Thursday, June 16, 2016

The F word. (5)

Word, phrase, whatever it is.  Dun dun dun... The Fundamental Theorem of Calculus.  The bane of my existence.  When calculus is put in front of me... this is what happens on the inside.

And outside really.  Don't tell my best friend Jo B, but I "have yet to" [i.e. can't] understand calculus.  If I were in a battle and I was propositioned with "Give Me Calculus or Give Me Death," it was nice knowing you.

So I activated my growth mindset and after another failed attempt of understanding any form of calculus thought, I said to myself "Lulu, you are capable of understanding this and you WILL get a deeper understanding."  Here I am, back at it again.  First, I went to to try to explore The Fundamental Theorem of Calculus for dummies.

Here is my now [much deeper] understanding of the (1st) FTC:
                               F(x)=xaf(t) dt

  1. It's important. Phew! That was a tricky one at first.  You did it! Press on...
  2. Then... we have a function "f(t)", okay I'm totally with you.  The function creates a line on our graph.
  3. Now... they want me to find the area under the curve? This is called F(x).  So this F(x) IS the area under the "curve" or the function.  I still feel okay, pending I'm not completely wrong.
  4. Now, the area that we are measuring starts at value a and ends at value x.  Makes sense.
  5. Now I'm getting lost... dt represents the derivative of f(t) which is the amount that it is increasing or decreasing?  
  6. And that's it!
                         \int_a^b f(x)\, dx = F(b)-F(a).
  1. Okay... so now we tackle the 2nd FTC, which I guess solves for all definite integrals?  Well they switched me from f(t) to f(x) but I guess they're the same thing?  Also, F(b) - F(a) is apparently F(x) evaluated from a to b... but where did b come from?  Now I am lost.  But hey! I got through at least half of the explanation without crying.  I call this a win all around.

1 comment:

  1. I appreciate you trying to consciously activate your growth mindset. I'm wondering how this works, and I'm hopeful.

    The thing missing in your understanding of the FTC is the relationship between f and F. The integral and the derivative are defined completely separate from each other, but - dun, Dun, DUN! - are almost inverses. Almost b/c we lose a constant from taking the derivative. How does that undetermined constant show up in the FTC?

    To be an exemplar, I'll encourage you to push on with the content. For consolidation, I'd be interested in your view of your understanding by the lens of growth mindset, but it's up to you!

    C's: 3/5
    clear, coherent, complete +