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!

You can try, for example, read "Elements of the Theory of Functions and Functional Analysis" A. N. Kolmogorov, S. V. Fomin. 
