Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Calculus is awesome!

  1. Sep 4, 2012 #1

    I just wanted to point out a fact obvious to most of you, the fact that:


    That is all,
  2. jcsd
  3. Sep 4, 2012 #2

    Stephen Tashi

    User Avatar
    Science Advisor

    It is amazing.

    I pity people who are introduced to in a gentle step by step fashion, making it all seems natural and obvious. It's much more fun when you find it totally confusing and then finally BAM! the light dawns.

    But don't expect too much from calculus. It's power in a vast number of situations can mislead you into thinking it can tackle anything. When it comes to things like finding computer algorithms to interpret pictures or decrypt codes, its capability is less impressive. Maybe we've yet to invent the best math for things like that.
  4. Sep 4, 2012 #3
    Well, it wasn't completely obvious, or gentle, really. But, now that my mind is oriented the way it should, it's really fun :smile:
  5. Sep 4, 2012 #4


    User Avatar
    Science Advisor

    This. Calculus is a sledgehammer. Sure you can open a walnut with a sledgehammer, but do you want to?

    I'm pretty sure you've seen the "fence by the river problem": you have a length of wood P long and you need to build a rectangular fence with one side the river bank. A student using calculus would set up the equations
    ##A = xy##
    ##P = 2x + y##
    then solve the second equation for y, then substitute into the first equation, then differentiate and find the stationary point, find y, and finally prove that you have a max. It'll take at least half a page.

    Or you can just use the AM-GM inequality
    ##A = xy = \frac{1}{2} \sqrt{2xy}^2 \leq \frac{1}{2} \left(\frac{2x+y}{2}\right)^2 = \frac{P^2}{8}##
    with equality when ##2x=y## and the problem is solved. Just because calculus can tackle a lot of different problems does not mean it is always the best tool for the job.
  6. Sep 5, 2012 #5
    Oh yes, I think that example is indeed pertinent. I had an algebra book that had a chapter devoted to inequalities, so when I see that problem or others like it, I think AM-GM.
  7. Sep 5, 2012 #6
    I'm glad it plays such an integral role in your life.
  8. Sep 5, 2012 #7


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    He derives much pleasure from it.
  9. Sep 5, 2012 #8
    Ah, our first derivative joke.

    Would anyone like to make a second derivative joke?
  10. Sep 5, 2012 #9
    So which "inventor" do you favor, Newton or Leibniz?
  11. Sep 5, 2012 #10
    I probably would have better understood calculus if the 3 classes I took were split up into 4 or 5 classes. We had to rush through a lot of things and not talk about a lot of things just to get through it in 3 semesters. I might take advanced calculus. Anyone know the prereq for it?
  12. Sep 5, 2012 #11
    Depends on the school, but if you've taken all 3 semesters, you should be fine. Maybe linear algebra would help (LA always helps).
  13. Sep 6, 2012 #12
    Newton was kind of a jerk
  14. Sep 6, 2012 #13
    Aw, now what makes you say that?
  15. Sep 6, 2012 #14
    He really was. Read up on his life, he was a really mean person. Nevertheless, he was insanely smart!
  16. Sep 6, 2012 #15


    User Avatar
    Gold Member

    As long as he doesn't drink and derive, he should be okay. :biggrin:
  17. Sep 6, 2012 #16
    Yeah, but both of those chicks had awesome hair.
  18. Sep 6, 2012 #17
    My dentist told me I have calculus in my teeth. I figure it fell down from my brain.
  19. Sep 6, 2012 #18


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    I wonder which one actually took the first derivative?
  20. Sep 6, 2012 #19
    Definitely Liebniz. All of Newton's work was rather *puts on sunglasses* derivative.
  21. Sep 6, 2012 #20


    User Avatar
    Science Advisor

    You don't happen to be a detective of a major network TV show called "CSI" by any chance?
  22. Sep 6, 2012 #21
  23. Sep 6, 2012 #22


    User Avatar
    Science Advisor

    Last edited by a moderator: Sep 25, 2014
  24. Sep 7, 2012 #23
    *studies finger nails*

  25. Sep 7, 2012 #24
    I don't know if you spell it differently in Europe, but my sources spell it Leibniz, even though it's pronounced like it was "Liebniz" here in the US.
  26. Sep 7, 2012 #25
    Yes it's Leibniz. My google doesn't even want to search 'Liebniz' and tells it searches for 'Leibniz' instead. But the observation is how often in English ei and ie are confused, while no German or Dutch will ever make that mistake.

    Pronounce it like l-eye-b-niths, not leabniths
    Last edited: Sep 7, 2012
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook