Episode 7: Integration - The Mechanical Universe
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- Опубліковано 10 лют 2025
- Episode 7. Integration: Newton and Leibniz arrive at the conclusion that differentiation and integration are inverse processes.
“The Mechanical Universe,” is a critically-acclaimed series of 52 thirty-minute videos covering the basic topics of an introductory university physics course.
Each program in the series opens and closes with Caltech Professor David Goodstein providing philosophical, historical and often humorous insight into the subject at hand while lecturing to his freshman physics class. The series contains hundreds of computer animation segments, created by Dr. James F. Blinn, as the primary tool of instruction. Dynamic location footage and historical re-creations are also used to stress the fact that science is a human endeavor.
The series was originally produced as a broadcast telecourse in 1985 by Caltech and Intelecom, Inc. with program funding from the Annenberg/CPB Project.
The online version of the series is sponsored by the Information Science and Technology initiative at Caltech. ist.caltech.edu
©1985 California Institute of Technology, The Corporation for Community College Television, and The Annenberg/CPB Project
This is the series I should have watched while studying my higher secondary physics. My bad I didn't have Internet. Absolute Gem of Knowledge on youtube. BRIGHT SIDE OF UA-cam
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@Gaurav Chaurasia same 😀
@@user-pl7tf9gv8e wat do you mean by deserve?
@@shankarganesh1230 nothing nvm
I love the reinactments and the music. Kudos to Caltech for such a high quality educational production.
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this series is too elegant and extraordinary thnx.......
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Thank you, Caltech!
This series is the best!
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Highest quality Teaching.
THANK YOU VERY MUCH, GOD BLESS THE TEAM WHO MADE THIS VIDEO
I just love the moments when the Utah Teapot make a role in the episodes
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It’s a gem of a series. Late to watch
Leibniz idea of small rectangles like that of a picket fence under a bounded curve was quite similar to the idea of the method of exhaustion that the greeks used with triangles to come up with the area of a parabolic segment or that of a circle..
Similar idea, but the Greeks lacked one essential tool: the concept of the mathematical limit.
25:30 LOL "The Answer to the Ultimate Question of Life, the Universe, and Everything"
Isaac also did Hooke wrong. Newton wasn't the only one who arrived to a conclusion of the discovery of gravity. Newton's position in politics, put him in an advantegoues position to not share credit to scientific discoveries with fellow scientists that came to same conclusions he did. I'm not downplaying or minimizing Isaac's contribution to physics and mathematics. But what I'm simply saying is that he was a bitter dude.
Hooke guessed at an inverse square law , but he didn't have the mathematical ability to prove it, or apply it to planetary motions etc
issac wasnt the only one to find gravity? name it who did, you are probably working for the tabloid newpaper, the only way that you can understand the laws of force is only by inventing calculus first. issac was totally more than nice enough to give the credit of the discovery of a halley's comet to edmond halley. at that time isaac already had equipped with calculus and laws of force at his disposal, he told edmond halley where to find the comet in his solution r(t) which means the position of the comet as a function of time.
@@abcdef2069 read my comment with comprehension this time.
@@sphakamisozondi the biggest mistake isaac newton ever made was to send the letter of discovery of calculus to weasel liebniz something like 10 ~15 years before liebniz trying to get a credit of it. some people said isaac was bitter like you, but these herd behaving people like parrots couldnt show and tell which part of isaac was bitter? his giving free scientific discovery credit to anyone? or shutting up their jealous mouths like hooke. besides, calling the spring force the hookes' law is already insulting to me, otherwise we will end up naming the items forces as many times as the number of chemical compounds, isaac fought with liebniz for 20 years till isaac died. hooke and liebniz the same, in my blatant opinion, "steal it from isaac then name it with mine". isaac basically sold the household name discovery of halley's comet's location to halley in exchange for publishing principle of mathematica, isaac was too poor to afford it alone.
Music is on point! Love this.
9:45 Do you know the name of this song?
Best of all possible worlds
The inner five electron is the other side of what it is that it's calculating the numbers for the process of being noticed
Are some of the dramatic scenes from Carl Sagan’s Cosmos? Or vice versa? The scenes of Kepler, in particular, are very familiar.
Yes, the scenes with Kepler are from Cosmos.
At the finish Newton is described as " not a very nice man " but actually during his lifetime he was described as being a "nice" man. Because in those days 'nice' meant 'particular 'or 'difficult' or 'prickly' etc
9:45 song name?
Our Math Prof would have said:-
One should see by accumulated Observation, ..the principle of probabilistic Correspondence in aligning the z-axis at zero-infinity, .dt, with the "collapsed" Functional Universal omnidirectional-dimensional Origin of self-defining infinitesimal i-reflection wave-particle Unit Circle containment Singularity-point positioning, and "One Electron" Theoretical time-timing Sublimation-Tunnelling "Holes", Renormalisation and Supersymmetric Resonance etc.., the point of nothing floating in No-thing Relativity.., here-now-forever sync-duration.
Hello I am curions to know if these sets of CALTECH courses very well made are a normal math courses for caltech students , or sessions for non-Caltech people like me ? And if it is a normal math course givrn to Caltech students in their cursus , may I know how old the caltech students are learning F=ma hence ?
does anyone know the name of that harpsichord tune?
For love of God someone send the music in the final of the vídeo
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@@beoptimistic5853 A thousand thanks for ye!
