These fucking symbols

What do they mean?

Sometimes, my prof or a book will use them in a literal sense. Actually plugging them into equations.

Sometimes theyll be in an equation then vanish for no apparent reason, as if theyre just notation

wtf do they mean?

Attached: 2scgjVP_d.jpg (640x476, 5K)

Other urls found in this thread:

en.m.wikipedia.org/wiki/Fréchet_derivative
twitter.com/SFWRedditGifs

Delta x means a change of that variable, for example delta x means change of time
dx means in respect to x, when you calculate derivative or integrate you have to specify in respect to what you do this

so dx is just notation? you dont plug it in? cuz my calc3 tutor is retarded then

You're in calc 3 and you don't know what dx means?

yea its just a notation

no you brainlet, dx is differential of x, which is just change of x over an infinitesimally small scale. For example, dy/dx is basically differential of x over the differential of y, which is basically the slope over an infinitesimally small scale.
Why the fuck do you think in the chain rule, dz/dx = dz/dy * dy/dx, the dys cancel out.

> x
> time

accidentally clicked submit
for integrals,
you have
[math]\frac{dy(x)}{dx} = f(x)[/math]
[math]dy(x) = f(x)dx[/math]
[math]\int_{a}^{b}dy = \int_{a}^{b}f(x)dx[/math]
[math]y(b) - y(a) = \int_{a}^{b}f(x)dx[/math]
note y(x) is y evaluated at x
you can see that derivatives are literally slopes, and integrals are literally cumulative sums

some autist is gonna reply to this and mention that you need to be able to convert to a differential form to have a ratio of differentials. I'll save him the trouble and go on to mention that your post describes a great mnemonic device for doing calculus quickly

dx is trash except you are talking bout differential forms.

>it’s ANOTHER calculus thread

Attached: 3D68AD77-5FE2-434B-9FD1-96F1D95E29A7.png (469x452, 277K)

....but it is just notation then.

differential form is the most intuitive interpretation tho

...and it helps you complete the task you set out to achieve

But the question is to understand if the object has a clear mathematical meaning, and your post implies it does but it ends saying actually no.

y = f(x)

since y is a function of x, it's derivative is with respect to x

D[y] = D(f(x))

dy = f'(x) dx

dy/dx = f'(x)

It isn't necessarily "math", rather the notation moves around as if we were multiplying both sides by dys and dxs. This isn't what's happening, it's just our notation

Yes. Do you?

Can you elaborate more?

still dont have a definitive answer as to whether dx is a notation or something i can work with algebraically

does multiplying both sides of an equation by dx make sense? does having dx as a component of a vector make sense?

In the first line of the table, the possible integer values of Δz. You can see that this is just a list of the integers, of course. Next is listed some integer values for other exponents of Δz. This is also straightforward. At line 7, it begins to look at the differentials of the previous six lines. In line 7, it is referencing line 1, just subtracting each number from the next. Another way of saying it is that it is looking at the rate of change along line 1. Line 9 lists the differentials of line 3. Line 14 lists the differentials of line 9. I think you can follow the logic on this.
1 Δz 1, 2, 3, 4, 5, 6, 7, 8, 9….
2 Δ2z 2, 4, 6, 8, 10, 12, 14, 16, 18….
3 Δz2 1, 4, 9, 16, 25, 36, 49 64, 81
4 Δz3 1, 8, 27, 64, 125, 216, 343
5 Δz4 1, 16, 81, 256, 625, 1296
6 Δz5 1, 32, 243, 1024, 3125, 7776, 16807
7 ΔΔz 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
8 ΔΔ2z 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2
9 ΔΔz2 1, 3, 5, 7, 9, 11, 13, 15, 17, 19
10 ΔΔz3 1, 7, 19, 37, 61, 91, 127
11 ΔΔz4 1, 15, 65, 175, 369, 671
12 ΔΔz5 1, 31, 211, 781, 2101, 4651, 9031
13 ΔΔΔz 0, 0, 0, 0, 0, 0, 0
14 ΔΔΔz2 2, 2, 2, 2, 2, 2, 2, 2, 2, 2
15 ΔΔΔz3 6, 12, 18, 24, 30, 36, 42
16 ΔΔΔz4 14, 50, 110, 194, 302
17 ΔΔΔz5 30, 180, 570, 1320, 2550, 4380
18 ΔΔΔΔz3 6, 6, 6, 6, 6, 6, 6, 6
19 ΔΔΔΔz4 36, 60, 84, 108
20 ΔΔΔΔz5 150, 390, 750, 1230, 1830
21 ΔΔΔΔΔz4 24, 24, 24, 24
22 ΔΔΔΔΔz5 240, 360, 480, 600
23 ΔΔΔΔΔΔz5 120, 120, 120
from this, one can predict that
1/2

Some of us didn't learn bullshit for engineers in our calc classes.

Maybe you should have because limits are used to define derivatives and integrals you fucking brainlet

It's a number smaller than every real non-zero number but greater than zero.

Yes, limit of quotients between the difference between a function with thd function evaluated at some point. and the difference of x as it approaches that point. Your limit is trivialy 0.

so it's 0 then ?

Delta x is used to represent a literal change in x that you can measure.
dx is notation that you should only see in front of an integral sign or in a derivative "fraction" until you do differential geometry and these become properly defined.
Most likely your prof was treating them as fractions as this is a consequence of the chain rule, that in most cases it will work out alright.

Thank you, finally i understood

Oh boy, this thread gave me cancer.
OK, what the fuck is the differential anyway?
We say that the function [math]y(x)[/math] is differentiable if [math]y(x+h)-y(x)=A(x)h+o(h)[/math]. This stuff [math]A(x)h[/math] is the differential [math]dy(x;h)[/math]. So, by the definition, the differential is a linear in [math]h[/math] function. It's not undefined magic notation or some nonsense, it's a function. Remember, children, the differential is a function.

So, what's the differential of the function [math]y(x)=x[/math]?
[math]x+h-x=h=dx[/math]

Now, it happens that [math]A(x)[/math] is actually the derivative [math]y'(x)[/math]. That's why we can write
[math]dy=y'(x)dx[/math]

Can we divide by [math]dx[/math]? Hell yes. It's just a function!
[math]\frac{dy}{dx}=y'(x)[/math]
So, the derivative is the coefficient of proportionality between the functions [math]dy[/math] and [math]dx[/math].

[math]\Delta x[/math] is a number.
[math]\text{d}x[/math] is a differential form.

delta x is for finite changes
dx is for differential changes

literally the only difference

delta x is just a difference. How stupid are you fucking people even? dx = x_2 - x_1

i always thought dx was the opposite of something infinitely large. Like 1/inf

length of a curve is therefore the sum of all ds
ds=sqrt(dy^2+dx^2)

That's just old notation that is used in diferential geometry. Also your algebra is useless for higher dimensional spaces, that's why the best definition is en.m.wikipedia.org/wiki/Fréchet_derivative

they're the same thing.E= VM
dE = dV/m which is also ΔE = ΔV/m