Common math functions tier list These are the ones most people use and are not the dumb math major functions.
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y = e^x is the goat im glad we can all agree
@h4lplays9322 ай бұрын
Bro just _built_ like that
@canyoupoop2 ай бұрын
Yes
@UndercoverDog2 ай бұрын
The real goat is y= e^-(x)^2
@ishansh00772 ай бұрын
E is just the goat of math in general
@helatard42722 ай бұрын
The goat of all eigenvectors.
@Lothane952 ай бұрын
constant functions: S tier
@canyoupoop2 ай бұрын
all constant functions are linear functions, so yes
@Goaw25512 ай бұрын
Constant is like y or x = num
@ErdemtugsC2 ай бұрын
Always has been
@yudoball2 ай бұрын
@@Goaw2551 But also a polynomial function which is in A tier. Just because your function is a special csse of another one in the list doesn't say anything about it's rating. Cubic functions are also polynomial functions and rightfully ranked very low
@gubblfisch3502 ай бұрын
But which constant is important, they’re only really good if they don’t show up on the number line
@ianweckhorst32002 ай бұрын
2:21 of the professor says the exam is 1 question, then the class *SHOULDNT* be cheering
@hanchen2672 ай бұрын
I would be terrified
@Destroyer01105Ай бұрын
better than a T/F advanced calc final
@xanmiddents6207Ай бұрын
Its the school equivalent to the scene of Star Wars when the Death Star pulls up to YavinIV
@Assadul-NamlАй бұрын
The example integral he showed would have broken my spirit. I don't think integration through brute force would be possible in ninety minutes for most students. Except if you're lucky and find the right substitutions first try.
@joseph_soseph96118 күн бұрын
Logarithms are S tier. Literally make huge multiplications into puny additions.
@ProactiveYellow2 ай бұрын
Whole vid is spot on except logarithm which is straight S
@quinten36282 ай бұрын
As an engineer I totally agree with the S Tier choices. However, logarithm definitely scores higher than x^2.
@staticnullhazard69662 ай бұрын
I agree. I feel like logarithms should be A or S tier
@Kiv_rin2 ай бұрын
As a physics I might add that everything Is a sprin mass system and spring mass systens are made with the x^2 function.
@nicolasreinaldet7322 ай бұрын
@@nicolasreinaldet732 Correct if you Use Lagrangian/Hamiltonian Approaches. But with Newton Mechanics you have no squares. Please correct me if I am wrong.
@staticnullhazard69662 ай бұрын
They deserve to be on the same tier. Parabolas are awesome, the fact that they reflect to a single point (why we use parabolic antennas), the fact that they are one of the conic curves and so much more. X^2 is definitely A tier material. But so is log(x), the fact that they convert products into adding is by itself worthy of A tier.
@3snoW_2 ай бұрын
@@staticnullhazard6966 It will be my pleasure to interact with you on this, altought not directly correct you. Sorry for the english It Is my second language and I am still working on my speeling. Yes indead your statement Is correct, the problem Is that Newtonian mechanics Is quite a lot more limited than Its 2 equivalents. Here are the list of advantages of the other 2: Thermodinamics, and the very little Introduction to statistical mechanics I do know, are very dependent on analysing the energy function of Isolated systems and thuss are much more cosely linked to hamiltonians ( there Is even a theorem about how x^2 terms In the energy function contributed all equaly to the average energy In a linear maner for classical estatistical mechanics ). Classical ( and also quantum ) field theory Is build upon Hamiltonian and Lagrangian mechanics, and so If you want to understand complex Interactions between a atoms and light you will be using hamiltonian and lagrangian mechanics, maybe there Is a way to do field theory from newton but from my superficial contact with the area It Is always introduced with hamiltonians and lagrangians. Quantum theory foundations are entirely hamiltonian and them when you get to quantum fields you get a lagrangian option, never a newtonian analog. I am still a undergraduate so I tried my best to only speak when I knew enought about the subject, but I can also think of a few more concepts of analytical mechanics that I belive to have a better treatment using lagrangian and hamiltonian mechanics like finding conserved quantities or how the hamiltonian perturbation theory Is a more formal and cokie cut way to aproximate solutions for systems where you have a big solvable part and a smaller un-solvable perturbation. But over thosse I do not know exactly how my observations would be correct because I am still going to take analytical mechanics next semester.
@nicolasreinaldet7322 ай бұрын
4:21 trig is both a blessing and a curse
@ianweckhorst32002 ай бұрын
Bro just saied nothing
@user-zg2th7fo9q2 ай бұрын
They cancel like x/x
@kanoruneАй бұрын
I abhor Trigonometry x Mathematical Induction crossover. I can't even prove P(1) is true with all the convoluted trigonometric conversion.
