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clearly, d/dx simplifies to 1/x
If not fraction, why fraction shaped?
Having studied physics myself I’m sure physicists know what a derivative looks like.
I still don’t know how I made it through those math curses at uni.
Why does using it as a fraction work just fine then?
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.
Let’s face it: Calculus notation is a mess. We have three different ways to notate a derivative, and they all suck.
I’ve seen e^{d/dx}
Division is an operator
Mathematicians will in one breath tell you they aren’t fractions, then in the next tell you dz/dx = dz/dy * dy/dx
Have you seen a mathematician claim that? Because there’s entire algebra they created just so it becomes a fraction.
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
Brah, chain rule & function composition.
(d/dx)(x) = 1 = dx/dx
Also multiplying by dx in diffeqs
vietnam flashbacks meme
What is Phil Swift going to do with that chicken?
The will repair it with flex seal of course
To demonstrate the power of flex seal, I SAWED THIS CHICKEN IN HALF!
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.
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.
I always needed practical examples, which is why it was helpful to learn physics alongside calculus my senior year in high school. Knowing where the physics equations came from was easier than just blindly memorizing the formulas.
The specific example of things clicking for me was understanding where the “1/2” came from in distance = 1/2 (acceleration)(time)^2 (the simpler case of initial velocity being 0).
And then later on, complex numbers didn’t make any sense to me until phase angles in AC circuits showed me a practical application, and vector calculus didn’t make sense to me until I had to actually work out practical applications of Maxwell’s equations.
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
I always chafed at that.
“Here are these rigid rules you must use and follow.”
“How did we get these rules?”
“By ignoring others.”
2+2 = 5
…for sufficiently large values of 2
Found the engineer
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
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)
0.1 + 0.2 = 0.30000000000000004
comparing floats for exact equality should be illegal, IMO
Statistician: 1+1=sqrt(2)
pi*pi = g
units don’t match, though
is this how Brian Greene was born?
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Chicken thinking: “Someone please explain this guy how we solve the Schroëdinger equation”
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
