These videos were created to accompany a university course, Numerical Methods for Engineers, taught Spring 2013. The text used in the course was "Numerical Methods for Engineers, 6th ed." by Steven Chapra and Raymond Canale.
Пікірлер: 25
@silverKirilljedi Жыл бұрын
This video was recorded 9 years ago, but here am I in 2022, happily watching these awesome videos that Jacob recorded and planning to apply it in my work 😄
@nurmuhammadsumon2729 Жыл бұрын
Now 2023 😊
@dieminestinkt8 жыл бұрын
ty. The only one on here who could explain it nice and simple
@ImanMatar8 жыл бұрын
I don't know if it has a sequel, but considering this video alone, it doesn't have an in-depth analysis for those having a test in numerical computing in few hours. It's just a nice clean overview on what to expect. Thank you for your effort
@kvyi8 жыл бұрын
+Iman Matar Thanks for the comment. It's part of a series of videos, which are organized into a playlist, but also organized by number. This is the seventh video in the second section of the fifth part of the video series...which is why it's labeled 5.2.7. I hope that helps.
@spkearney168 жыл бұрын
+Iman Matar funny... i have a test in numerical computing in a few hours
@snake1625b4 жыл бұрын
the best explained video on this topic.
@bettertony10 жыл бұрын
Hi Jacob, Thanks for sharing. There is one question. As for the natural spline, my understanding is that the second derivatives on starting and ending points are zeros. For a quadratic function, it seems to be not possible. We know that quadratic function only has one stationary point. In your video, you got conclusion that "a1=0", then it is going to be a linear function.
@kvyi10 жыл бұрын
Hi Wenliang, Thanks for the question. You are exactly right. If we constrain the second derivative to be zero at the endpoint, it will mean that the first segment is a linear function. An alternative is to let the second derivatives be equal at the first or last interior knot (typically at the first, x1). This is the not-a-knot condition. Since these already share a point, and the first derivatives are equal, when we add the condition that the second derivatives are equal, this implies that the two functions are the same. For a cubic spline, the not-a-knot condition says to let the third derivatives at the first and last interior knots to be equal. Contrast this with the natural spline condition, which (as you correctly pointed out) says to let the second derivatives be equal to zero at the endpoints. Similar to this situation, the natural spline condition means that for a cubic spline, the first and last segments are quadratic, not cubic.
@kvyi8 жыл бұрын
+Everett You Correct. I am not showing that condition. Perhaps it would be better to do so.
@chunchen34504 жыл бұрын
Thanks for the video. Nice hand on explanation on quadratic splines
@shivakumarnatrajan3 жыл бұрын
This is awesome, could you make another video in b spline surface fitting?
@Bonehand7 жыл бұрын
Nicely explained, thanks!
@tag_of_frank5 жыл бұрын
Looks like more conditions than unknowns. If there are 2 intervals then there are 2 equations with 3 unknowns each, a,b, and c. = 6 unknowns 2 equations. The equations are equal at the interior points => 6 unknowns, 3 equations. They pass through endpoints => endpoints are known, that is 2 equations, 1 for each endpoint. 6 unknowns, 5 equations. First derivatives are equal at the knots => 6 equations, 6 unknowns a1 = 0 => 6 equations, 5 unknowns.
@anasuyadr56 жыл бұрын
Thank u for nice explanation. could u pl explain how to ensemble average the cubic splined graphs to get a final pattern
@super-panda7 жыл бұрын
great video, thank you!
@MarkElDeiry3 жыл бұрын
Did I miss it? Is the quadratic spline identical to the sine wave?
@jonahbranch56252 жыл бұрын
no, just very very close
@eggtimer22 жыл бұрын
Anyone got a derivation of the spline in tension?
@M43STR0_dnb2 жыл бұрын
How did I end up here
@SuprafluidHD8 жыл бұрын
Wir haben das grade.
@mswoonc6 жыл бұрын
nice
@Joshua-dc4hu10 жыл бұрын
For this video, you seem unprepared at points and were vague at points. For improvement, you could make a script so you know what you are doing.
@kvyi10 жыл бұрын
Thank you for the feedback. That's a good idea.
@yashshah82649 жыл бұрын
Jacob Bishop None the less, its very informative and gets the point across. Thanks for uploading this.