@nothingbutpain863Ай бұрын
i never in my life though i would see functions tier list
@Mandq.2 ай бұрын
Yet here it is. The function waited for us to get pain acknowledged by us
@shivkumar0810Ай бұрын
glad you choose not to trigger every engineering grad PTSD with Heaviside and Dirac functions
@andredecastro58982 ай бұрын
Why did the Dirac function fail it’s driving test? It couldn’t stay within the limits. 😎
@forthehomies70432 ай бұрын
I think those are classified as distributions, they are not well-defined functions.
@themachine93662 ай бұрын
@@forthehomies7043 ahh yes the dad jokes that are actually funny
@nariTheLoveableWorm2 ай бұрын
Isn't the Heaviside function just a shifted sgn?
@methatis30132 ай бұрын
@@themachine9366 Heaviside is a perfectly defined function, one of the simplest ones
@toxic_narcissist2 ай бұрын
The goat e^x every engineer’s favorite because you never have to calculate it, just leave it as is.
@megablademe49302 ай бұрын
I need more math shitposting in my life
@MemeAnt2 ай бұрын
same fam
@albireothestarthebacklight29902 ай бұрын
Okbuddyphd
@tanishkchaudhary7 күн бұрын
"BEAT HERE" 💀
@jimmy_42 ай бұрын
for whatever reason my mental image of the e^x function is a chill looking dude with sunglasses smoking a massive blunt
@Itual2 ай бұрын
S tier - simple functions B tier - Borel measurable C tier - Riemann integrable D tier - Lebesgue integrable F tier - the rest
@icelick69122 ай бұрын
🤓
@probasteelchiquitoahorapro14902 ай бұрын
@@probasteelchiquitoahorapro1490🤡
@David280GG2 ай бұрын
It's been a while since I've brushed up on my measure theory, but S, B and C are all lebesgue integregrable aren't they? So they're also in D
@epicmarschmallow5049Ай бұрын
A-tier: Analytic/smooth functions (depending on personal taste) (Also, all tiers implicitly exclude the previous tier.
@btf_flotsam478Ай бұрын
where tf a functions
@carrabianАй бұрын
“BEAT HERE”
@bluefur2 ай бұрын
Non-elementary functions:
@maxpopkov14322 ай бұрын
S tier
@user-ct1iv9dq1b2 ай бұрын
@@user-ct1iv9dq1b😮😮😮
@tiktik94132 ай бұрын
Analytic functions are A Tier or S tier, also sin and cos are linear combinations of e^{ix} and are so much easier to deal with once you realise this fact.
@magma902 ай бұрын
I did complex numbers for like a week in linear algebra so I didn't really get to work with them that much. What other classes would you use e^{ix} in?
@KedronCL2 ай бұрын
@@KedronCL It's pretty common when solving second order differential equations, as when you get complex roots for the charecteristic polynomial, complex exponentials becomes the answer. As for when that happens in physics, is basically any time you have a oscillatory or wave like system.
@gustavjacobsson33322 ай бұрын
analytic and numeric solutions to PDEs. fourier transform
@reedoken61432 ай бұрын
@@KedronCL complex analysis
@mistafizz51952 ай бұрын
@@KedronCL They show up in electromagnetic waves, quantum physics and computing, and for electrical engineering when finding power(The real part of the complex power at any given moment is it’s instantaneous power) using the phasor transformation.
@ChaosKnight_1002 ай бұрын
Here I am procrastinating on studying for my math exam by watching people rank math functions.
@railgun12582 ай бұрын
Bro made cubic dirty, it could just be a part of the polinomial equations
@lakilopis70812 ай бұрын
Cirno do you do well in Math class
@fireblazenotbulgaria30532 ай бұрын
@@fireblazenotbulgaria3053that's Aqua in their pfp but they're both dummies and related to water so you get a pass
@a_soulspark2 ай бұрын
At least they have a closed form for roots
@Sammy-qt9it2 ай бұрын
cause cubic functions are in general useless. at least high degree polinomial can be used to approximate functions
@bruh-yd8dn2 ай бұрын
As a math teacher, I laughed when you said peice wise are only used for teaching limits Becuase that’s the truest thing I’ve ever heard 😭💀
@julliette8023Ай бұрын
This is the kind of nerd content I'm glad to see in my recommendations, thank you
@kanoruneАй бұрын
The first tier list I 100% wholeheartedly agree with. Good job!
@ywangato3449Ай бұрын
3:35 missed opportunity for literally any domain expansion meme
@hello-rq8kf2 ай бұрын
Complex numbers: 🗿
@Shinchan-xt4pb2 ай бұрын
Engineers watching this video: 🥳 High school students:
@Noobprokermit2 ай бұрын
My teacher letted us use calculator in the exam and i discovered by myself how to calculate the opposite of a trig
@David280GG2 ай бұрын
Logarithmic functions not being s tier is an absolute crime.
