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  1. #1 calculu 
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    which part of calculus is still not understood by great scientists


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    • #2  
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      Partial differential equations, i would say.


      I demand that my name may or may not be vroomfondel!
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      partial differential equations are pretty well handled, that is, linear problems. the problem scientists have is dealing with non-linearities in both partial and ordinary differential equations as well as in much simpler systems.
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      A la Chaos Theory.
      I demand that my name may or may not be vroomfondel!
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      It's really hard for me to understand about Partial differential equations!
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      Does that make you a great scientist?

      I would not say there is any part of "Calulus" that any scientist, much less a great one, does not understand.


      (I would NOT include specific mathematical fields such as"chaos theory" or "tensor calculus". While they use Calculus, they are not part of Calculus.)
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      Quote Originally Posted by lance View Post
      partial differential equations are pretty well handled, that is, linear problems. the problem scientists have is dealing with non-linearities in both partial and ordinary differential equations as well as in much simpler systems.
      And unfortunately most problems in science are highly non-linear which is way we use models and a variety of iterative models to find solutions.
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      Well, calculus is the study of instantaneous change of continuous systems. But we don't even know for certain if the universe is continuous! In fact physics tells us there's something called the Planck length, which is the smallest unit of space that we can sensibly talk about. Even though physicists use the real numbers to model the dimensions of space; they don't know for sure if actual space is like that!

      So the biggest mystery about calculus is ... is it true?
      Last edited by someguy1; November 26th, 2013 at 01:40 AM.
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      It's not meant to be "true" or "false." It's just a tool that been shown to be useful to represent real phenomena.
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      Quote Originally Posted by someguy1 View Post
      Well, calculus is the study of instantaneous change of continuous systems. But we don't even know for certain if the universe is continuous! In fact physics tells us there's something called the Planck length, which is the smallest unit of space that we can sensibly talk about. Even though physicists use the real numbers to model the dimensions of space; they don't know for sure if actual space is like that!

      So the biggest mystery about calculus is ... is it true?
      You are asking about applications of Calculus to Physics. That has nothing at all to do with the understanding of Calculus, let alone whether it is "true". (That is not even a question a mathematician would ask. The question would be whether or not Calculus is valid. And that was settled in the late 19th century.)
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      Quote Originally Posted by HallsofIvy View Post
      Quote Originally Posted by someguy1 View Post
      Well, calculus is the study of instantaneous change of continuous systems. But we don't even know for certain if the universe is continuous! In fact physics tells us there's something called the Planck length, which is the smallest unit of space that we can sensibly talk about. Even though physicists use the real numbers to model the dimensions of space; they don't know for sure if actual space is like that!

      So the biggest mystery about calculus is ... is it true?
      You are asking about applications of Calculus to Physics. That has nothing at all to do with the understanding of Calculus, let alone whether it is "true". (That is not even a question a mathematician would ask. The question would be whether or not Calculus is valid. And that was settled in the late 19th century.)
      Mr. Halls, That is exactly the point. There is philosophical meaning in what I wrote. I recognize your handle from Physicsforums.com. That site has an excellent math section, but any hint of philosophical relevance in a post is grounds for chastisement and official sanction points being applied to the poster's account.

      I was trained in math but I always had philosophical and historical interests as well. I left Physicsforums.com because I was tired of having my posts censored and sanctioned by the moderators. I never ever trolled or abused that site, but I repeatedly had my well-meaning posts deleted over there. I took it personally and I got sick of it.

      On this forum, there is not as much sophisticated math as there is on Physicsforums.com. However this is a much more friendly and conversational place, where all points of view and all contributions are welcome.

      If you are simply noting that my remark is philosophical, then you are correct. But if you genuinely think that the question of whether the world of calculus does or does not accurately represent the physical world is an unimportant question; then I would say that it's you who are missing the point.

      Physicsforum is of course within its rights to have no sense of humor, no sense of collegial conversation, and a policy of strictly banning, deleting, and sanctioning any mathematical remarks that have philosophical overtones.

      But you are not on that forum right now. I for one do not appreciate the tone of your comment, putting it as I do in the context of who I know you to be on Physicsforums. The forum we're on here is a much more casual place where people are free to say what they like without fear of having self-righteous moral scolds tell us what we can post. I for one hope this place stays this way.

      If you're wondering why I'm calling you out, it's because you did the exact same thing to me yesterday on a different math board. You are exploring other online math forums, and bringing your Physicsforums sensibilities to them without realizing that not every forum is as humorless and intolerant as Physicsforums is.

      I respect PF for what it is. The math content is at a very high level. A lot of students are helped. But idle chit-chat, humor, and philosophy are sharply rebuked in the math section. Not everyone enjoys that. From other online forums I know that I'm not the only person who feels as I do.

      So lighten up. You are not on PF right now. That tight-ass style of moderation has its place. But when you attempt to bring that style to more informal, friendlier, more casual forums, expect some pushback.

      I speak for myself and not the moderators, owners, or other members of this site.
      Last edited by someguy1; November 26th, 2013 at 11:39 PM.
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    • #12  
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      Quote Originally Posted by someguy1 View Post
      But if you genuinely think that the question of whether the world of calculus does or does not accurately represent the physical world is an unimportant question; then I would say that it's you who are missing the point.
      That depends on your point of view. If your point of view is mathematics, then no, it isn't important whether calculus accurately represents the physical world. Of course, physics quite rightly takes the opposite view.
      There are no paradoxes in relativity, just people's misunderstandings of it.
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