Advanced engineering mathematics is a subject of its own, building up from simple notions of functions, series, integration techniques and brief review of linear algebra which leads to transform methods (Laplace, Fourier, Z and sometimes Hilbert), with strong emphasis of course on ODE and some elements of PDE and finally ends with complex variables and conformal mapping.
With that I've just described the table of content of probably 99% of books out there on advanced engineering mathematics. Kreyszig, Zill, Stroud, Duffy et. al. falls squarely in this category. This is not to say such an approach is without value, in fact the standardization and consistency of a subject is probably a sign of very mature development of the field which is great for an introduction to engineering mathematics and provides great motivation for applied mathematics in general.
But the lack of variation between these texts leaves me wonder if there is a book that covers material that is even more advanced, more comprehensive than what has been described above. For engineering students, it is often crucial to have motivation when it comes to studying a subject and such motivation usually comes from engineering examples (circuit theory, mechanical system, modeling) so an advanced text that is typically used and cherished by math majors just won't do.
Can someone recommend a text that is most advanced or comprehensive when it comes to engineering mathematics covering topics that goes beyond the standard curriculum that could potentially be engaging for a mathematically mature engineering student who wish to know more about techniques used in mathematics for engineering applications? Please let me know if this is a bit too much to ask.