@josephblattert63112 ай бұрын
Rational functions with no asymptotes are S tier too ngl.
@Foxxey2 ай бұрын
*no vertical asymptotes
@Foxxey2 ай бұрын
Arent they just polynomials then
@theblinkingbrownie46542 ай бұрын
@@theblinkingbrownie4654 No they aren't. For example f(x)=(x^4+1)/(x^2+1) is defined everywhere, thus no vertical asymptotes (for rational functions vertical asymptotes always come with undefined points at that place e.g. x/(x-1) at 1). In fact the provided f(x) doesn't have horizontal nor oblique asymptotes either since lim x->±inf of f'(x) doesn't equal 0 nor any other constant value. As far as I can tell, this is enough to show, that one particular rational function has no asymptotes. Thus you are incorrect.
@Foxxey2 ай бұрын
@@Foxxey oh right i forgot that the denominator can have no real roots lol
@theblinkingbrownie46542 ай бұрын
Good luck with arctangent lol
@parqtetАй бұрын
I would bump trigonometrics up to S tier just because of Fourier transformation. They are huge in anything related to waves, which is almost everything.
@mishtrong2 ай бұрын
The Fourier transform is actually a type of Laplace transform which makes use of, you guessed it, e^ix. Which is already rightfully in S Tier.
@locinolacolino13022 ай бұрын
I was subconsciously waiting for this!
@Fire_Axus2 ай бұрын
y=x : "Who are you? " y=x²/x : "I am you, but discontinued at 0" Edit: I guess it's working for all y=(x^n/x^(n-1)), n ≥ 2
@mazmuz9872 ай бұрын
interesting ...
@nariTheLoveableWorm2 ай бұрын
y=x³/x² entered chat
@melonenlord27232 ай бұрын
@@melonenlord2723 Don't bring the [y=(x^n/x^(n-1), n ≥ 2] family 💀
@mazmuz9872 ай бұрын
@@mazmuz987 x^(1/2) / x^(-1/2) 💀
@melonenlord27232 ай бұрын
the partial derivitive. Awesome going forward. A nightmare undoing them
@ericknutson83102 ай бұрын
that’s an operator, not a function
@thegoofiestgoooberr2 ай бұрын
@@thegoofiestgoooberrur mom is an operator and not a function
@NotBroihon2 ай бұрын
@@NotBroihon T_T why u bully him?
@extreme41802 ай бұрын
@@extreme4180 because im evil 😈😈😈
@NotBroihon2 ай бұрын
@@thegoofiestgoooberran operator is definitionally a function
@hawkohakker16362 ай бұрын
As a person more interested in human sciences, i think this is very cool finally knowing the applications of what some day i called "abstract bs".
@nadie87672 ай бұрын
you can't perform any kind of science without understanding data, which requires math.
@mrosskne2 ай бұрын
No, you don't know the applications of what you call "abstract bs" I doubt you have the capacity
@SomeAndrian2 ай бұрын
@@SomeAndrianFirst, i don't call this abstract bullshit anymore, because the video explains it perfectly and now i know the value. Second, idk if i have or not the capacity of the aplication of maths before being in a material space were you can aply this knowledge. That is the difference of learn math in school from math in a place where you have an interest/objetives, like workplaces or field research. Third, "I doubt you have the capacity". No intention of making a personal attack, but if something is bullshit, is this fretful attitude. Not only is it a personal attack (quite cheap to be honest, come on, I'm not even attacking mathematics as an area of study), it is that it directly discourages the passion for knowing new things. Do us a favor and not replicate this in real life, *NOBODY* needs it.
@nadie87672 ай бұрын
@@SomeAndrian ok Terrence Tao
@muralibhat87762 ай бұрын
@@muralibhat8776 Terrence Tao is doing mostly pure math. Thanks for playing
@SomeAndrian2 ай бұрын
He put logarithms in B tier and thought we wouldn't notice.
@user-ks8bs8hv8s2 ай бұрын
Non-elementary functions S+ infinity
@maxpopkov14322 ай бұрын
Non-quadrature functions: SS+ tier 💀
@qbert86952 ай бұрын
This is actually outstandingly correct tier list
@Missingno73Ай бұрын
trig for sure the hardest thing for me to memorize but really rewarding
@jayhunter72 ай бұрын
Reciprocal can be cool for physics theory. Asymptotes can potentially be used for exploring black hole aspects, which is neat given that vertical asymptotes can correlate with "holes" that may represent where gravitational influence might be strong enough to create an event horizon on a 2-dimensional plane.
