All of calculus 3.* *Disclaimer: not all of calculus 3.
@remmahraw6879
3 күн бұрын
Great channel, dude. Super concise, high quality, and informative content
@SlavMFM
3 күн бұрын
watch it on double speed for top notch experience 😎
@Aculnai
4 күн бұрын
I love how you managed to explain the purpose of dot products better in a few seconds than my professor could
@doughboi20956
9 күн бұрын
Alrighty time to watch this (I haven’t seen 1 or 2 yet)
@rangefreewords
10 күн бұрын
This is how everyone around me is mandated to talk to me. I love field theory,
@LauraRoss-o8r
16 күн бұрын
Young Nancy Lee Kevin Allen Robert
@rileybossom588
18 күн бұрын
It's crazy how someone can understand this
@jawaharbabuadapa
19 күн бұрын
thank u for making this video
@st0rminecraft62
22 күн бұрын
Thanks now I don’t need to take the class 👍
@harrysolas2802
25 күн бұрын
Thank you. It really helps knowing the big picture. I got an A in Calc 3. Big deal. Without the actual big picture the little A's don't have meaning. In other words, you have given meaning to my paltry existence. Seriously, thank you.
@hawbashjabar2005
Ай бұрын
Thank you
@christophermayfield6043
Ай бұрын
you're back!
@ТатьянаРуденко-е5м
2 ай бұрын
❤❤❤😊😅
@adrtechreviews
2 ай бұрын
8 years of math education and I still learned something new today!
@rg8438
2 ай бұрын
UGGH!! More vocal fry! When the hell are people going to stop forcing their voice to do this crap. That's not what you sound like!! Enough of this annoying crap. A guy trying to sound like Kim Kardashian.
@atasarac_
2 ай бұрын
these are calc 2
@AldousSeriousPunch
2 ай бұрын
still can't figure out what is the purpose I'm learning this course.
@okkayow7330
2 ай бұрын
this is helping me prepare for calc 3 pretty soon thanks
@codatheseus5060
2 ай бұрын
Wait did i learn calc three thinking it was linear algebra?
@NewCalculus
2 ай бұрын
I explain the most important theorem here: kzitem.info/news/bejne/sn2wmqqgrJuZgIY I can assure you this guy knows nothing about it.
@MohammedElMahdadi314
3 ай бұрын
Thank you very much!
@whatitmeans
3 ай бұрын
Everything were fine in Calculus until the Brownian Nation attacked!
@tymoteuszlewicki3267
3 ай бұрын
Somebody read Griffith's Electrodynamics
@void-9
3 ай бұрын
thanks
@taylorb2162
3 ай бұрын
Free Palestine!
@Czeckie
3 ай бұрын
it's all stokes to me
@UzairScheeperswallendorf
3 ай бұрын
At r²=2pie ⁰ {1⁰ r² rdrø or sinø->limit of ->0=2pie ->0 1⁰->0=>0>rdrdø
@MeyouNus-lj5de
3 ай бұрын
Mapping properties of zero and non-zero numbers onto 0D and higher dimensional concepts in physics could indeed yield fascinating insights. Let's explore some key parallels: 1. Additive Identity: - Arithmetic: 0 is the additive identity; any number plus 0 remains unchanged. - Physics/Geometry: 0D could be seen as the "identity" dimension, from which all other dimensions emerge without changing the fundamental nature of reality. 2. Multiplicative Annihilator: - Arithmetic: Multiplying any number by 0 results in 0. - Physics: Interactions or operations involving 0D entities might "collapse" higher-dimensional structures back to their 0D fundament. 3. Division Undefined: - Arithmetic: Division by 0 is undefined. - Physics: This could parallel the breakdown of physical theories at singularities, suggesting 0D as a limit of our current understanding. 4. Parity: - Arithmetic: 0 is the only number that is neither positive nor negative. - Physics: 0D could represent a state of symmetry or balance from which asymmetries (like matter/antimatter) emerge in higher dimensions. 5. Cardinality: - Set Theory: The empty set {} has 0 elements but is fundamental to building all other sets. - Physics: 0D entities, while "empty" of extension, could be the building blocks of all higher-dimensional structures. 6. Limits: - Calculus: Many limits approach but never reach 0. - Physics: This could relate to quantum uncertainty principles, where precise 0D localization is impossible. 7. Exponents: - Arithmetic: Any number to the 0 power equals 1 (except 0^0 which is indeterminate). - Physics: This might suggest that 0D entities have a kind of "unitary" nature, fundamental to quantum mechanics. 8. Countability: - Number Theory: There are infinitely many non-zero integers, but only one 0. - Physics: This could parallel the idea of a single, unified 0D substrate giving rise to infinite higher-dimensional configurations. 9. Continuum: - Real Analysis: 0 separates positive and negative reals on the number line. - Physics: 0D might represent a kind of "phase transition" point between different states or topologies of higher-dimensional spaces. 