@@rodolfodias9034 did you ever find out??
Interessante , o calculo integral então , é uma espécie de fórmula geral , para se calcular a área de quaisquer figuras . eu acho que , o primeiro teorema fundamental do cálculo e o segundo teorema fundamental do cálculo , falam a respeito da integral indefinida e da integral definida , respectivamente . Lamentável essa briga de Newton e Leibniz .
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42! Nice!
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A new world just opened in front of me 🤯
Can anyone tell me the song at the end-credits please
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This is so annoying. Whoever put the Annenberg Media logo at the front of these videos really made a mistake. It throws the whole audio off the video. I have watched these lectures more than once, so I know there was not always this Annenberg Media introduction. Can someone please put it back to what it was?
Due to copyright issues (which I suspect since I had been a UA-cam user since 2008), they tried to alter the film speed to frustrate UA-cam's copyright algorithm mechanisms.
What about the inner other side
4:55 who was this mathematician ?
Galileo
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Which is a5electron
after this video I want to make some integrations hah
25:33 what is 42 ?
I think it’s just an example number
The answer to life, universe and everything.
just calculus in math? as being a 1st person to know about the calculus, he invented the differential eqs, how to solve differential eq with power method, every numerical method you can think of, how to solve ultimate nonlinear multi-dimensional coupled equations, jacobian matrix..... just say whole mathematics, if liebniz really knew about the calculus, he would have come with something in math but had none, because when liebniz received the calculus letter from issac newton, he knew how important it would be... so liebniz invented the calculus notations and everyone can make notations.
when liebniz published calculus, it made issac newton so mad that issac newton had to quit everything he was woking on and fight for the calculus credit for 20 YEARS until he died. issac wasted his greatest mind on this credit garbage. imagine what more he would and could have complished with his riped and ripened scientific mind. if one understands to solve nonlinear multi-dimensional coupled equations, tears may form in your eyes they are the epitome of all things.
@@abcdef2069 wrong, they literally showed in the video how Leibniz’s practical approach to calculus was different from Newton’s, like Leibniz had his own system of integration for example, also Newton’s method for calculating the derivative doesn’t work 100% of the time, were as Leibniz’s does as such we don’t use Newton’s calculus at all anymore in the modern day. Don’t get me wrong Newton is my ultimate all time hero so I am in no way attempting to discredit him here, I’m just trying to say that it’s unfair to just write off Leibniz when he was by far the superior mathematician.
@@Gh0stily111 people often say leibniz published 1st, publication was not that important around 17th century, people even might get a church's death inquisition, or people might do math-duel for a beer back then . there is an isaac newton's letter to leibniz about calculus 20 years before leibniz publication, this letter is more than a publication enough to me, and this fact annoyed issac newton so much he did nothing but wasted his greatest mind fighting for the calculus credit for 20 years until he died (age about from 60 to 80). leibniz cheated from the issac's letter and he published without giving a single credit as to where he got the calculus idea. when i looked at how to solve the issac's nonlinear muti-dimensional coupled eqs, i found no doubt he was the greatest genus, maybe more than einstein. the more people say publication 1st in youtube,without mentioning the letter, i will have to discredit leibniz
@@abcdef2069 1) I never said anything about who published first, that’s irrelevant to me I’m talking about who was the more talented mathematician.
2) Newton had a brilliant propaganda team, which does influence the public conscious a little bit into seeing Newton as the superior mind.
3) I doubt he would have made any contributions at the age of 60+, and even if he did the same could be said for Leibniz, who was also busy arguing with him at that time.
4) To believe Newton’s the greatest mathematician you have to accept that other people are on par with him since many have made the same discoveries as him, think Raphson, Madhava and of course Leibniz.
5) I know Newton’s formulas can seem more complex than Leibniz’s but in mathematics you want quickness and efficiency in your formulas, not complexity. Also he basically just recycled stuff from Euclid as he believed the ancient Greeks had divine enlightenment, so his infinite series probably could have been discovered by Archimedes or Leibniz, only they didn’t hold that stuff in as high regard as he. Just goes to show what an influence your interests have on your abilities.
6) Weather Leibniz was a good person or not is irrelevant to my argument, also why should he have credited him, all he did was present him with the already discovered works of old which Newton used to privately invent his calculus, he did this to see if Leibniz was smart enough to do the same independently, which makes it very impressive that Leibniz had the better which he came up with from scratch, but even if you believe the version were Newton flat out showed him his completed calculus, but even then Leibniz made improvements Newton never could have, wether that be due to busyness with other things on Newton’s part or what. But no matter what you believe at the end of the day Leibniz couldn’t have done it without Newton’s influence.
It was I, the starter of the meme.
i was late watching this.
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These series are awesome. The only thing that bothers me are that teacher's jokes.
I look forward to Prof. Goldstein’s opening remarks as well as the closing statements. There is a lot of insight in them. I wish Caltech would provide videos of the full lectures, though.
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You will be okay 👌, Just breathe ❤
which is a
Poor Isaac, I wonder what writers of this series got against him.
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I don't think they have anything. It's based on historical accounts.
You have to admit the part about him dying a virgin was very funny
@@bigchungus711 His problem in getting along with people was clearly because he never got laid.
Brian May vs Ronnie James Dio
Pronounced Prinkipia not Prinsipia.
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War made lebinezt evil