobson & S. J. Bence (2006) Mathematical Methods for Physics and Engineering, 3rd edition, Cambridge University Press.
  2. J. Miles (1971) Integral Transforms in Applied Mathematics, Cambridge University Press (reprinted 2008).
    (For discrete eigenfunction expansions, Bessel functions, and orthogonal polynomials, but minimal coverage of Hankel and Mellin transforms.)
  3. D. G. Duffy (2004) Transform Methods for Solving Partial Differential Equations, 2nd edition, Chapman and Hall/CRC Press.
  4. Brian Davies Integral Transforms and Their Applications, 3rd edition 2002, Springer. (Beware of typos . . . )
  5. I. N. Sneddon Fourier Transforms, Dover reprint 1995, chapters 1 to 3.
  6. L. C. Andrews and B. K. Shivamoggi (1999) Integral Transforms for Engineers, SPIE Press.
  7. R. Piessens “The Hankel Transform”
  8. J. Bertrand, P. Bertrand and J.P. Ovarlez, “The Mellin Transform” available from http://www.jeanphilippeovarlez.com
  9. Two chapters of The Transforms and Applications Handbook, 2nd edition (2000) CRC Press.
    (Both chapters contain far more material than is necessary, though the expansions in discrete sums \( \sum_n a_n J_0(\alpha_n r) \) from earlier lectures also appears in the Hankel transform chapter as the “finite Hankel transform”.)
Last modified: Tuesday, 14 March 2023, 7:40 PM