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.
same when he says that you will have an exam that if you don't score 100% you have to do it again and get a detention if you fail again until you get it right... pure pain
@@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.
@@lucass4827 basically because static friction is higher than kinetic friction it means if you graph the force of friction to an object is resisting a force applied to it with it goes like this: At first it changes proportionally to whatever force os acting upon it Then it does some wierd friction stuff Then it settles into being just u(k)N (a flat line)
@@MysteriousObjectsOfficial yes, which means they also make multiplication and division into addition and subtraction, which is fundamentally easier. It can turn all kinds of hard problems with products into subs and coefficients, which means you can apply linear algebra to the problem, then you just undo the logs at the end and you've solved it without crazy multiplication. They're also the perfect example of a group isomorphism and why they're so useful.
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?
@@Kcl-Integrator29 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.
@@Kcl-Integrator29 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.
@@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.
@@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.
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.
2:10 thats really cool, I never know why do we learnt a numerical way to solve the null space of a matrix, now that I know. it can be used to perform partial fraction decomposition, and by doing so, simply the integration with perfect multiples in the numerator! Holy cow! this is incredible!!!
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.
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
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
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.
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.
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.
@@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
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.
It was actually surprisingly easy to solve without a calculator. Since the coefficient of the second term was so small, I figured that factoring should result in numbers with a close absolute value. 221 is very close to a square number 225. 225 is 15 squared so absolute value of those numbers must be close to fifteen. 13 and 17 looked right just based on the ones place, and doing (13)(20)-(13)(3) quickly checked my answer. Since the constant is negative and the coefficient is positive, the number with the higher value must be positive and the other negative. That’s how I reached (X-13)(X-17). This all happened in the span of like 20 seconds. Idk why I felt like saying this but yeah…
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.
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.
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.
same when he says that you will have an exam that if you don't score 100% you have to do it again and get a detention if you fail again until you get it right... pure pain
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
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.
Yeah thats fair @@nothingbutpain863
trig is so annoying especially with the Fourier series, I hate it with my everything
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.
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 😭💀
Hey! They are useful for friction.
@@FinnishArsonistwhen
@@lucass4827 basically because static friction is higher than kinetic friction it means if you graph the force of friction to an object is resisting a force applied to it with it goes like this:
At first it changes proportionally to whatever force os acting upon it
Then it does some wierd friction stuff
Then it settles into being just u(k)N (a flat line)
Laplace Transforms rn:
Noway goofy ahh math teacher who uses skull emoji ??? Hella based
Logarithms are S tier. Literally make huge multiplications into puny additions.
Whole vid is spot on except logarithm which is straight S
but they make subtraction and addition into division and multiplication like log(100) - log(10) = log (100/10). and log (10) + log(10) = log(100)
@@MysteriousObjectsOfficial yes, which means they also make multiplication and division into addition and subtraction, which is fundamentally easier. It can turn all kinds of hard problems with products into subs and coefficients, which means you can apply linear algebra to the problem, then you just undo the logs at the end and you've solved it without crazy multiplication.
They're also the perfect example of a group isomorphism and why they're so useful.
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.
for whatever reason my mental image of the e^x function is a chill looking dude with sunglasses smoking a massive blunt
"BEAT HERE" 💀
I need more math shitposting in my life
same fam
Okbuddyphd
real
“BEAT HERE”
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
This is the kind of nerd content I'm glad to see in my recommendations, thank you
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
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
Logarithmic functions not being s tier is an absolute crime.
3:35 missed opportunity for literally any domain expansion meme
DOMAIN EXPANSION: COMPLEX NUMBERS
Non-elementary functions:
S tier
@@АннаСивер-г8м😮😮😮
S Tier for basically the same reason as Complex Numbers. Just built like that and I respect it.
Here I am procrastinating on studying for my math exam by watching people rank math functions.
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?
@@Kcl-Integrator29 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
@@Kcl-Integrator29 complex analysis
@@Kcl-Integrator29 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.
He put logarithms in B tier and thought we wouldn't notice.
we have math function tier list before GTA 6 lol
Complex numbers: 🗿
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
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
I was subconsciously waiting for this!
This video might be based on a lot of personal grief, but it seems very fair
You did logarithms dirty - they're so important in engineering and are like e^x's twin
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
1:11 all of chemical thermodynamics, “I am a joke to you?”
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
As a college freshman this is exactly the type of content I needed rn
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.
