Just a couple of weeks to go before I hand in my thesis and I should all be happy about these times. Yet there is this deep pain whenever I understand that my basics in mathematics are anything but strong. This has also delayed the writing of the thesis but honestly the pleasure in understanding these basic concepts, even if it consumes time, far outweighs the satisfaction I would derive by submitting without clearly understanding what I did.
I wanted to understand the proof of the second derivative test (SDT) but it seems that it is a bit involved and hence not listed anywhere in the internet or in the some of the books I have skimmed through. What bothered me was that, these concepts were so simplified at the undergraduate level that it becomes double work to understand them now. First, I have to unlearn all the “math” that is already there in my head – the kind which encourages manipulating symbols without a clear knowledge of the reasons behind. Second, gaining all this knowledge from proper sources.
Calculus has been dumbfounding me of late so why not get a textbook which explains it in a neat way? Went through the text Calculus by Michael Spavik and I have to say that it is a real gem, though it did not have the proof for the SDT. Still searching.