You must log in or register to comment.
This very nice Romanian lady that taught me complex plane calculus made sure to emphasize that e^j*theta was just a notation.
Then proceeded to just use it as if it was actually eulers number to the j arg. And I still don’t understand why and under what cases I can’t just assume it’s the actual thing.
Why does using it as a fraction work just fine then?
What is Phil Swift going to do with that chicken?
Division is an operator
Chicken thinking: “Someone please explain this guy how we solve the Schroëdinger equation”
It was a fraction in Leibniz’s original notation.
And it denotes an operation that gives you that fraction in operational algebra…
Instead of making it clear that
dis an operator, not a value, and thus the entire thing becomes an operator, physicists keep claiming that there’s no fraction involved. I guess they like confusing people.
Mathematicians will in one breath tell you in one breath they aren’t fractions, then in the next tell you dz/dx = dz/dy * dy/dx
This is until you do multivariate functions. Then you get for f(x(t), y(t)) this: df/dt = df/dx * dx/dt + df/dy * dy/dt
Have you seen a mathematician claim that? Because there’s entire algebra they created just so it becomes a fraction.
(d/dx)(x) = 1 = dx/dx
Also multiplying by dx in diffeqs
vietnam flashbacks meme
Derivatives started making more sense to me after I started learning their practical applications in physics class.
d/dxwas too abstract when learning it in precalc, but once physics introducedd/dt(change with respect to time t), it made derivative formulas feel more intuitive, like “velocity is the change in position with respect to time, which the derivative of position” and “acceleration is the change in velocity with respect to time, which is the derivative of velocity”Possibly you just had to hear it more than once.
I learned it the other way around since my physics teacher was speedrunning the math sections to get to the fun physics stuff and I really got it after hearing it the second time in math class.
But yeah: it often helps to have practical examples and it doesn’t get any more applicable to real life than d/dt.
yea, essentially, to me, calculus is like the study of slope and a slope of everything slope, with displacement, velocity, acceleration.
I found math in physics to have this really fun duality of “these are rigorous rules that must be followed” and “if we make a set of edge case assumptions, we can fit the square peg in the round hole”
Also I will always treat the derivative operator as a fraction
2+2 = 5
…for sufficiently large values of 2
Engineer. 2+2=5+/-1
I mean as an engineer, this should actually be 2+2=4 +/-1.
Computer science: 2+2=4 (for integers at least; try this with floating point numbers at your own peril, you absolute fool)
comparing floats for exact equality should be illegal, IMO
pi*pi = g
units don’t match, though
Statistician: 1+1=sqrt(2)
i was in a math class once where a physics major treated a particular variable as one because at csmic scale the value of the variable basically doesn’t matter. the math professor both was and wasn’t amused
is this how Brian Greene was born?
Except you can kinda treat it as a fraction when dealing with differential equations
Oh god this comment just gave me ptsd
Only for separable equations
Look it is so simple, it just acts on an uncountably infinite dimensional vector space of differentiable functions.
fun fact: the vector space of differentiable functions (at least on compact domains) is actually of countable dimension.
still infinite though
When a mathematician want to scare an physicist he only need to speak about ∞
When a physicist want to impress a mathematician he explains how he tames infinities with renormalization.
Is that Phill Swift from flex tape ?
De dix, boss! De dix!
Little dicky? Dick Feynman?