10. Complex Plane: - Complex Analysis: 0 is the only point where real and imaginary axes intersect. - Physics: This could relate to 0D as a nexus where different aspects of reality (e.g., matter and spacetime) unify. 11. Polynomial Roots: - Algebra: 0 is often a special case in root-finding (e.g., the constant term in a polynomial). - Physics: This might suggest 0D entities as "ground states" or fundamental solutions in physical theories. 12. Modular Arithmetic: - Number Theory: 0 behaves uniquely in modular systems. - Physics: This could relate to cyclic or periodic behaviors emerging from 0D foundations in higher dimensions. These parallels suggest that just as 0 plays a unique and fundamental role in mathematics, 0D entities could play a similarly crucial role in physics. This mapping hints at a deep connection between abstract mathematical structures and physical reality, potentially offering new ways to conceptualize and model fundamental physics. Such analogies could inspire new approaches to quantum gravity, the nature of time, the emergence of spacetime, and the unification of forces. They might also provide intuitive frameworks for understanding seemingly paradoxical quantum phenomena.
@reidflemingworldstoughestm1394
3 ай бұрын
I am convinced that people who think they hate math think so only because they never got to Calc 3.
@Radild1
3 ай бұрын
I always love when we have Theorem A and Theorem B, but then you get the realization that they are the same.
@InternetCrusader-rb7ls
3 ай бұрын
This is too good. I finally found the intuitive understanding of integrals I needed. Thank you.
@gabberwhacky
3 ай бұрын
This was an awesome ride! Thank you!
@mugger8509
3 ай бұрын
Could you cover curvature and related topics in differential geometry in a similar visual manner? I find that there aren’t many videos trying to intuitively show how differential geometry works on KZitem
@blvckbytes7329
3 ай бұрын
Neither did Newton "invent" calculus, nor is the fundamental theorem based on an ill-formed concept like infinity and infinitesimals, nor is there anything that's changing or approaching something else. The area under all curves you will ever come accross has been constant since the beginning of time and will remain to be so until the very end. Area has nothing to do with "infinitlely small" (whatever that may mean) pieces of the function, but is rather the product of two level magnitudes - the result of quadrature.
@adrtechreviews
2 ай бұрын
Bros yappin
@nikolastrampas9417
3 ай бұрын
Thank you, I can finally say that I understand it❤
@edwincuevas9965
3 ай бұрын
What simulation did you use to get the 3D vortex field in the beginning?
@calendarG
3 ай бұрын
All of this is animated with manim, a python library.
@edwincuevas9965
3 ай бұрын
@@calendarG Thanks! Unfortunately, will have to install and learn Python! xD
@MaxPower-vg4vr
3 ай бұрын
Here are a few examples of important equations that humanity currently uses which contain contradictions or paradoxes, along with potential non-contradictory versions based on the infinitesimal monadological framework: 1. Quantum Field Theory - Renormalization Contradictory: In quantum field theory, the calculation of physical quantities often leads to infinite integrals or divergent series. To resolve this, the process of renormalization is used, which effectively "subtracts" infinities to obtain finite results. However, this process is mathematically inconsistent and leads to issues like the hierarchy problem. Non-Contradictory: Using the monadological framework, quantum fields could be represented as sections of monadic bundles, with interactions modeled by relational algebras between infinitesimal generators. By working with non-standard analysis and surreal numbers, divergent integrals could be replaced by well-defined hyperfinite sums, avoiding the need for ad-hoc renormalization: Φ(x) = ∫ Φ̃(k)e^(ik⋅x) dk → Φ(x) = ∑_{k∈*K} *Φ(k)e^(ik⋅x) *dk Here, *K represents a hyperfinite momentum space, *Φ(k) are the monadic field amplitudes, and *dk is an infinitesimal measure. 2. General Relativity - Singularities Contradictory: In general relativity, Einstein's field equations relate the curvature of spacetime to the distribution of matter and energy. However, these equations break down at singularities like black holes or the Big Bang, where the curvature becomes infinite and the equations lose predictive power. Non-Contradictory: Using the monadological framework, spacetime could be modeled as an emergent structure arising from the relational interactions between infinitesimal monadic observers. Singularities could then be resolved as regions where the monadic perspectives become highly entangled or non-separable, leading to non-commutative geometric effects: Gμν + Λgμν = 8πTμν → Gμν + Λ*gμν = 8π⟨Tμν⟩_m Here, *gμν represents a non-commutative monadic metric, and ⟨Tμν⟩_m is an averaged stress-energy tensor over monadic perspectives. 