History of analysis?

Question

Any sites detailing the history of analysis post 1820 (to mid 1900s?) - vis-à-vis Cauchy, Weierstrass, Riemann, Bolzano, ..., Kuratowski, Hilbert?

It's something that appears quite interesting and I would like to have a knowledge of the direction analysis took and how things like topological spaces were motivated and viewed (pedagogically they're an extension of a metric space though I think there is much, much more to the history than this though I might be incorrect).

Being a poor student purchasing "mathematical analysis by its history" isn't an option (for two reasons; I need money for food and core material, but more importantly - mathematically the comments would be worthless as post 1900 detail is not included).

I looked to the library for history and - understandably - the books look at geometry, calculus (not analysis! Leibniz versus Newton) etc.

Answer 1

Many old books are available freely :
(Gutenberg)
Smith(1906) 'History of Modern Mathematics'
Rouse Ball(1908) 'A Short Account of the History of Mathematics'
(archive.org)
Struik(1948) 'A concise history of mathematics'
Bell(1937) 'Men Of Mathematics'
and so on... Excellent reading!

Answer 2

The St Andrew's history of maths website may be a good starting point. This link leads to the history topics index.

Answer 3

This is a general history, but it has a quite detailed overview of "analysis". Morris Kline's Mathematical Thought from Ancient to Modern Times is very thorough, well written, and most importantly cheap. It comes in three volumes in paperback. I believe you'd want volumes two and three.

Answer 4

Try these books:

• Analysis by Its History by Hairer and Wanner.
• A History of Analysis by Jahnke (ed).
• A Radical Approach to Real Analysis by Bressoud.