View source for Books:Analysis - Part 1: Elements - Krzysztof Maurin

==Alec's progress==
{| class="wikitable" border="1"
|-
! colspan="2" | Book progress
|-
|<book>9b96e8ef01c6bb182da0aa81f518f690</book>
| 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: "{{M|1=x-x_0:=h}}, {{M|1=f(x+h)-f(x)=f'(x)h+r(x,h)}}" should read:
** "{{M|1=x-x_0:=h}}, {{M|1=f(x_0+h)-f(x)=f'(x_0)h+r(x_0,h)}}" otherwise we're dealing with {{M|1=f(2x+x_0)-f(x)}} on the LHS and there are problems. If you swap {{M|1=h=x-x_0}} to {{M|1=h=x_0-x}} the {{M|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 {{M|x}} with {{M|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 {{M|\Vert\cdot\Vert:V\rightarrow\mathbb{C} }}, see the norm page (there's a warning note on the first line of the definition section)