Integration makes trig functions F tier
2:10 thats really cool, I never know why do we learnt a numerical way to solve the null space of a matrix, now that I know. it can be used to perform partial fraction decomposition, and by doing so, simply the integration with perfect multiples in the numerator! Holy cow! this is incredible!!!
As a wannabe engineer who has his eng school admission exams this week, this should help with the integral area problem questions
I was gonna say this tierlist was bad. But then I realised it is objectively correct. Have a good day.
Non-elementary functions S+ infinity
Non-quadrature functions: SS+ tier 💀
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.
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
The fact that the Taylor Expansion exists should make polynomials a solid S-tier.
It's midnight. I'm sitting in front of my pc and eat. I watch a video of a guy rating functions.
It is midterm season and I am making videos on calculus instead of studying calculus.
@@Kcl-Integrator29Which subject do u study?
@@multiamphetaminsaft aerospace engineering
This is actually outstandingly correct tier list
3:48 'beat here'
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.
ok, this is the best tier list ever made
trig for sure the hardest thing for me to memorize but really rewarding
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) 💀
Never in my life have I agreed with any tier list so much, but imo absolute value and trigonometric functions should change places
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
This is nostalgia. We don't have these things in accounting course. I'll spend my Christmas break re-studying these again.
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
The most functional tier list to ever function.
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.
I never thought I'd enjoy this video as much as I did
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.
In spite of the fact that my english bad, I comprehended each moment of your video. Math really universal language
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.
Rational: Please make the decision to ignore these functions when possible. That's a Smoove move indeed
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.
e^x gagged, cleared, ended, delivered, devoured, presented, provided and just did it all.
3:45 “Beat here”???
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
1:34
*a tier.*
2:21 imagine having everything correct in the question but you forget to put the +C
Calculus tier list
U sub: S tier. Trig sub: F tier.
derivatives: S tier
anti derivative: b tier
@@Kcl-Integrator29trig sub is my favorite integration technique by far :(
This was basically a calc tier list
2:24 imagine doing all of that just to forget the + c (constant of integration)
0:08 "linear" "1/2 x + 8" you had one job
That is a linear equation
Thats linear
@akshatmodi8607 @@mashucha no, that's affine
You and 6 other people are incredibly stupid.
I’ve learnt 9 of these so far, still need to learn, logarithmic, nth root, trig and rational
0:52 (X-13) (X+17)
H-how?
Impossible
This is sorcery!
nerd
It was actually surprisingly easy to solve without a calculator. Since the coefficient of the second term was so small, I figured that factoring should result in numbers with a close absolute value. 221 is very close to a square number 225. 225 is 15 squared so absolute value of those numbers must be close to fifteen. 13 and 17 looked right just based on the ones place, and doing (13)(20)-(13)(3) quickly checked my answer. Since the constant is negative and the coefficient is positive, the number with the higher value must be positive and the other negative. That’s how I reached (X-13)(X-17). This all happened in the span of like 20 seconds.
Idk why I felt like saying this but yeah…
A good first math course list! Would love to the step function and the dirac function aswell. They are quite interesting.
Linear Function is the Goat 🗣🔥
I believe logarithmic functions are the same as exponential ones though.
You forgor the +C
i remember rudin calls e^x ‘the most important function in mathematics’ (and therefore everything). euler formula really is a gem
2:53 e^x +c*
This man really put the cubic function in D tier, 😂. WHO LET BRO COOK?!
You forgot gaussian distribution
Trig and power functions must be at the S tier man you feel me :') without them there is no fourier transform or taylor expansion
2:41 they’re only at all useful when you’re making desmos art or something stupid like that
We got maths functions tier lists before GTA 6. Crazy
2:50: +c
I was game for this until my man basically put Bézier in D-tier
Missing Hyperbolic. Dislike
Reciprocal...
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
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.
We got function tier list before GTA 6
Babe wake up new math functions tierlist just dropped 🗣️🗣️🔥
one must imagine sin happy
goes up and falls down again, repeating for eternity...
imagine a calculus question with e^f(x) where f(x) is a function in x
Therapist: ignore the intrusive thoughts
*intrusive thoughts*
y = x^3 being all sad in D tier until it remembers it's a polynomial
Glad you’re a fellow trig appreciator. Good vid
You know what is amazing about trigonometry func. once you achieve the eq. in cos or sin you will get very near to range
"Very beautiful, very powerful"
I used trig functions to make the Last Prism (terraria weapon) in Minecraft, so yeah, circles also.
Fun fact I got 50 pages of math homework until 7th grade
the best math video of the week for me
Riemann zeta function:
This is all very valid except logarithmic functions deserve a b tier and not a c tier