Binge watched the first 10 videos at 2x with a little skipping of the routine parts. Simply superb. No need to take notes. It just makes sense. Beautiful rhythm, intonation, gestures, movement. Master class.
0:56 "If there were no air resistance, we would pick up velocity until we smash into the ground... or pull a parachute." Listen man I don't think there is any easy way to say it but a parachute aint gonna do anything for you there if there's no air resistance...
The formula for air resistance(or drag, generally) is the following: F_d=1/2*density*surface area*drag coefficient(the role of the shape, basically)*velocity^2. Velocity squared! That means that air resistance isn’t proportional to velocity, rather velocity squared. You could see at any point of the video, that the units of measurement don’t match up. That’s because what he wrote as dv/dt=g-kv isn’t true( or reflective of the real world). Anyways, the mathematical explanation is still right, so if we theoreticized a world where air resistance is proportional to velocity in a linear way, then ok. But the physics behind it is not accurate. In the previous application video, in one of the examples v=-10 as he writes it, but that doesn’t give the answer that he wrote. That’s because it’s positive 10.
Thank you for the lecture. It is definitely helping me out understand 'linearity' and the theorem, dy/dx + P(x)*y = f(x) . Just a question, for the first question, that is dv/dt = 32 - 1.6v, why did you not substitute v = distance/time. Since we are 'leaning' on 't' as our independent variable, why not just make the right side explicit by writing it in the form, dv/dt = 32 - 1.6*Distance/Time . My intuition is that since we want to plot a graph, and we want to include 'm' ( slope ) as an axis, we let 'm' represent the x axis. Now since anything along the 'x' axis acts as an independent variable, we cannot let 't' be on the right side, that would mean that there are two independent variables in the same equation, each on a different side. Thus, letting 'v' be the y axis ( on the right side ) would make the most sense. I'm on the fence about this idea, not completely sure. Can anyone help out? Thanks!
Solving the helicopter differential equation exactly, it can be shown that in theory you never actually reach the point where your acceleration reaches 0 after jumping out of the helicopter. However, in reality, variations in the air and various currents will cause you to reach terminal velocity and continue to accelerate and decelerate slightly. Tumbling will affect this a fair bit. G and air density is assumed to be constant because of the relatively small scale. It can get pretty complicated if you try to take everything into account.
This video was excellent, because he didn’t give the full picture, you had to crunch it.. so the Y was implicit, you don’t how hot it relates to the independent variable yet , and if you paid attention to the first videos, you would know that a coefficient times rate of change, integrate that and you get an exponential, and the exponential shows here graphically, and it just makes sense.
Can someone help me?! How is what Prof. Leonard is doing different from constructing direction fields for a given differential equation that only has one variable. For example, consider the differential equation y' = y(4 - y), where y' = dy/dt. I don't think Prof. Leonard addresses this type of problem...or does he?
what are homogeneous differential equation and linear differential equations and how do we differentiate between different kinds of differential equations.I am dealing with this topic in school and is currently confused a lot.kindly discuss these topics in one of your video lectures.How to form differential equation
I don't understand what you get with g - kv when you take an acceleration (m/sec^2) and subtract a velocity (m/sec). They're not even the same units...unless somehow k is a pure number/sec...but what does that mean?
I know it's been 2 years, but yes constants of proportionality can have units, take the most common one V=IR, R has the units of ohms and v and i don't have the same units, but the equation is dimensionally homogenous. So the constant has some units for example, it might depend on the dimensions(length) of the object falling and other factors.
36:10 So, a population won't decrease if it's at the limiting factor? I accept the assumptions of both population and "food" growth being only based on the population itself, but the change at 40 population units suggests that the "food supply" is being affected by the model. If "food supply" does affect the model so much, how can it claim that a population higher than what is sustainable (40 units and below) won't have "food supply" and, consequently, population decreases?
38:06 I understand that populations will decrease if they're not able to be fully sustained, but this is suggesting that population and "resources" are directly proportional, and that isn't acknowledged in the original deq at all, which I would think would be important in a fully accurate model of real life, as he's suggesting
34:51 Is this to say, theoretically, a population can never die out? Also, is the whole idea of the population equation oppositional to the idea that life evolved from nothing?
first SLOPE filed i saw was one where the dy/dx was on the y axis and it only had a x variable like this drag example....so i just drew a cartesian graph where v was the input and dv/dt the y-value measured....i got a straight line with a negative slope of 1.6 the y value is the accel and its zero when v=20.....slope mainly for 2 variables but this shit sure clears up some holes for me or atleast cements....until i get to the solving part lmao save me
@@StuBonham hes still correct, without air resistance you would still accelerate until you hit the ground even with the parachute, which is what he said.