@austinpittman15992 ай бұрын
My tier list (with some functions added) S: Linear, e^x A: Quadratic, Logarithm, Trigonometric, Gaussian (Bell Curve) Distribution B: Polynomial, 1/x, Gamma Function (Extension of Factorial) C: Square Root, Absolute Value, Inverse Trig D: Cubic, Rational Function, n-th Root, Floor/Ceiling F: Piecewise, Hyperbolic Trig Placements based on usefulness and simplicity
@jesseli66222 күн бұрын
half angle indentities
@johnthecrouton2 ай бұрын
Rational: Please make the decision to ignore these functions when possible. That's a Smoove move indeed
@thor.halsli2 ай бұрын
we have math function tier list before GTA 6 lol
@syrex67632 ай бұрын
You did logarithms dirty - they're so important in engineering and are like e^x's twin
@bird5119Ай бұрын
A good first math course list! Would love to the step function and the dirac function aswell. They are quite interesting.
@pepsi-hf8fq2 ай бұрын
The cubic function is easy to remember if you put effort. Really just a copy paste, sign switch, add the -b/3a at the end. But yeah to memorize it for the first time is daunting af
@ChrisP9992 ай бұрын
probably the tier list i most agree with. Piercewise may be dumb, you only need one, but they are really good at explaining limits and discontinuities
@bananacorn437515 күн бұрын
I never thought I'd enjoy this video as much as I did
@user-hz8wr2kp4c2 ай бұрын
e^x is S+. not only is it cool af like u described but its super useful for casual real world problems
@otty40002 ай бұрын
also seems clear to me you have definitely encountered maths from an applied perspective. im chill with it but biased af
@otty40002 ай бұрын
As a wannabe engineer who has his eng school admission exams this week, this should help with the integral area problem questions
@akcdipro10362 ай бұрын
nah but i personally would put Rectangular hyperbolas in A tier or maybe even S , they can tell you so much about range of linear fractional functions.
@AnanyKumarRai2 ай бұрын
This is all very valid except logarithmic functions deserve a b tier and not a c tier
@aliwajeehuddin9552 ай бұрын
0:08 "linear" "1/2 x + 8" you had one job
@LaTortuePGMАй бұрын
I was gonna say this tierlist was bad. But then I realised it is objectively correct. Have a good day.
@zdwlees76472 ай бұрын
Glad you’re a fellow trig appreciator. Good vid
@freshmaggot2 ай бұрын
i remember rudin calls e^x ‘the most important function in mathematics’ (and therefore everything). euler formula really is a gem
@TheRevAlokSingh2 ай бұрын
2:21 imagine having everything correct in the question but you forget to put the +C
@Xertus_YT8 күн бұрын
Logaritmic functions are S tier. You can use them for logaritmic derivation. Pretty cool properties. You can use It to adjust data to power and exponential functions with just a linear regression
@rmv91942 ай бұрын
I agree with almost everything 👍 Maybe 2 or 3 I would put a rank below or above, but I would have done the exact same tier list apart from those 👌
@skarma96732 ай бұрын
the best math video of the week for me
@raynboy64482 ай бұрын
You would think that you are done linear algebra in 9th grade, but nothing can prepare you for the horrors that wait post-secondary linear algebra.
@mrdr49342 ай бұрын
Linear Function is the Goat 🗣🔥
@Alex-ng1ts2 ай бұрын
pretty solid tier list
@vaddokxАй бұрын
Very valid list, I agree
@Gamer2002Ай бұрын
engineer tier list with exp and linear functions in s tier moment
@nablahnjr.6728Ай бұрын
You know what is amazing about trigonometry func. once you achieve the eq. in cos or sin you will get very near to range
@hiden620220 күн бұрын
ok, this is the best tier list ever made
@FPNader2 ай бұрын
You've managed to capture what we've subconsciously felt about these functions the entire time. I agree with almost everything, except for f(x) = 1/x. He's a nice little guy and should be higher.
@Dom-qo9cf2 ай бұрын
This video might be based on a lot of personal grief, but it seems very fair
@ezrachen89762 ай бұрын
Sending this to my Math Teacher
@cherryappleproductions58222 ай бұрын
trig functions are s tier, super useful everywhere in physics and all kinds of other things
@dyzphoriia2 ай бұрын
2:37 Dirichlet's function is actually pretty cool. Piecewise functions (especially complex/hypercomplex piecewises) are quite interesting when one (not you, obviously) understands them.
@Gordy-io8sb7 күн бұрын
Thanks. I agree, this was objectively correct.
@modolief2 ай бұрын
imagine a calculus question with e^f(x) where f(x) is a function in x
@gamings3658Ай бұрын
Therapist: ignore the intrusive thoughts *intrusive thoughts*
@cpeir8460Ай бұрын
I have just started A level maths this year and after the logarithm I begun to think what have I just witnessed?
