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/sci/ - Science & Math

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7335721 No.7335721 [Reply] [Original]

Which of these is the best notation?

Which do you like best?

>> No.7335733

>>7335721
None, <span class="math">\frac{df}{dx}(x)[/spoiler].

>> No.7335734

I tend to use newton's for time derivatives, otherwise Leibnitz. Don't know about best, but i don't like lagranges.

>> No.7335742

>>7335721
There all good for different things.

>> No.7335753
File: 7 KB, 248x200, 248px-Linalg_projection_3.png [View same] [iqdb] [saucenao] [google]
7335753

>>7335733
That's not even proper notation

>> No.7335758

>>7335721
Newton's is a good shortcut when it is already clear from context what you are doing and you have only one variable.
For everything else Leibniz's is clearer and it's nice to use a similar notation for derivatives and integrals.

>> No.7335761

>>7335753
Yes it is, f is the function not f(x), that's it's value at x. And the derivative is again a function which the other notations fail to acknowledge.

>> No.7335765

>>7335734

Same. That's what most people use, I think. At least once they get into multivariable calc.

>> No.7335766

>>7335721
Leibniz's in most cases

>> No.7335768

>>7335761
Actually yeah, you're right. It's proper. I thought it read df/dx f(x)

>> No.7335778

Honestly, I kinda like the Lagrange and Newton notations, they seem simple and clear. But Leibniz is standard, and I dont much use Euler's way.

>> No.7335779

>>7335721
lagrange because im lazy as fu

>> No.7335784

>>7335778
>>7335779
Lagrange confirmed for best

>> No.7335786

>>7335778
>Honestly, I kinda like the Lagrange and Newton notations, they seem simple and clear.

They don't specify what it is a derivative with respect to, so they are only useful as shorthand when it is clear from context.

>> No.7335792

>>7335721
I use Lagrange and Newton, but I don't punt the dot's on Newtons notation, I put the apostrophes on the "y" just like in the Lagrange Notation.
Makes more sense to me.

>> No.7335800

>>7335786
Lagrange I get it, but with Newton in OP's pic is deriving "y" respect to "t", right?
If you want more variables just write dt dg on the denominator and you're good.

>> No.7335803

>>7335721
I pretty much always use Euler's notation. Easier to write on college ruled paper.

>> No.7335805

>>7335792
Newton used apostrophe's for antiderivatives and dots for derivatives.
>>7335721
I prefer Euler's. Simple and completely descriptive
But I rarely use it.

I use Newton's for time derivatives and Leibniz for everything else

>> No.7335817

>>7335786
>They don't specify what it is a derivative with respect to, so they are only useful as shorthand when it is clear from context.
What? Have you never seen this before:
<span class="math">f''_{xy}(x,y)[/spoiler]

>> No.7335820

Lagrange for single variable functions in maths.
Newton for single variable functions of time in physics.
Leibniz for multivariable calculus in physics.
Euler for multivariable calculus in maths.

Checkmate.

>> No.7335824

I mix them all up for maximum confusion. Leibniz's is most useful if I want to multiply by dx and integrate.

>> No.7335831

Why is Euler wearing underwear on his head?

>> No.7335834

Lagrange. Only physicists are maths impaired enough to answer Leibniz.

>> No.7335839

>>7335817
><div class="math">f''_{xy}(x,y)</div>
Sexy

Lagrangefags unite

>> No.7335843

Depends what youre doing with it but Euler's is the most descriptive when you have conciseness in mind

>> No.7335846

>>7335843
Lagrange still takes less effort to write.

>> No.7335967

>>7335721
euler's

>> No.7335993

>>7335817
I usually don't use apostrophes when using subscripts, your example would be:
<span class="math">f_{xy}(x,y)[/spoiler]
Then again, I usually use Leibniz's notation.
I also subscripts for derivatives when dealing with tensors using Einstein's notation (even if it's a bit different, e.g. <span class="math">\varepsilon_{ij,kh} = \frac{\partial^2 \varepsilon_{ij}} {\partial x_k\ \partial x_h}[/spoiler]).