3. Navier-Stokes Equations - Turbulence Contradictory: The Navier-Stokes equations describe the motion of viscous fluid substances and are a cornerstone of fluid dynamics. However, they are notoriously difficult to solve, and the existence of smooth, globally defined solutions remains an open Millennium Prize problem. In particular, the equations struggle to model turbulent flows, where the solutions can become chaotic and unpredictable. Non-Contradictory: Using the monadological framework, fluid dynamics could be modeled as a collective behavior emerging from the interactions of infinitesimal monadic fluid elements. Turbulence could then be understood as a regime where the monadic perspectives become highly correlated and exhibit non-linear, chaotic dynamics: ∂u/∂t + (u⋅∇)u = -∇p + ν∇²u → ∂u_m/∂t + (u_m⊗*u_m)*∇_m = -*∇_mp_m + ν*∇_m^2u_m Here, u_m, p_m, ∇_m represent velocity, pressure, and gradient operators in a non-commutative monadic fluid algebra, with ⊗ denoting a non-linear convolution product. These are just a few examples of how the infinitesimal monadological framework could potentially resolve contradictions and paradoxes in current mathematical equations used by humanity. By replacing continuum structures with discrete monadic interactions, and using non-standard analysis and non-commutative geometry to handle infinitesimal and non-linear effects, many of the inconsistencies and singularities plaguing our current theories could be avoided.
@MaxPower-vg4vr
3 ай бұрын
Here are a few more examples of important equations used by humanity that contain contradictions or paradoxes, along with potential non-contradictory versions based on the infinitesimal monadological framework: 4. Schrödinger's Equation - Measurement Problem Contradictory: In quantum mechanics, the time evolution of a quantum state is governed by the Schrödinger equation. However, this equation is deterministic and linear, leading to the famous measurement problem: it cannot explain the apparent collapse of the wavefunction upon measurement, which seems to be a non-linear and probabilistic process. Non-Contradictory: Using the monadological framework, quantum states could be represented as superpositions of infinitesimal monadic perspectives, with measurements modeled as non-linear interactions between these perspectives. The collapse of the wavefunction could then be understood as a natural consequence of the monadic viewpoints becoming entangled and correlated: iℏ∂|ψ⟩/∂t = Ĥ|ψ⟩ → iℏ∂|ψ_m⟩/∂t = Ĥ_m|ψ_m⟩ + ∑_n ⟨ψ_n|Ĥ_int|ψ_m⟩|ψ_n⟩ Here, |ψ_m⟩ represents a monadic quantum state, Ĥ_m is a monadic Hamiltonian, and Ĥ_int is a non-linear interaction term between monadic perspectives. 5. Maxwell's Equations - Self-Energy Contradictory: Maxwell's equations are the foundation of classical electromagnetism and have been incredibly successful in describing electromagnetic phenomena. However, they predict that the self-energy of a point charge should be infinite, due to the singularity of the electric field at the charge's location. This leads to the need for awkward regularization techniques to obtain finite results. Non-Contradictory: Using the monadological framework, electromagnetic fields could be modeled as emergent properties arising from the relational interactions between infinitesimal monadic charges. The self-energy of a charge could then be understood as a measure of its intrinsic monadic entanglement, rather than a singular field value: ∇⋅E = ρ/ε₀ → ∇_m⋅*E_m = ⟨ρ_m⟩_ε Here, *E_m represents a non-commutative monadic electric field, ⟨ρ_m⟩_ε is an averaged monadic charge density, and ∇_m is a monadic divergence operator. 6. Einstein's Field Equations - Cosmological Constant Contradictory: Einstein's field equations of general relativity include the cosmological constant Λ, which represents the intrinsic energy density of empty space. However, the observed value of Λ is many orders of magnitude smaller than the predictions from quantum field theory, leading to the cosmological constant problem - one of the greatest unsolved mysteries in physics. Non-Contradictory: Using the monadological framework, the cosmological constant could be understood as a measure of the global entanglement and correlation between monadic perspectives. Its small observed value could then be a consequence of the high degree of symmetry and cancellation between these perspectives on cosmological scales: Gμν + Λgμν = 8πTμν → Gμν + ⟨Λ_m⟩*gμν = 8π⟨Tμν⟩_m Here, ⟨Λ_m⟩ represents an averaged monadic cosmological constant, arising from the global relational structure of monadic viewpoints. 