@tudorganea-arnold9562Ай бұрын
Babe wake up new math functions tierlist just dropped 🗣️🗣️🔥
@abstracdai38732 ай бұрын
Id say log in a tier cause theyre pretty cool with the whole turning multiplication into addition and division into subtraction and vice versa
@attoblaze33952 ай бұрын
When you put linear functions to S-tier, I was glad
@DarkRedZane2 ай бұрын
I am a sciences (physics) students, and piecewise functions can actually get pretty useful in both math and physics, both as an exercice (for things other than limits, such as convergence), and as a tool. That type of function is notably used as an example of not-Riemann-integrable functions
@CorpusVakarian2 ай бұрын
The integrator said, nah I'd win
@itzmeB22 ай бұрын
I was game for this until my man basically put Bézier in D-tier
@dhjerth2 ай бұрын
yo is that a chris smooth reference what a throwback
@provianАй бұрын
Bro it's been 3 days since I touched my books bruh u made me wanna study math as a freaking nerd so much ...u made my day
@ORANUSYTАй бұрын
Gaussian functions are a pain to integrate (error function sometimes requires a calculator if it's not over the entire domain), but it's Fourier transform is also a gaussian, which makes things a lot easier. I would give them A or B. I agree with most of your tier list choices
@Iosurin2 ай бұрын
what about the infamous Heaviside function and delta function. They help a lot in solving SOME differential equations.
@leocaers14082 ай бұрын
Goated video 🔥
@DrJamesMaths28 күн бұрын
You forgot gaussian distribution
@RasberryPhi2 ай бұрын
I was only here to see if e^x was rated correctly and I am satisfied
@peterkujawski13702 ай бұрын
bro, cubic functions are the basis for cubic splines, which allow us approximate basically any continuous function to a degree that is virtually indistinguishable by the human eye, no way they are D tier.
@API-Beast2 ай бұрын
Good luck finding their factors
@botjdjdjd2 ай бұрын
@@botjdjdjdif you use a Catmull-Rom spline then the factors are implicit in the data points and very simple to compute, just increase number of points until the error is acceptable
@API-Beast2 ай бұрын
@@API-Beast I haven't read cubic functions at that level, i am a high school sophomore
@botjdjdjd2 ай бұрын
In the world of computing you can just use bezier curves or trilinear interpolation instead of cubic splines.
@locinolacolino13022 ай бұрын
as an engineering major, you are spot on. I would like to add that the exponential brings out a whole new world when using complex numbers and it's just the best function out there for any kind of signal processing, wavefunctions, dynamic systems, second order linear differential equations, etc.
@zokalyx2 ай бұрын
This man really put the cubic function in D tier, 😂. WHO LET BRO COOK?!
@user-ls3zc3mz6g2 ай бұрын
Trig fluctuates between S tier and F tier with great frequency
@talbotstites6116Күн бұрын
Where my boy signum
@G4naD2 ай бұрын
Trig and power functions must be at the S tier man you feel me :') without them there is no fourier transform or taylor expansion
@r418r_Ай бұрын
People don't give linear enough credit, thank you for putting it in S
@ssharkiggo6432Ай бұрын
pade approximations are rational functions, and theyre cool
@SCidejump2 ай бұрын
Very appropriate ranking I like it.
@varadchougule69552 ай бұрын
2:24 imagine doing all of that just to forget the + c (constant of integration)
@AeiwkАй бұрын
The fact that I integrated that 1/(x⁵+1) function by hand some years ago💀
@arbabashraf11262 ай бұрын
Calculator soup clutched up during functions he the goat 🔥🔥🔥
@theshadowking31982 ай бұрын
I believe logarithmic functions are the same as exponential ones though.
@Ging-Freecs2 ай бұрын
Love the broken subtiles xd
@MegaMieb2 ай бұрын
It's always product over the sum, or addition or subtraction. 🎶
y = e^x is the goat im glad we can all agree
Bro just _built_ like that
Yes
The real goat is y= e^-(x)^2
E is just the goat of math in general
The goat of all eigenvectors.
constant functions: S tier
all constant functions are linear functions, so yes
Constant is like y or x = num
Always has been
@@Goaw2551 But also a polynomial function which is in A tier. Just because your function is a special csse of another one in the list doesn't say anything about it's rating. Cubic functions are also polynomial functions and rightfully ranked very low
But which constant is important, they’re only really good if they don’t show up on the number line
2:21 of the professor says the exam is 1 question, then the class *SHOULDNT* be cheering
I would be terrified
better than a T/F advanced calc final
Its the school equivalent to the scene of Star Wars when the Death Star pulls up to YavinIV
The example integral he showed would have broken my spirit. I don't think integration through brute force would be possible in ninety minutes for most students. Except if you're lucky and find the right substitutions first try.
Logarithms are S tier. Literally make huge multiplications into puny additions.
Whole vid is spot on except logarithm which is straight S
As an engineer I totally agree with the S Tier choices. However, logarithm definitely scores higher than x^2.
