Very, very nice presentation. So, ( apologies if I am spoiling your next video ) .....where, exactly, is vector N pointing?? - toward a very special point. Your current and recent videoes have already given us the answer. It is staring right at us.
@@bprpcalculusbasics Bang on!! So now break up the acceleration vector, R ' '(t) , into 2 rectangular componenets (not a_x and a_y) : instead, one in the direction of the tangent (a_t) and perpendicular to the tangent (a_n). This normal component point of acceleration, a_n, points right at the Center of Curvature. And if a point mass is moving along the curve, it's the a_n component of the accelaeration that makes it turn, whereas a_t increases or decreases the speed = |vector v|. So cool. Thanks, yet again, for another great video - Newton is smiling.
@@ianfowler9340 yes. I actually just did that video two days ago! And you can probably guess what comes after that! Btw, I am following the calc book by Thomas and I think it’s a fantastic book.
Hello, thank you for the very nice video. I've got one question. By a physical point of view, you often refer to t as "time" and r'(t) as "speed" (as many books do). I claim this may not be the case, because, a curve is parametrized with a spatial parameter (e.g. an angle to parametrize every point of a circumference). If it would be parametrized by time, we would have the equation of motion of a point along the curve, not the curve itself! Am i right?
I feel that the calc3 videos are in the wrong order somehow. For example, the Unit Tangent Vector has been mentioned i several videos already, but isn't explained until now. But the explanation is excellent, as per usual.
I hear your frustration. But differentials are defined in such a way so as to force "the operation: [d by dx][of y]" to actually equal "the division: (differential of y)/(diffrerential of x)". That is, to force "dy by dx" to behave like a fraction - at least for mult. and division. There are no restrictions on the size of the diff. of x (or dx) - large or as small as you want, because: dx is defined as delta x and dy is defined as f '(x)*delta x = f '(x)dx. Re-arranging we obtain: "(diff. of y) divided by (diff. of x)" is indeed equal to f ' (x).
Super cool that you’re doing calc III videos now. Very interesting and well explained as always 💯
Thank you!
Calculus 3 videos are very interesting! Can't wait for the next one
Glad you like them!
Loving this new series, please keep it up
Appreciate your help! Truly grateful!
Happy to help!
Very, very nice presentation. So, ( apologies if I am spoiling your next video ) .....where, exactly, is vector N pointing?? - toward a very special point. Your current and recent videoes have already given us the answer. It is staring right at us.
You mean N is pointing at the center of curvature, right? 😃
@@bprpcalculusbasics Bang on!! So now break up the acceleration vector, R ' '(t) , into 2 rectangular componenets (not a_x and a_y) : instead, one in the direction of the tangent (a_t) and perpendicular to the tangent (a_n). This normal component point of acceleration, a_n, points right at the Center of Curvature. And if a point mass is moving along the curve, it's the a_n component of the accelaeration that makes it turn, whereas a_t increases or decreases the speed = |vector v|. So cool. Thanks, yet again, for another great video - Newton is smiling.
@@ianfowler9340 yes. I actually just did that video two days ago! And you can probably guess what comes after that! Btw, I am following the calc book by Thomas and I think it’s a fantastic book.
THANK YOU
Hello, thank you for the very nice video. I've got one question. By a physical point of view, you often refer to t as "time" and r'(t) as "speed" (as many books do). I claim this may not be the case, because, a curve is parametrized with a spatial parameter (e.g. an angle to parametrize every point of a circumference). If it would be parametrized by time, we would have the equation of motion of a point along the curve, not the curve itself! Am i right?
At 8:30 why are we allowed to drop the absolute value signs, I thought they were used for the magnitude and not absolute value?
i have this same doubt
@@grahamrvalladarez4038 Bcz ds/dt is positive...
I feel that the calc3 videos are in the wrong order somehow. For example, the Unit Tangent Vector has been mentioned i several videos already, but isn't explained until now. But the explanation is excellent, as per usual.
String
Differential Geometry is the coolest! Well, coolest except for Clifford Algebra and Geometric Calculus :-)
Deetee deeree! T! Deetee? Plus N! TNT. Boom!
Blind person be like: Why there are so many dt 😂 😂
Nice video. But please stop saying divide by dt (as in 1:53). It is not how derivative works.
I hear your frustration. But differentials are defined in such a way so as to force
"the operation: [d by dx][of y]" to actually equal "the division: (differential of y)/(diffrerential of x)".
That is, to force "dy by dx" to behave like a fraction - at least for mult. and division. There are no restrictions on the size of the diff. of x (or dx) - large or as small as you want, because:
dx is defined as delta x and
dy is defined as f '(x)*delta x = f '(x)dx. Re-arranging we obtain: "(diff. of y) divided by (diff. of x)" is indeed equal to f ' (x).
Dang why did this one fail so badly? The algorithm did you dirty
It will remain useful for students for years to come.