@@pistonsoup3749 That doesn't change the truth of my statement. you will still accelerate all the way down to the ground unless another force acts upward.
@@sangansplan Wich is exactly why it changes the truth of your statement! The force acting upwards is air resistance. Much like the ground acts a normal force upon you. At terminal velocity you net force is 0! You wont accelerate unless there is no atmosphere.
I have a complaint tho, you represented this idea as imprecise and an approximation.. but the validation of this is graphical, so you get an answer, just not algebraic one, but you do get one. If a computer does this job, it gets the same result and answer if you do it with integration
It would still be just an approximation even if a computer does it. It might be a pretty good approximation, it might be a useful approximation, but it is still an approximation and not an exact, precise, mathematical formula that you could, for example, back-substitute into the differential equation and check its validity, or transform it some more with the rules of algebra.
Binge watched the first 10 videos at 2x with a little skipping of the routine parts. Simply superb. No need to take notes. It just makes sense. Beautiful rhythm, intonation, gestures, movement. Master class.
I'm getting closer to zen with each second of these videos
You actually explained physics better than my physics teacher.
Thank you so much for these valuable videos, your efforts, and your time.
This episode, professor Superman is going to talk about how to be a Superman.
0:56 "If there were no air resistance, we would pick up velocity until we smash into the ground... or pull a parachute." Listen man I don't think there is any easy way to say it but a parachute aint gonna do anything for you there if there's no air resistance...
Hmmm so parachute design is all about changing the K...Thanks Prof Leonard!
Awesome video sir. You are a great soul .😎😍😍. I learned more from you. 😘😘😘
The formula for air resistance(or drag, generally) is the following: F_d=1/2*density*surface area*drag coefficient(the role of the shape, basically)*velocity^2. Velocity squared! That means that air resistance isn’t proportional to velocity, rather velocity squared. You could see at any point of the video, that the units of measurement don’t match up. That’s because what he wrote as dv/dt=g-kv isn’t true( or reflective of the real world). Anyways, the mathematical explanation is still right, so if we theoreticized a world where air resistance is proportional to velocity in a linear way, then ok. But the physics behind it is not accurate. In the previous application video, in one of the examples v=-10 as he writes it, but that doesn’t give the answer that he wrote. That’s because it’s positive 10.
This makes it so cool!
World Teacher's Day (Professor Leonard) 5 October.
Its necessary to all thanks for sharing sir
Thank you for the lecture. It is definitely helping me out understand 'linearity' and the theorem, dy/dx + P(x)*y = f(x) . Just a question, for the first question, that is dv/dt = 32 - 1.6v, why did you not substitute v = distance/time. Since we are 'leaning' on 't' as our independent variable, why not just make the right side explicit by writing it in the form, dv/dt = 32 - 1.6*Distance/Time .
My intuition is that since we want to plot a graph, and we want to include 'm' ( slope ) as an axis, we let 'm' represent the x axis. Now since anything along the 'x' axis acts as an independent variable, we cannot let 't' be on the right side, that would mean that there are two independent variables in the same equation, each on a different side. Thus, letting 'v' be the y axis ( on the right side ) would make the most sense.
I'm on the fence about this idea, not completely sure.
Can anyone help out? Thanks!
Hope that Laplace Transform is coming soon Prof!
+DAKINGINDANORF
There are several good Laplace Transform videos on the site Khan Academy.
Solving the helicopter differential equation exactly, it can be shown that in theory you never actually reach the point where your acceleration reaches 0 after jumping out of the helicopter. However, in reality, variations in the air and various currents will cause you to reach terminal velocity and continue to accelerate and decelerate slightly. Tumbling will affect this a fair bit. G and air density is assumed to be constant because of the relatively small scale. It can get pretty complicated if you try to take everything into account.
Thanks
This video was excellent, because he didn’t give the full picture, you had to crunch it.. so the Y was implicit, you don’t how hot it relates to the independent variable yet , and if you paid attention to the first videos, you would know that a coefficient times rate of change, integrate that and you get an exponential, and the exponential shows here graphically, and it just makes sense.
Could you explain it?
Thank for the lecture, helped with my research paper due for my college course. But GOD DAMN them biceps are freaking huge!
thanks
Can we still use slope fields given a higher order differential equation ?
@1:00, if you pull a parachute with no air resistance you still go splat.
Today's rhyme: low grow, high die
wouldn’t the slopes scale with the y-axis? so like a slope of 32 would look like approx. like a slope of 6 on this because 6 boxes represent 30 ft/s.
