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inkyvoyd
Epsilon delta definition of a limit and application of it for definite integrals (Riemann sums)
Anyone know of resources I could learn more about this topic?
@RnR , I do not believe that Khan academy does a rigorous justification of riemann sums in combination with epsilon-delta limit definition. @Kanwar245 , that's kind of trivial to mention, but I guess I might recheck the pages. Wikipedia is often very mathematically rigorous but not friendly to the layman like me...
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In that case refer to some book
I had to do these this year and last year, mostly I just googled around and "borrowed" notes from other Universities on it (sharing is caring!). But if you have any questions on it I could try and answer them, though it is an awfully boring topic in my opinion haha
we know that integration means, area under the graph how can we approximate that? -> say using rectangles..
definition of a derivative \[ \lim_{\Delta x\to0}\frac{\Delta y}{\Delta x}={dy\over dx} \]
Well I'm reading Thomas and Finney, and they intrduce both topics, but I'm hoping for some sort of more rigorous justification such that calculus feels more solid. Also, I'm hoping understanding the proofs for the FTC will help me comprehend the applications of integrals in Calc II I'm struggling for
@inkyvoyd are you looking only for a reference?
Yes @electrokid . I'm wondering if I could find a nice book on calculus that was fairly rigorous. I've tried reading a real analysis book but that hurt my poor brain with rigor.
but it would not be a bad idea to engage into some hardcore discussion here. I am sure people would not bother to answer such topics unless they know what they are talking about!
@electrokid okay I will copy down what the textbok mentions and what I don't understand. Thanks!
One way of looking at a riemann sum is:|dw:1363819858302:dw| The limit of the bigger rectangles, the Upper Sum, and the Lower Sum as delta x tends to 0. The inequality is as such: L<theintegral<U. Though this isn't very rigorous. The upper and lower sum's themselves can be defined as the supremum and infimum of a summation.