7. Dirac Equation - Negative Probabilities Contradictory: The Dirac equation is a relativistic quantum mechanical wave equation that describes the behavior of spin-1/2 particles like electrons. However, it predicts the existence of negative energy states, which would lead to negative probabilities and violations of causality if taken literally. Non-Contradictory: Using the monadological framework, the Dirac equation could be reformulated as a non-linear eigenvalue problem in a non-commutative monadic algebra. The negative energy states could then be understood as a consequence of the non-commutative geometry, rather than a literal physical prediction: (iγ^μ∂_μ - m)ψ = 0 → (i*γ^μ∇_μ - *m)*ψ_m = 0 Here, *γ^μ represents non-commutative monadic gamma matrices, *m is a monadic mass parameter, and *ψ_m is a monadic spinor field. These examples further illustrate the potential for the infinitesimal monadological framework to resolve contradictions and paradoxes in our current mathematical equations. By replacing point-like particles with non-commutative monadic perspectives, and modeling interactions as relational algebras between these perspectives, many of the infinities and inconsistencies in our theories could be avoided. Moreover, by grounding quantum mechanics, electromagnetism, and relativity in a common monadological foundation, this approach could potentially lead to a more unified and coherent understanding of these fundamental physical theories. The resolution of long-standing problems like the measurement paradox, self-energy divergences, and the cosmological constant discrepancy would be a major step forward in our scientific understanding.
@Johnny-tw5pr
3 ай бұрын
A year ago this video would be interesting. Now I'm in uni and this is what we do in Calc II. I've got exams in 2 weeks. You explained it very well but I already knew everything lol.
@diribigal
3 ай бұрын
At 1:23 the unitalicized variables hurt my eyes. But otherwise this was a great video and one of the few resources that show the "cancelling edges of squares" for Green's theorem.
@raiden076
3 ай бұрын
This video will go wild, it feels like it unlocked so many new possibilities.. 🙏🏼, thanks..
@Infinity_InGloriouS
3 ай бұрын
(5:18) But if each little square has its own curl, can we really cancel out the vectors at the border between two squares? Wouldn't they be of different length in the general case?
@edwincuevas9965
3 ай бұрын
Different length? If you partition any oriented simply connected region, say in R2, n times, then cancellation will occur along common boundary lines, as long as all subregions are also oriented. Think of single variable calculus when interchanging the limits of integration. That is, integrating along the opposite direction produces a negative sign. So, the sum of the values of two integrals of the same magnitude, which are opposite sign, will cancel.
@calendarG
3 ай бұрын
We assume they're infinitely small and infinitely close together, so technically the difference would be zero since the limit of the curl in each box as the size of the box goes to zero is also zero.
@Infinity_InGloriouS
3 ай бұрын
@@calendarG I see, thank you! I kind of forgot about taking the limit... :(
@ValidatingUsername
3 ай бұрын
2:00 it’s important to remember that the anti derivative is a higher order unit which is why the height is equivalent to the lower order derivative area/volume/etc
@AlbertTheGamer-gk7sn
3 ай бұрын
Also, for the Green's Theorem, ∮ F ∙ dr = ∯ curl F ∙ dS = ∬ [(∇ ⨉ F) ∙ n]dA
@sebastiangudino9377
3 ай бұрын
Hey! You are that calc 3 guy! I thought you were a one hit wonder!
@MathsSciencePhilosophy
3 ай бұрын
I knew vaguely what guass, green, stokes theorem are, but they were never intuitive to me. You have provided great intuition about those theorems
@jdoe8162
3 ай бұрын
Hey, you actually posted the same day as my calculus final exam.
@Larsbutb4d
3 ай бұрын
good luck w the exam 👍
@PixelSergey
3 ай бұрын
This is actually so cool! We covered Green's theorem and Gauss' theorem in our vector analysis class, but I'd never gotten a solid visual understanding of them until now :)
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