>> No.7335995

>>7335993
>I also subscripts
*I also use subscripts

>> No.7336013

>>7335721
Newtons whenever I'm doing something involving time derivatives, Leibniz's when I'm doing something more general and Lagrange's when I'm making quick notes about something.

>> No.7336019

Euler's I guess.

Usually Df instead of Dy.

>> No.7336030

>>7335721
Euler for partial derivatives
Leibniz for regular derivatives

>> No.7336039

>>7335721
I always found f'(x) the easiest to read and write.
- only one you can type without Latex
- the d/dx notation gets beginners in trouble because they start trying to treat "dx" as an algebraic variable that they can move around the equation
- the dots often imply "derivative with respect to time"

>> No.7336053

Leibniz because of there's a convenient way to represent a derivative as a function and differentiation as an operator.

Lagrange for higher order derivatives.

>> No.7336077

>>7335721
>2015
>Not inventing a clearly superior notation that uses the same symbol for everything and isn't at all confusing.

<span class="math">
{\diamondsuit _x}F = \frac{{dF}}{{dx}}
[/spoiler]

<span class="math">
{\diamondsuit _{yy}}F = \frac{{{d^2}F}}{{d{y^2}}}
[/spoiler]

<span class="math">
{\diamondsuit ^x}F = \frac{{\partial F}}{{\partial x}}
[/spoiler]

<span class="math">
{\diamondsuit ^{xx}}F = \frac{{{\partial ^2}F}}{{\partial {x^2}}}
[/spoiler]

<span class="math">
{\diamondsuit ^{xyzw}}F = \frac{{{\partial ^4}F}}{{\partial x\partial y\partial z\partial w}}
[/spoiler]

<span class="math">
^X\diamondsuit Y = {\nabla _X}Y
[/spoiler]

<span class="math">
_X\diamondsuit Y = {D_X}Y
[/spoiler]

>> No.7336084

>>7336077
looks like ass

>> No.7336095
File: 32 KB, 740x308, math.png [View same] [iqdb] [saucenao] [google]
7336095

I am taking graph theory next year. What is the best textbook to buy and how should I prepare for the course. Note: highest math class I have taken is Calculus II.
>>7336084
Yeah it does tbh

>> No.7336097

>>7336077
Lets add this too

<span class="math">
\diamondsuit \omega = d\omega
[/spoiler]

>> No.7336098

>>7336077
This is the best thing ever.

I'm gonna use this everywhere from now on, but defined in the exact opposite way.

>> No.7336114

>>7335721
Personally I find the notation of Lagrange and Newton to be the most comprehensible to myself.

>> No.7336121

>>7336097
and this

<span class="math">
\mathop \diamondsuit \limits_F L = \frac{{\delta L}}{{\delta F}}
[/spoiler]

>> No.7336132

>>7335721

what the FUCK is euler wearing in that pic? is that a rag on his head?

>> No.7336166

>>7336132
Possibly 18th century academic garb. Or maybe he thought that if he wore a funny enough hat people wouldn't notice his eye.

>> No.7336650
File: 141 KB, 1280x720, wasa_the_following.jpg [View same] [iqdb] [saucenao] [google]
7336650

[X,Y]

>> No.7336662

>>7336095
Fleeing the wreckage from your other shit thread?

>> No.7336679

>>7336077
It should be possible to have a concise notation for both partial and total derivatives of a function over a function, right?

>> No.7336741

>>7336650
Lie Derivative?

>> No.7337310

>>7336030
This. Especially because Euler's allows for things like D_a, where a is a multiindex

>> No.7337326

Lagrange for first and second derivatives in single variable calculus. Because I'm a lazy fuck.
Euler for everything else.

>> No.7337336

Why restrict yourself to just one though, they are all nice

>> No.7337439

>>7336662
No, they expect one of us in the wreckage brother.

>> No.7337908

>>7335721
I was taught Lagrange in high-school, so...