*Slope Field Plotter:*
www.geogebra.org/m/W7dAdgqc
How about second and higher derivatives though? ;)
Oml thanks
Can someone help me?! How is what Prof. Leonard is doing different from constructing direction fields for a given differential equation that only has one variable. For example, consider the differential equation y' = y(4 - y), where y' = dy/dt. I don't think Prof. Leonard addresses this type of problem...or does he?
what are homogeneous differential equation and linear differential equations and how do we differentiate between different kinds of differential equations.I am dealing with this topic in school and is currently confused a lot.kindly discuss these topics in one of your video lectures.How to form differential equation
He will for sure answer your questions in the next couple of videos.
I don't understand what you get with g - kv when you take an acceleration (m/sec^2) and subtract a velocity (m/sec). They're not even the same units...unless somehow k is a pure number/sec...but what does that mean?
I know it's been 2 years, but yes constants of proportionality can have units, take the most common one V=IR, R has the units of ohms and v and i don't have the same units, but the equation is dimensionally homogenous. So the constant has some units for example, it might depend on the dimensions(length) of the object falling and other factors.
but how do we know that air resistance is linearly dependent on velocity?
That's the domain of scientists and physicists. They study that stuff. You just need to be able to crunch the numbers.
Professor Can u please upload more of permutations and combinations lecture
Prof , this video is showing error as “ video is private “
36:10 So, a population won't decrease if it's at the limiting factor? I accept the assumptions of both population and "food" growth being only based on the population itself, but the change at 40 population units suggests that the "food supply" is being affected by the model. If "food supply" does affect the model so much, how can it claim that a population higher than what is sustainable (40 units and below) won't have "food supply" and, consequently, population decreases?
38:06 I understand that populations will decrease if they're not able to be fully sustained, but this is suggesting that population and "resources" are directly proportional, and that isn't acknowledged in the original deq at all, which I would think would be important in a fully accurate model of real life, as he's suggesting
34:51 Is this to say, theoretically, a population can never die out?
Also, is the whole idea of the population equation oppositional to the idea that life evolved from nothing?
first SLOPE filed i saw was one where the dy/dx was on the y axis and it only had a x variable like this drag example....so i just drew a cartesian graph where v was the input and dv/dt the y-value measured....i got a straight line with a negative slope of 1.6
the y value is the accel and its zero when v=20.....slope mainly for 2 variables but this shit sure clears up some holes for me or atleast cements....until i get to the solving part lmao save me
1:15 you would still crash into the ground with a parachute without air resistance xDD
Sure, but this is about acceleration not velocity...
@@StuBonham hes still correct, without air resistance you would still accelerate until you hit the ground even with the parachute, which is what he said.
@@sangansplan False, its called terminal velocity. Fnet = 0 a =0
@@pistonsoup3749 That doesn't change the truth of my statement. you will still accelerate all the way down to the ground unless another force acts upward.
@@sangansplan Wich is exactly why it changes the truth of your statement! The force acting upwards is air resistance. Much like the ground acts a normal force upon you. At terminal velocity you net force is 0! You wont accelerate unless there is no atmosphere.
Im pretty sure population needs at least 2 to grow
I didnt know clark Kent taught odes
After watching this video I think that hunting elk and boar from a helicopter might not be ideal afterall :)
28:58 ... but if you wait several billion years, simple cells could form which could eventually turn into fish ;) lol
if there's no air resistance... that parachute isn't going to do you any good. =)
I have a complaint tho, you represented this idea as imprecise and an approximation.. but the validation of this is graphical, so you get an answer, just not algebraic one, but you do get one. If a computer does this job, it gets the same result and answer if you do it with integration
It would still be just an approximation even if a computer does it. It might be a pretty good approximation, it might be a useful approximation, but it is still an approximation and not an exact, precise, mathematical formula that you could, for example, back-substitute into the differential equation and check its validity, or transform it some more with the rules of algebra.
@@bonbonpony Limits are approximation tho, so literally all of calculous is based on an approximation, a pretty good one, but one nonetheless.
approximate deez nuts slapping yo chin
@@franciscopen1681 Only when you base calculus on limits. This is not the only way to do calculus though. But that's a whole another story...
Professor leonard plz suggest us a book.for doing diff equation plz
You do not need one.
@@kostasmerenidis1307 no.no.I.need this,,,,dear
@@JawadAli-tj3ec What is your major?
@@kostasmerenidis1307 didn't get ur point ,,pursuing BS MATHEMATICS,,
@@JawadAli-tj3ec Well then you do need a textbook.
"Its like when you shoot a gun downwards".... What?...America....
Fun fact: 0.0225/0.0003 gives the equilibrium population of 75
hi rock hudson(:
28:55 Checkmate, atheists
The only thing that has changed that you're married
23rd like
I feel like he'd do a great job teaching calculus based physics but I have a feeling he'd cringe at the thought.
Who disliked this video >:(
Probably a flat-earther that doesn't believe that gravity is real