Difference between revisions of "Books:Analysis - Part 1: Elements - Krzysztof Maurin"
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(Created page with "==Alec's progress== {| class="wikitable" border="1" |- ! colspan="2" | Book progress |- |<book>9b96e8ef01c6bb182da0aa81f518f690</book> | Key * Blue boxes are unread pages * Gr...") |
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| + | ==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. | ||
Revision as of 12:10, 7 January 2016
Alec's progress
| Book progress | |
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Key
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Mistakes
- p59 - the line in the middle that reads: "[ilmath]x-x_0:=h[/ilmath], [ilmath]f(x+h)-f(x)=f'(x)h+r(x,h)[/ilmath]" should read:
- "[ilmath]x-x_0:=h[/ilmath], [ilmath]f(x_0+h)-f(x)=f'(x_0)h+r(x_0,h)[/ilmath]" otherwise we're dealing with [ilmath]f(2x+x_0)-f(x)[/ilmath] on the LHS and there are problems. If you swap [ilmath]h=x-x_0[/ilmath] to [ilmath]h=x_0-x[/ilmath] the [ilmath]f(x_0)-f(x)[/ilmath] 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 [ilmath]x[/ilmath] with [ilmath]x_0[/ilmath] is the easiest and most straightforward solution.