>> No.7337965

>>7335800
> deriving

Cringe

>> No.7337978

>>7335721
Lagrange's and Newton's notation aren't equivalent

>> No.7337999

Leibniz. Lagrange can't even easily do separation of variables

>> No.7338180

>>7335721
For all intensive purposes, I prefer either Lagrange or Leibiniz.

If I have no need to separate variables, bet your sweet tits I'm writing Lagrange. It looks neater, and fits on one line.

>> No.7338199

>>7335721
use lagrange and newton as appropriate

>> No.7338203

>>7338180
>For all intensive purposes
Could you be more pacific as to the purposes?

>> No.7338214
File: 20 KB, 460x276, walruse.jpg [View same] [iqdb] [saucenao] [google]
7338214

>>7338203

>> No.7338229

>>7336077
I am using this from now on.

>> No.7338280

whenever possible i just use f_x.
if the function itself already has a sub, i use eulers notation

>> No.7338382

>>7335721
Lagrange if you are completely familiar with the function and need to make a quick note. Leibniz otherwise.

Euler is too abstract without being concise, you may as well use Lagrange and write less. Also why does he have a crackhead face and crumpled up newspaper around his head. Newton tends to convolute everything he does; as a scientist he has great ideas, but he's not a good "consolidator."

>> No.7338391

>>7336095
Whatever textbook your professor uses, retard.

>> No.7338411

Lagrange

Because everything past the 3rd isnt even usefull

>> No.7338426

>>7338411
>everything past the 3rd isnt even usefull

How is undergrad maths working out for you?

>> No.7338446

>>7335721
I am biased towards Leibniz because that is what I learned first. However I do feel it is the best because
>Shows that a differential is the gradient of a function on a cartesian graph
>Can be manipulated by moving and cancelling the dx or dy terms like fractions
>Specifies what the rate of change is respect to. eg m dot in newton notation could be dm/dt, dm/dv, dm/dQ, you just don't know.

>> No.7338459

all notations have their uses. this discussion is useless and OP should feel bad.

>> No.7338462

>>7338446
>>Can be manipulated by moving and cancelling the dx or dy terms like fractions
Oh god my autism is flaring up.
Please be trolling.

>> No.7338484

>>7338462
I think he isn't even trolling, probably a physicist.

>> No.7338490

>>7335742
newton's notation is literally the worst.

>> No.7338492

>>7338462
Please tell me when this ever isn't valid. For all practical purposes dy/dx is a fraction. Autistic math rigour nobody cares about.

>> No.7338496

>>7338490
what about for second order LODE's involving physical applications? I use that notation all the time when i'm solving springs and shit

>> No.7338497

>>7338462
You can rigorously justify treating df/dx like a fraction in a lot of situations.

What are you sperging out over?

>> No.7338498

>>7338490
If nothing else it's the one that uses the least ink.

>> No.7338504

>>7335721
Are those two's by euler and newton to the power of 2 or just the amouny derived?

>> No.7338505

>>7338498
lagrange's uses just as little ink and isn't bound to
>muh time

>> No.7338508

>>7338498
>doing math in pen

>> No.7338513

>>7338505
You can write Newton's so that it isn't bound to time.

And almost everything is a time derivative in physics.
>>7338504
Amount differentiated
Newton's isn't the right hand of the equation anyway. They're defining it with respect to Leibniz's notation

>> No.7338517

>>7338508
Pencils are for children and carpenters.

>> No.7338540

>>7338462
Deal with it faglord

(Δy/Δx)Δx = Δy
(dy/dx)dx = dy

dblah means "indexed along the blah plane"

Of course you can divide dimensions fagtron

>> No.7338546

>>7338462
>>7338484
>>7338497
>muh hyperreal manipulations!

No one cares mathfaggots. It just werks.

>> No.7338743

>>7335721
Newton's dot notation is strictly for time-derivatives. Leibniz's notation makes solving DE's a little simpler, so I like it best. (Yeah, yeah, abuse of notation.. fuck off)

>> No.7338749

>>7336019
This Is my favorite. It makes way for having partials written as D_1 f, D_2 f, etc. It's less cluttered and confusing than having dx and dy everywhere.

