Unfortunately, since Taylor Series is very technical and involves a lot of subtle details, it's difficult to come up with good solid examples to illustrate all of these examples. (Math gets increasingly theoretical as you progress through the years)
I tried to give some 'down to earth' explanations of why the Taylor Series stuff was true in my tutorials (I'm currently TAing the course), like the fact that a Taylor Series is only a local approximation comes alive (in my opinion) by looking at a bounded function like sin(x)...the approximations Tn(x) all blow up to either + or - infinity, and so are 'eventually' crappy estimates.
But unfortunately not all of the subtle details are so easily identified. Personally, I like the textbook a lot better than other textbooks I've gotten my hands on.
To the original poster, (again, speaking as TA of the course) my advice would be to go see your TAs/profs regularly during their office hours. Don't feel like you're imposing, or wasting our time, it's what we're paid for! There will inevitably be times when you're missing some small, very subtle detail that will snowball into a larger problem. Namely, you're missing out on some easy fact or technique that could easily be explained to you, and the material builds on it resulting in a lot of confusion.
The students who jumped from 1LS3 to 1AA3 all seem to be handling it well this term...in particular the ones who come see me regularly.
I would recommend taking the course during the year (and not the summer) since you have essentially twice as long to digest the material...in the summer it's faster paced and while not overly difficult, you want to make sure you have opportunities to ask questions and learn things at a better pace.
Last edited by Mowicz : 03-30-2010 at 10:59 AM.
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