I agree. I feel like logarithms should be A or S tier
As a physics I might add that everything Is a sprin mass system and spring mass systens are made with the x^2 function.
@@nicolasreinaldet732 Correct if you Use Lagrangian/Hamiltonian Approaches. But with Newton Mechanics you have no squares. Please correct me if I am wrong.
They deserve to be on the same tier. Parabolas are awesome, the fact that they reflect to a single point (why we use parabolic antennas), the fact that they are one of the conic curves and so much more. X^2 is definitely A tier material. But so is log(x), the fact that they convert products into adding is by itself worthy of A tier.
@@staticnullhazard6966 It will be my pleasure to interact with you on this, altought not directly correct you. Sorry for the english It Is my second language and I am still working on my speeling. Yes indead your statement Is correct, the problem Is that Newtonian mechanics Is quite a lot more limited than Its 2 equivalents. Here are the list of advantages of the other 2: Thermodinamics, and the very little Introduction to statistical mechanics I do know, are very dependent on analysing the energy function of Isolated systems and thuss are much more cosely linked to hamiltonians ( there Is even a theorem about how x^2 terms In the energy function contributed all equaly to the average energy In a linear maner for classical estatistical mechanics ). Classical ( and also quantum ) field theory Is build upon Hamiltonian and Lagrangian mechanics, and so If you want to understand complex Interactions between a atoms and light you will be using hamiltonian and lagrangian mechanics, maybe there Is a way to do field theory from newton but from my superficial contact with the area It Is always introduced with hamiltonians and lagrangians. Quantum theory foundations are entirely hamiltonian and them when you get to quantum fields you get a lagrangian option, never a newtonian analog. I am still a undergraduate so I tried my best to only speak when I knew enought about the subject, but I can also think of a few more concepts of analytical mechanics that I belive to have a better treatment using lagrangian and hamiltonian mechanics like finding conserved quantities or how the hamiltonian perturbation theory Is a more formal and cokie cut way to aproximate solutions for systems where you have a big solvable part and a smaller un-solvable perturbation. But over thosse I do not know exactly how my observations would be correct because I am still going to take analytical mechanics next semester.
4:21 trig is both a blessing and a curse
Bro just saied nothing
They cancel like x/x
I abhor Trigonometry x Mathematical Induction crossover. I can't even prove P(1) is true with all the convoluted trigonometric conversion.
i never in my life though i would see functions tier list
Yet here it is. The function waited for us to get pain acknowledged by us
glad you choose not to trigger every engineering grad PTSD with Heaviside and Dirac functions
Why did the Dirac function fail it’s driving test? It couldn’t stay within the limits. 😎
I think those are classified as distributions, they are not well-defined functions.
@@forthehomies7043 ahh yes the dad jokes that are actually funny
Isn't the Heaviside function just a shifted sgn?
@@themachine9366 Heaviside is a perfectly defined function, one of the simplest ones
The goat e^x every engineer’s favorite because you never have to calculate it, just leave it as is.
I need more math shitposting in my life
same fam
Okbuddyphd
"BEAT HERE" 💀
for whatever reason my mental image of the e^x function is a chill looking dude with sunglasses smoking a massive blunt
S tier - simple functions B tier - Borel measurable C tier - Riemann integrable D tier - Lebesgue integrable F tier - the rest
🤓
@@probasteelchiquitoahorapro1490🤡
It's been a while since I've brushed up on my measure theory, but S, B and C are all lebesgue integregrable aren't they? So they're also in D
A-tier: Analytic/smooth functions (depending on personal taste) (Also, all tiers implicitly exclude the previous tier.
where tf a functions
“BEAT HERE”
Non-elementary functions:
S tier
@@user-ct1iv9dq1b😮😮😮
Analytic functions are A Tier or S tier, also sin and cos are linear combinations of e^{ix} and are so much easier to deal with once you realise this fact.
I did complex numbers for like a week in linear algebra so I didn't really get to work with them that much. What other classes would you use e^{ix} in?
@@KedronCL It's pretty common when solving second order differential equations, as when you get complex roots for the charecteristic polynomial, complex exponentials becomes the answer. As for when that happens in physics, is basically any time you have a oscillatory or wave like system.
analytic and numeric solutions to PDEs. fourier transform
@@KedronCL complex analysis
@@KedronCL They show up in electromagnetic waves, quantum physics and computing, and for electrical engineering when finding power(The real part of the complex power at any given moment is it’s instantaneous power) using the phasor transformation.
Here I am procrastinating on studying for my math exam by watching people rank math functions.
Bro made cubic dirty, it could just be a part of the polinomial equations
Cirno do you do well in Math class
@@fireblazenotbulgaria3053that's Aqua in their pfp but they're both dummies and related to water so you get a pass
At least they have a closed form for roots
cause cubic functions are in general useless. at least high degree polinomial can be used to approximate functions
As a math teacher, I laughed when you said peice wise are only used for teaching limits Becuase that’s the truest thing I’ve ever heard 😭💀
This is the kind of nerd content I'm glad to see in my recommendations, thank you
The first tier list I 100% wholeheartedly agree with. Good job!
