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inkyvoyd Group Title

Epsilon delta definition of a limit and application of it for definite integrals (Riemann sums)

  • one year ago
  • one year ago

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  1. inkyvoyd Group Title
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    Anyone know of resources I could learn more about this topic?

    • one year ago
  2. Kanwar245 Group Title
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    wikipedia?

    • one year ago
  3. RnR Group Title
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    Khan academy?

    • one year ago
  4. inkyvoyd Group Title
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    @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...

    • one year ago
  5. electrokid Group Title
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    |dw:1363819630711:dw|

    • one year ago
  6. Kanwar245 Group Title
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    In that case refer to some book

    • one year ago
  7. paddyfitz Group Title
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    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

    • one year ago
  8. electrokid Group Title
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    we know that integration means, area under the graph how can we approximate that? -> say using rectangles..

    • one year ago
  9. electrokid Group Title
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    definition of a derivative \[ \lim_{\Delta x\to0}\frac{\Delta y}{\Delta x}={dy\over dx} \]

    • one year ago
  10. inkyvoyd Group Title
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    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

    • one year ago
  11. electrokid Group Title
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    @inkyvoyd are you looking only for a reference?

    • one year ago
  12. inkyvoyd Group Title
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    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.

    • one year ago
  13. electrokid Group Title
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    ok

    • one year ago
  14. electrokid Group Title
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    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!

    • one year ago
  15. inkyvoyd Group Title
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    @electrokid okay I will copy down what the textbok mentions and what I don't understand. Thanks!

    • one year ago
  16. paddyfitz Group Title
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    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.

    • one year ago