Ghosts of Departed Quantities: Calculus and its Limits - Professor Raymond Flood

[@berylgreen1973]

This is the clearest explanation of differentiation and integration, and their relationship, that I've ever seen. Thank you! And I love that you get somewhat heated, nearly 300 years after the fact, when rebutting Berkeley's arguments against the calculus. Bravo!

[@Redrios]

thank for keeping this priceless video lecture series for people to watch despite the years!

[@stevencapps7641]

I generally despise math and I am only in high school at them moment but I could not help but watch this start to finish even taking some notes while doing it. Great video and some very interesting information.

[@nicorobinorsomething]

Steven Capps What're you up to 4 years later?

[@robertstuckey6407]

Now I want to know too

[@PedroTricking]

What are you up to 5 years later?

[@chrisg3030]

"Calculus is probably the most important mathematical technique ever devised" says Professor Flood. He could have added the qualification "since counting and measurement", though he was doubtless assuming that. The great advantage of putting numbers to a changing quantity at different times is that we can spot a difference that would otherwise elude us until too late. One big flock of sheep can look very much like another, or like it was last week, but 275 and 273 are immediately distinguishable. Numbering is a kind of magnifying glass for the present, and a telescope for the future. This is also true in more modern times for double differentiation used in finding the inflection point on a curve long before the change in the rate of change becomes obvious. That phrase "ghost of departed quantities" is one-sided since the point of both these techniques is to reveal, or at least warn of, quantities to come.

[@MrRichygm]

A brilliant and engrossing lecture. Thank you, Dr Flood.

[@mms9076]

The formalized concept of the limit came after differentiation and integration!? What an amazing lecture! I really wish he would have gotten a little more into how Newton and Leibniz responded to the challenges they would receive during their debate of who originated the calculus. I will always think of ghosts of departed quantities when thinking about limits from now on! Amazing that Leibniz and Newton both just intuitively assumed the notion of a point getting infinitely close to another and developed their theories around it without giving it a formal treatment, considering how analytical their minds where.

[@davidwilkie9551]

Great lecture, worth revisiting. Description follows a narrative path. The final destination is always beyound a vanishing point over the horizon and the reverse case is "down from the sunset sky" that is eternally unchanging, so from a pivotal position here-now, the apparent destination is over the horizon, ..rising up into the morning from the mapped landscapes around us and printed on the night sky in bright vanishing points of the stars..., "obviously". Transferring the visibly apparent images onto symbolic maps in usable mathematical proportions has become differentiated into multiple disciplines for "life's journey", in QM-TIME. The above lecture is an excellent example of assembling such key features of obvious importance, but because they're derived mostly from practical usage and therefore assembled by the intuition of broad experience, the natural fit of these features is not so recognisable in the ubiquitous "forest" of the Quantum Fields Mechanism, ..radially divided pivot at zero difference= instantaneous connection-reflection, of tangential phase-states here-now in the there-then perspective of infinite-eternity. The Universe is a field of quantum points of potential, density-intensity proportions at temporal superposition-singularity. Differentiation, division of numerical powers is simultaneously pivotal and tangential, (as stated at the beginning of the lecture), and identifies, in one way, the phase-states of symmetry and modulation by the curvature, time state-rate of dimensional, orthogonal-discreteness in the context of Polar-Cartesian coordinates. "In other words" the basic principle of connection has infinitely arranged compounds/languages of identity.

[@Davemac1116]

I got a 'C' in calculus. I think the furthest I got was Fourier Series, which I didn't understand, and by that time my brain had suffered catastrophic implosion. My mind then helpfully chirped in: "Dave, you have the intellectual capacity of a squashed apricot. Even the mouse that lives behind the wall helped you with the algebra for extra cheese. And then told you to piss off when you didn't know that 1/x is the same as x power minus one."

[@VickiNikolaidis]

very interesting history The feature I enjoy most about calculus is the ability to set limits.

[@AlexanDrMoskalenko]

so interesting and inspiring, thanks

[@IngridMacherTV]

very informative, thanks for sharing this video!

[@ellabrendairianto5211]

This helps more than school

[@shohamsen8986]

Raymond Flood Rocks.. :P

[@theatchico]

Anyone know when Professor Flood returns to the topic mentioned at 45:06 ?

[@k.spraygod3873]

This was awesome !!!

[@jcasaubon]

Awesome video!

[@ikikikiikik]

I've seen all of his videos :)

[@AlfaHanen1]

Thanks for that good INFO

[@lexinaut]

Higher than any fireworks finale, Longer than any Empire, Is the pure flight of the curve seeking infinity.

[@ianian8022]

Chris G: yes or maybe no.... probably....uhmm.....yeeeeaah.....so, do you have those aspirins for me then?

[@giuseppeguccione7437]

molto interessante

[@sebastianbalbo1906]

Calculus came from INDIA from there the British acquired the knowldege of INDIAN Way for math Cochin KOLKATA GOA were the cities from where BRITISH FOUND THE MATH TEXTS

[@aloysiuspendergast7221]

I like the punny title

[@SubstratumMaxima]

Infinite/taylor series for various trigonometric functions such as sine,cosine,arctangent,tangent and pi were discovered by Madhava of sangamgrama (who was an Indian mathematician living in 14 th century) way before leibnitz and newton. Madhava and his school worked with calculus of finite differences and was able to integrate/differentiate these selected trigonometric functions. Using methods of calculus such as interpolation/iterative approximations/differentiation/integration madhava was able to calculate sine values of any angle with accuracy of 8 digits after decimal place. here is my source- en.wikipedia.org/wiki/Madhava_series#Madhava.27s_sine_series en.wikipedia.org/wiki/Madhava%27s_sine_table His pupils and his school produced results which would today could be counted as calculus. I hope you take notice of this in your next videos. for more details about development of calculus in India(before similar developments in Europe by atleast 150 yrs) these links are useful- en.wikipedia.org/wiki/Yuktibh%C4%81%E1%B9%A3%C4%81 en.wikipedia.org/wiki/Madhava_of_Sangamagrama en.wikipedia.org/wiki/Nilakantha_Somayaji Show less

[@raghavarvoltore6517]

You forgot to mentioned that they also discovered instantaneous velocity.