Mathematical analysis - text book recommendation sought A rather subjective question, I admit, but I'm looking for a recommendation for a textbook to help me improve my understanding of mathematical analysis.
I come from a computing background, with a University level degree. My high-school mathematics was all focused on mechanics/physics rather than pure maths and statistics.  I've followed formal undergraduate courses on signal processing, and informal postgraduate lecture series subsequently - for personal interest, not credit.  I feel confident that I have the skills to digest any well-written undergraduate or masters-level text.
I recognise that I am (relatively) weak with respect to analysis when I read the Wikipedia pages for subjects such as:


*

*http://en.wikipedia.org/wiki/Non-analytic_smooth_function

*http://en.wikipedia.org/wiki/Distribution_%28mathematics%29

*http://en.wikipedia.org/wiki/Mollifier

*http://en.wikipedia.org/wiki/Holomorphic_function 

*etc. etc.


I am interested to bolster my understanding of the principles of mathematical analysis and to go on from this to improve my understanding of distributions and how they relate to both analytic and non-analytic functions.  While I recognise the value of proofs, and I'm not looking for a reference book from which to crib formulae, my principal interest is in the practical application of theory rather than its elegant abstract justification.  For this reason, I'm drawn more to presentations with intuitive over formal justifications for theorems.
Suggestions?

For distributions and mollifiers you might want to check out "Functional Analysis and Applications" by Kesavan.
