![]() ![]() The textbook is practically unrivaled as the entry into Real Analysis, and has been around since the 1970s (Edit: published 1953) with three editions. You’d think three editions would be enough to cross all the t’s and dot all the i’s. I have been having fun digging through the Special Functions chapter in the book. My first round through the text, when I took the class, we only briefly touched on some elements with the Gamma function and then moved on. What caught my particular interest was the sine and cosine section, where Rudin develops both functions without any geometry. 3rd edition, by Walter Rudin (also known as Baby Rudin, or That Grueling. So I took my own route, and rather than starting with Euler’s formula, like Rudin does, I began with the differential equation y’’ = -y. Besides the fact that it's just plain harder, the way you learn real analysis. I think it’s so cool how you can take such a different route from the historical development of these functions, and get the same results. I have all the details in this video here, if you want to see my take on it.īut then Rudin wraps up the section with two references. The second paper treats not Euler’s formula nor the differential equation as fundamental, but rather the functional equation representing the sum of angles formulas. If you haven’t noticed while going through the book, Rudin is terrible at citations. One thing I really hate about it is that most of the commonly named theorems, aren’t given names. ![]() I only picked them up later when reading other texts. ![]() And in the whole book, Rudin only has 26 citations. ![]()
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