Euler's Exponentials - Professor Raymond Flood
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- Опубліковано 12 чер 2024
- A thorough examination of the life and work of one of histories greatest mathematicians, the "Shakespeare of Numbers", Leonhard Euler: www.gresham.ac.uk/lectures-and...
Leonhard Euler was the most prolific mathematician of all time. He introduced the symbols e for the exponential number f for a function and i for √-1. He discovered what many mathematicians consider to be the most beautiful expression in mathematics, e ix = cosx + i sinx: a relation connecting the exponential and trigonometric functions. The exponential function and its inverse the logarithm function appear throughout mathematics and its applications, in physics, engineering, mathematical biology, chemistry and economics.
The transcript and downloadable versions of the lecture are available from the Gresham College Website: www.gresham.ac.uk/lectures-and...
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I can't get enough of Prof. Flood.
These are so good!
About that Irish Coffee question: the trick to keeping the cup/glass warm the longest is to WHIP the cream just enough to incorporate air at 20-25% by volume, and let the cream integrate slowly into the coffee as its whipping fails.
While it still sits atop the coffee with air emulsified in it, the cream will greatly slow heat loss from the entire top surface of the coffee. :-)
Euler discovered the identity 158^4 = 134^4 + 133^4 - 59^4 . Checking it out on my calculator from memory I input 159^4 -134^4 -133^4 = 3810304 which is 1952^2. Removing the two common terms from both equations gives 159^4 = 158^4 +59^4 +1952^2. So there you have it, a trio of interrelated quadruples I have called Euler - Bateman quadruples. They are in fact Pythagorean quadruples. Many similarly related trios are also found in cubic quadruples.
At the time I had this strange feeling that Euler was whispering in my ear but alas I didn't know what he was saying as I can't speak German.
An excellent lecture that was easy to follow and listen to.
Quote "We have not the slightest idea of what this equation means, but we may be certain that it means something very important"
This is why we love this stuff! That quote to my mind, sums up the mystery and excitement of the pursuit of knowledge. Superb quote.
Any engineering student will agree that Euler is the go to dude in structural support column acceptable load to prevent catastrophe.
Yes, he brilliantly brought back the mystery with i^i
great video! thank you
What if you took the milk out of the refrigerator, and either added it immediately, or left the milk out for 30 minutes and then added it?
Anybody know where to get the full version of the image shown at the 8 min mark?
thank you, sir, for your great lecture
24.40 Now we come to the most important part, witch is, PRRRRRRRRRRR :p
United States here - had no issues with the dialect. Quite enjoyed the lecture.
Euler, the swiss quality.
The father of russian mathematics school
39:30 more detail at this point would have been helpful for me, such as some additional terms in the cos n(theta) series.
+Mark W This comes from : (cos(t) + i*sin(t))^n = cos(n*t) + i*sin(n*t)
(i^i)^2 = (1/(e^pi)) ...
What if you put in milk before you put in coffee?
Profesor your voice goes away, i cannot understand the end of your sentences.
Sound tech speaking: most of that's not the fault of the professor's voice, but of the technician's over-reaction to its natural variations (the clue is how drastically the room's reverb varies with the overall level of volume).
Rather than working volume changes in gently and in tiny increments to keep the "average" tracking smoothly, the tech far too often waits until excess/insufficient volume gets really hard for even casual listeners to ignore.
great video..i think it was north east of england accent.
Northern Irish accent
ohk thanks :)
"... one of histories greatest mathematicians" should read "... one of history's greatest mathematicians" or rather "... history's greatest mathematician".
Not being an Englishman, it was not easy to follow the dialect.
+Don R. Mueller, Ph.D. It's a Northern Irish accent and not easy to follow even for an Englishman like me
oh, but what a beautiful accent that it is! It's not easy to follow, but it shows the richness and beauty that the English language can demonstrate.
There seems to be some confusion between dialect & accent. The dialect is standard English. The accent is Ulster.