An overview of analysis I'm looking for a book that gives an overview of analysis, a bit like Shafarevich's Basic Notions of Algebra but for analysis. The book I have in mind would give definitions, theorems, examples, and sometimes sketches of proofs. It would cover a broad swathe of analysis (real, complex, functional, differential equations) and discuss a range of applications (i.e. in physics and in prime numbers). I've looked at the Analysis I volume of the Encyclopaedia of Mathematical Sciences which Shafarevich's book is also a part of, but it focuses more on methods and isn't quite what I have in mind.
Thank you!

There is a series of books titled Princeton Lectures in Analysis that i'd recommend; it's a 3 volume series covering Fourier, complex and real analysis. They're considered introductions, but I would hardly consider them that; it assumes you are already familiar with basic mathematical analysis. I own the first volume (Fourier analysis) and it's surpassed my expectations - there are quite a lot of applications (entire chapters devoted specifically to certain applications, like BVPs and the Heisenberg Uncertainty Principle). To boot, it provides a bit of historical context, which is always nice. The only downside is that, after a few examples, the author starts skipping steps in the remaining examples - it can be a bit difficult to follow, but if you work through the example yourself, you can fill in the gaps.
Here's a link to the Fourier analysis book: 
http://www.amazon.com/Fourier-Analysis-Introduction-Princeton-Lectures/dp/069111384X
