Objectives: 10. Find the length of a space curve. 11. Parameterize a curve with respect to arc length. 12. Give the properties of arc length parameterizations. 13. Define and compute curvature for curves in 2-space and 3-space.
Пікірлер: 30
@1light4love3 жыл бұрын
my College Calc3 with Engineering Applications Professor just spent 2 & 1/2 hours attempting to explain this exact section and I guarantee you that not one person had the slightest understanding of what he was talking about. (which is normal, unfortunately.) thank GOD for you, Professor.... and thank you for your straightforward, easily understood approach. 🙏 (Our first Exam is next week!)
@alexandraniedden53373 жыл бұрын
Good luck!
@xiaoyangwang91912 жыл бұрын
I'm not saying my cal3 professor is bad at teaching, however, you have explained it clearly that I'm actually understanding it, thanks so much for these cal3 videos, it really helped me.
@butx15552 жыл бұрын
29:00 my professor used a slightly different method. He did not find the arc length parametrization, instead, he used K(t)= the norm of T'(t)/the norm of r'(t) Update: 33:30 you explained my teacher's method. You are literally the best teacher!
@charliezhou65144 жыл бұрын
be my professor
@sundaymanali58542 жыл бұрын
great lectures.
@brendanbuckner25613 жыл бұрын
At 29:28 why did the "a" values disappear when taking the derivative of vector r(s)?
@alexandraniedden53373 жыл бұрын
When taking the derivative of the first term, for example, remember that a is a constant. The derivative of acos(s/a) would be a*-sin(s/a)*1/a (1/a from Chain Rule). That a*1/a gives us 1.
@nolfre13822 жыл бұрын
I love your videos but this one in specific was way too fast for me to understand everything. Maybe it's just me but i got frustrated for the first time. Anyways thank you, this actually helps.
@butx15552 жыл бұрын
Do you go to school in Madison?
@nolfre13822 жыл бұрын
@@butx1555 nop
@devanarayanababu19963 жыл бұрын
ms.budden why is there a need to parameterise the arc length? (what is the use?)
@alexandraniedden53373 жыл бұрын
We often choose to parameterize in terms of arc length for analysis purposes. Using s as a variable is significantly more meaningful (and convenient) as compared to an arbitrary variable, like u. Around 14:00, the example at the bottom shows one way that arc parametrization is helpful. If I move 5 units, where am I now?
@backup01973 жыл бұрын
@@alexandraniedden5337 oohk......thank you ma'am
@nuhaalnahwi56183 жыл бұрын
For example 2 why is the integral from 0 to t? how did u pick which point from the reference point?
@alexandraniedden53373 жыл бұрын
We are asked for the arc length parametrization, which is a general vector rather than a specific vector. This is why the upper limit is t, rather than a number (also follows the arc length parametrization formula). To find the lower bound, we must consider the reference point. Setting (1, 0, 0) = (cost, sint, t) will help us find the t value at which this point occurs. Hence cost = 1, sint = 0 and t = 0. The only place this happens is t = 0.
@uzairahmed.17903 жыл бұрын
Can you please share the notes of chapter 12 and 13?
@alexandraniedden53373 жыл бұрын
Chapter 12: kzbin.info/aero/PLGOk2-zeLtjBuFyoBkgdoRh0qhuaqrBdi Chapter 13: kzbin.info/aero/PLGOk2-zeLtjAG7o5KUBbGAgaKyAN4ZFd6 A few lectures may be missing, but this should be most of them. Good luck!
@uzairahmed.17903 жыл бұрын
@@alexandraniedden5337 Thanks alot! These lectures are far better than my college lectures.
@jakeb1103 жыл бұрын
How did you get 5pi in ex1 I've been working on it and I can't seem to get it.
@alexandraniedden53373 жыл бұрын
Under the square root, 9sin^2t + 9cos^2t simplifies to 9 (remember that sin^2t + cos^2t = 1). Then we have the integral of sqrt(9 + 16) which gives us the integral of 5 from 0 to pi. I hope that makes sense. Good luck!
@jakeb1103 жыл бұрын
Also for the last problem formula 3 I keep getting 2(t^2+ 2t+ 2) instead of 2(t^2+2) I'm getting lost on how you get rid of the 16t^2 inside the root im pretty sure.
@alexandraniedden53373 жыл бұрын
@@jakeb110 The 4t^4 + 16t^2 + 16 factors. I factored out a 4 leaving (t^4 + 4t^2 + 4) which then factors to 4(t^2 + 2)^2.
@jakeb1103 жыл бұрын
@@alexandraniedden5337 Those are more clear now, thank you very much!