3:35 missed opportunity for literally any domain expansion meme
Complex numbers: 🗿
Engineers watching this video: 🥳 High school students:
My teacher letted us use calculator in the exam and i discovered by myself how to calculate the opposite of a trig
Logarithmic functions not being s tier is an absolute crime.
Rational functions with no asymptotes are S tier too ngl.
*no vertical asymptotes
Arent they just polynomials then
@@theblinkingbrownie4654 No they aren't. For example f(x)=(x^4+1)/(x^2+1) is defined everywhere, thus no vertical asymptotes (for rational functions vertical asymptotes always come with undefined points at that place e.g. x/(x-1) at 1). In fact the provided f(x) doesn't have horizontal nor oblique asymptotes either since lim x->±inf of f'(x) doesn't equal 0 nor any other constant value. As far as I can tell, this is enough to show, that one particular rational function has no asymptotes. Thus you are incorrect.
@@Foxxey oh right i forgot that the denominator can have no real roots lol
Good luck with arctangent lol
I would bump trigonometrics up to S tier just because of Fourier transformation. They are huge in anything related to waves, which is almost everything.
The Fourier transform is actually a type of Laplace transform which makes use of, you guessed it, e^ix. Which is already rightfully in S Tier.
I was subconsciously waiting for this!
y=x : "Who are you? " y=x²/x : "I am you, but discontinued at 0" Edit: I guess it's working for all y=(x^n/x^(n-1)), n ≥ 2
interesting ...
y=x³/x² entered chat
@@melonenlord2723 Don't bring the [y=(x^n/x^(n-1), n ≥ 2] family 💀
@@mazmuz987 x^(1/2) / x^(-1/2) 💀
the partial derivitive. Awesome going forward. A nightmare undoing them
that’s an operator, not a function
@@thegoofiestgoooberrur mom is an operator and not a function
@@NotBroihon T_T why u bully him?
@@extreme4180 because im evil 😈😈😈
@@thegoofiestgoooberran operator is definitionally a function
As a person more interested in human sciences, i think this is very cool finally knowing the applications of what some day i called "abstract bs".
you can't perform any kind of science without understanding data, which requires math.
No, you don't know the applications of what you call "abstract bs" I doubt you have the capacity
@@SomeAndrianFirst, i don't call this abstract bullshit anymore, because the video explains it perfectly and now i know the value. Second, idk if i have or not the capacity of the aplication of maths before being in a material space were you can aply this knowledge. That is the difference of learn math in school from math in a place where you have an interest/objetives, like workplaces or field research. Third, "I doubt you have the capacity". No intention of making a personal attack, but if something is bullshit, is this fretful attitude. Not only is it a personal attack (quite cheap to be honest, come on, I'm not even attacking mathematics as an area of study), it is that it directly discourages the passion for knowing new things. Do us a favor and not replicate this in real life, *NOBODY* needs it.
@@SomeAndrian ok Terrence Tao
@@muralibhat8776 Terrence Tao is doing mostly pure math. Thanks for playing
He put logarithms in B tier and thought we wouldn't notice.
Non-elementary functions S+ infinity
Non-quadrature functions: SS+ tier 💀
This is actually outstandingly correct tier list
trig for sure the hardest thing for me to memorize but really rewarding
Reciprocal can be cool for physics theory. Asymptotes can potentially be used for exploring black hole aspects, which is neat given that vertical asymptotes can correlate with "holes" that may represent where gravitational influence might be strong enough to create an event horizon on a 2-dimensional plane.
My tier list (with some functions added) S: Linear, e^x A: Quadratic, Logarithm, Trigonometric, Gaussian (Bell Curve) Distribution B: Polynomial, 1/x, Gamma Function (Extension of Factorial) C: Square Root, Absolute Value, Inverse Trig D: Cubic, Rational Function, n-th Root, Floor/Ceiling F: Piecewise, Hyperbolic Trig Placements based on usefulness and simplicity
half angle indentities
Rational: Please make the decision to ignore these functions when possible. That's a Smoove move indeed
we have math function tier list before GTA 6 lol
You did logarithms dirty - they're so important in engineering and are like e^x's twin
A good first math course list! Would love to the step function and the dirac function aswell. They are quite interesting.
