Riemann Sums
Let's face it, Bernhard Riemann was a pretty incredibly guy. What I still don't understand though is why it took around 200 years for the Riemann sum definition of a definite integral to come around. It seems kind of obvious and intuitive. Then again, most things do seem that way after one learns them. I just spent the last hour computing definite integrals with Riemann sums and it is an incredible pain. My computation for:
⌠2
│ x³ dx
⌡1
takes up 2/3 of a page. That's most likily due to this horrendous habit of writing my math neatly, which is being ingrained into me at my class at PCC (we're starting derivatives!! Woohoo!). My theory is that they do so little teaching there that they have to teach something that can be done quickly and easily, so they may as well force you to write neatly. What a waste of time. As long as the answer is legible, and it's right, that's what matters. I don't know what all of this nonsense about process and such is. Blah, blah, blah. The answer is 3.75, by the way. The experience has turned me into a big fan of Newton and especially Leibniz.
Yeah, once you get to actual integration techniques, rather than Riemann sums, it gets pretty easy.
The most amazing things I found in calculus include Newton's method for finding zeros, Taylor's series approximation, Lagrange multipliers, and multiple integration, the latter two you unfortunately will not cover.
But anyway, why I actually came here for. There's an article about the latest "Operation Catapult" thing, which I really want you to go to next year, since I'm gonna try to be a counselor. Apply for scholarships for it if you do it, though. It's definitely one of the best times you will ever have.
And yes, I'm going to continue pushing this on you until you agree to do it, or I die.
Why do you have to do all that work? Isn't that why computers were invented? What teacher do you have?
It is annoying having to read comments for each entry. Seeing as how most of the posts have little to do with the entry, I think you should combine all comments at the top of the page. However, you are lazy and won't.
That is incredibly astute Me, I think we should give Adam no food or sleep until he does said thing, water is okay. Now hving said that, I think your idea is supremely terrible, but whatever.
Why is my idea extremely terrible??
I have the same one that you had last summer. Gibson is her name, I believe. She's a pretty bad teacher in my opinion.
I know another guy who has/had her. He just sits/sat in the back and plays cards. I'm curious... are any of you starting to get stuff from colleges? Adam, you never answered why you bothered to do all that work.
Gibson? I think the teacher I had and am referring to is Kim Webb.
Her name is something like Kim Webb-Gibson. She got married. I do work that involves learning because I like to learn. I like to learn just like you and Spoonman enjoy playing computer games.
I guess that is her name...
What makes you think I like playing computer games. That is rather assumptive.