>> No.7338830

>>7335721
Depends.

Newton's notation is generally used to represent time derivatives. Going beyond 3 dots, the notation becomes messy.

Lagrange's notation is similar to Newton's notation except it isn't assumed that derivatives are time related. You can also represent what you are taking a derivative with respect to f'(x), f''(x). Still gets messy past 3 derivatives.

Leibniz notation is a bigger notation but allows you to represent derivatives with the respect to a variable clearly. It's cleaner when representing derivatives past 3.

Euler's notation is similar to Leibniz notation but is more compact.

From what I've seen, the most common notation is Leibniz notation, closely followed by Lagrange notation. You generally only see Newton's notation in a physics related field since it's tied to time derivatives. Euler's notation is by far the least common.

>> No.7338858

>>7338743
I think you mean abusive notation.

>> No.7338863

>>7338830
Lagrange notation allows higher derivatives
<span class="math"> f^{(50)}(x) [/spoiler] for the 50-th derivative with respect to x
<span class="math"> f^{(n)}(x) [/spoiler] for the <span class="math"> n [/spoiler]-th derivative with respect to x

>> No.7338867

>>7336098
Go to bed, commutative algebra.

>> No.7339071

>>7335721
I prefer Leibniz notation:

1) segregates the numerator from the denominator which can then be manipulated algebraically (assuming appropriate rules/conditions hold true regarding continuity and smoothness). Very useful when solving differential equations not expressible as a direct integral/antiderivative.

2) Simple easy to understand implicit differentiation methods. (e.g. y^2 + x^2=1; 2y* dy/dy + 2x*dy/dx=0; dy/dx = -x/y)

3) facilitates conversions from one "coordinate" system to another in an intuitive fashion (y= f(x); u = g(x) then dy/du = dy/dx* dx/du)

4) clear representation in multivariate cases.

>> No.7339076

Euler, as it hints that differentiation is a linear operator, which is actually somewhat profound.

>> No.7339130

>>7338863
Ya you're right. I was just retarded.

>> No.7339388

>>7336077
Skip the diamond entirely and just do <span class="math">_{x}F = \frac{dF}{dx}[/spoiler], <span class="math">^XY = \nabla _XY[/spoiler] etc.

>> No.7339411

>>7338484
a physicist would know that newtons notation is only used for time derivatives

>> No.7339419

>>7335721
Lagrange if ther is no doubt about the variable
Leibniz otherwise

>> No.7339434

Lagrange in single variable context, obviously. Otherwise something like Euler's notation (<span class="math">\partial_{i_1, ...,i_n} f[/spoiler])

>> No.7340937

>>7335721
Leibniz > Newton > Euler > Lagrange

>> No.7340959

>>7340937
Lagrange>Leibniz>Newton>Euler
Lagrange/Leibniz close,but Euler is easily the worst

>> No.7340982

>>7340959
>Euler is easily the worst
You clearly never deal with a lot of partial derivatives.

>> No.7341662

I've been thinking about notation recently

Parentheses to indicate functions is stupid
Functions are so common and grouping stuff together is so common that you think they would make a different notation for each

>> No.7341732

>>7335721

Newtons notation when doing physics, otherwise Lagrange's notation to keep it nice and simple. do not see the purpose in overloading one side of the equation with long as fuck notations if you do not really do anything with them.

>> No.7341750

>>7335721
leibniz's notation if there is a chance of ambiguity, otherwise lagrange or newton (they are the same as far as I'm concerned)

I prefer to write D inside matrices

>> No.7341757

>>7341662
Functions do indeed look a lot like algebraic multiplication.

Truthfully, by comparison I really like coding languages for their clarity and exactness. And the motherfucking piles of documentation that usually accompanies each language.
Watching math profs/teachers switch between notations and conventions at random, and the use of ambiguous variable names and symbols, is actually really frustrating to me.