The cubic function is easy to remember if you put effort. Really just a copy paste, sign switch, add the -b/3a at the end. But yeah to memorize it for the first time is daunting af
probably the tier list i most agree with. Piercewise may be dumb, you only need one, but they are really good at explaining limits and discontinuities
I never thought I'd enjoy this video as much as I did
e^x is S+. not only is it cool af like u described but its super useful for casual real world problems
also seems clear to me you have definitely encountered maths from an applied perspective. im chill with it but biased af
As a wannabe engineer who has his eng school admission exams this week, this should help with the integral area problem questions
nah but i personally would put Rectangular hyperbolas in A tier or maybe even S , they can tell you so much about range of linear fractional functions.
This is all very valid except logarithmic functions deserve a b tier and not a c tier
0:08 "linear" "1/2 x + 8" you had one job
I was gonna say this tierlist was bad. But then I realised it is objectively correct. Have a good day.
Glad you’re a fellow trig appreciator. Good vid
i remember rudin calls e^x ‘the most important function in mathematics’ (and therefore everything). euler formula really is a gem
2:21 imagine having everything correct in the question but you forget to put the +C
Logaritmic functions are S tier. You can use them for logaritmic derivation. Pretty cool properties. You can use It to adjust data to power and exponential functions with just a linear regression
I agree with almost everything 👍 Maybe 2 or 3 I would put a rank below or above, but I would have done the exact same tier list apart from those 👌
the best math video of the week for me
You would think that you are done linear algebra in 9th grade, but nothing can prepare you for the horrors that wait post-secondary linear algebra.
Linear Function is the Goat 🗣🔥
pretty solid tier list
Very valid list, I agree
engineer tier list with exp and linear functions in s tier moment
You know what is amazing about trigonometry func. once you achieve the eq. in cos or sin you will get very near to range
ok, this is the best tier list ever made
You've managed to capture what we've subconsciously felt about these functions the entire time. I agree with almost everything, except for f(x) = 1/x. He's a nice little guy and should be higher.
This video might be based on a lot of personal grief, but it seems very fair
Sending this to my Math Teacher
trig functions are s tier, super useful everywhere in physics and all kinds of other things
2:37 Dirichlet's function is actually pretty cool. Piecewise functions (especially complex/hypercomplex piecewises) are quite interesting when one (not you, obviously) understands them.
Thanks. I agree, this was objectively correct.
imagine a calculus question with e^f(x) where f(x) is a function in x
Therapist: ignore the intrusive thoughts *intrusive thoughts*
I have just started A level maths this year and after the logarithm I begun to think what have I just witnessed?
Babe wake up new math functions tierlist just dropped 🗣️🗣️🔥
Id say log in a tier cause theyre pretty cool with the whole turning multiplication into addition and division into subtraction and vice versa
When you put linear functions to S-tier, I was glad
I am a sciences (physics) students, and piecewise functions can actually get pretty useful in both math and physics, both as an exercice (for things other than limits, such as convergence), and as a tool. That type of function is notably used as an example of not-Riemann-integrable functions
The integrator said, nah I'd win
I was game for this until my man basically put Bézier in D-tier
yo is that a chris smooth reference what a throwback
Bro it's been 3 days since I touched my books bruh u made me wanna study math as a freaking nerd so much ...u made my day
Gaussian functions are a pain to integrate (error function sometimes requires a calculator if it's not over the entire domain), but it's Fourier transform is also a gaussian, which makes things a lot easier. I would give them A or B. I agree with most of your tier list choices
what about the infamous Heaviside function and delta function. They help a lot in solving SOME differential equations.
Goated video 🔥
You forgot gaussian distribution
I was only here to see if e^x was rated correctly and I am satisfied
bro, cubic functions are the basis for cubic splines, which allow us approximate basically any continuous function to a degree that is virtually indistinguishable by the human eye, no way they are D tier.
Good luck finding their factors
@@botjdjdjdif you use a Catmull-Rom spline then the factors are implicit in the data points and very simple to compute, just increase number of points until the error is acceptable
@@API-Beast I haven't read cubic functions at that level, i am a high school sophomore
In the world of computing you can just use bezier curves or trilinear interpolation instead of cubic splines.
as an engineering major, you are spot on. I would like to add that the exponential brings out a whole new world when using complex numbers and it's just the best function out there for any kind of signal processing, wavefunctions, dynamic systems, second order linear differential equations, etc.
This man really put the cubic function in D tier, 😂. WHO LET BRO COOK?!
Trig fluctuates between S tier and F tier with great frequency
Where my boy signum
Trig and power functions must be at the S tier man you feel me :') without them there is no fourier transform or taylor expansion
People don't give linear enough credit, thank you for putting it in S
pade approximations are rational functions, and theyre cool
Very appropriate ranking I like it.
2:24 imagine doing all of that just to forget the + c (constant of integration)
The fact that I integrated that 1/(x⁵+1) function by hand some years ago💀
Calculator soup clutched up during functions he the goat 🔥🔥🔥
I believe logarithmic functions are the same as exponential ones though.
Love the broken subtiles xd
It's always product over the sum, or addition or subtraction. 🎶