The last five years have seen an immense growth in the use of symbolic computing and mathematical software packages such as Maple. The first three chapters of this book provide a user-friendly introduction to computer-assisted algebra with Maple. The rest of the book then develops these techniques and demonstrates the use of this technology for deriving approximate solutions to differential equations (linear and nonlinear) and integrals. In each case, the mathematical concepts are comprehensively introduced, with an emphasis on understanding how solutions behave and why various approximations can be used. Where appropriate, the text integrates the use of Maple to extend the utility of traditional approximation techniques. Advanced Mathematical Methods with Maple is the ideal companion text for advanced undergraduate and graduate students of mathematics and the physical sciences. It incorporates over 1000 exercises with different levels of difficulty, for which solutions are provided on the Internet.

Review

'The aspect of the book that I particularly liked followed from the background of the author, who is not a physicist but an applied mathematician. This background meant that a wider view of the material was presented than we might expect from a physicist. For example, most physicists, when asked about perturbation theory might first talk about how a small change in an operator would lead to a small change in eigenvalues and the associated eigenfunctions. It is hard to do full justice here to a substantial book, over 800 pages in length, with its content of interesting and, at times, novel material. ... [The book] represents very good value. Final year undergraduates in theoretical or mathematical physics and theoretically and mathematically oriented postgraduates or researchers should give very serious consideration to purchasing this book.' D. Waxman, Contemporary Physics

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