VCE Stuff > VCE Specialist Mathematics
Resources/Guides: For advanced students
TrueTears:
So here I'll post some guides on some topics that are above VCE level for those keen students, however you can grasp these concepts to a sufficient degree with VCE knowledge. However some topics actually aren't necessarily "harder" than your VCE maths, rather they emphasize rigour and solid proofs.
To get started, here's a nice guide on epsilon-delta proofs. Used quite a lot in real analysis.
Before you get into it, here's a bit of background on what these are.
I'm sure most of you guys have done differentiation by first principles, you know, where you limit the h to 0 and etc. Yes, that stuff. Now remember the last step? Where you guys just thought "hmm just means I can sub h = 0 in, after canceling out the h's" Well a really basic way of extending that limit stuff to a more rigorous approach is using epsilon delta proofs. What you will find is that you are actually not "substituting h = 0 everytime you see h", rather you are using a very intuitive approach formalised by using an epsilon-delta proof.
Now go read.
Also I attached them as pics because VN won't let me attach as a rar file o.O
Vic Mod edit: re-added attachments
taiga:
Finally some of your maths I can understand :P
TrueTears:
haha :P
Anyways, for those who are quite keen, here's a challenge question, the method to prove this one is a bit different from the examples that you've read above, however the general jist is the same, if you understood the overall concept, have a good at this one, post a solution even if you think it's not right! Have a shot!
Show that
xZero:
if then , since , we have to adjust the epsilon part of the proof, let M=any positive number, f(x)>M (this means that as you approach the point a, f(x) becomes larger than any finite number)
let
, a=0
This completes the proof, hence
Think this is correct :S
TrueTears:
Nice :]
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