Books:Analysis - Part 1: Elements - Krzysztof Maurin

Alec's progress

Book progress
	Key Blue boxes are unread pages Green pages are read once Orange are read more than once Red are read the most frequent

Mistakes

• p59 - the line in the middle that reads: "$x-x_0:=h$, $f(x+h)-f(x)=f'(x)h+r(x,h)$" should read:
  • "$x-x_0:=h$, $f(x_0+h)-f(x)=f'(x_0)h+r(x_0,h)$" otherwise we're dealing with $f(2x+x_0)-f(x)$ on the LHS and there are problems. If you swap $h=x-x_0$ to $h=x_0-x$ the $f(x_0)-f(x)$ part of the definition is negative what it ought to be; although the linear map's (the differential) argument is negated so it still sort of works out, either way replacing $x$ with $x_0$ is the easiest and most straightforward solution. This is inline with the definition of differentiability (Banach Space) given on p161
• p149 - wrongly (and explicitly) states that a norm may be a function of the form $\Vert\cdot\Vert:V\rightarrow\mathbb{C}$, see the norm page (there's a warning note on the first line of the definition section)