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Mathacy
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Vectors
Vectors are one of the most powerful entities in mathematics. They are crucial in various fields such as engineering, physics, computer science and mathematics. They can be added, scaled and follow algebraic rules that allow them to solve real world problems
In this video, we completely explain what vectors are and how to use them, from addition to the vector straight line equation. Multiplying vectors together will be covered in the next video.
Problem Sheet: mathacy.com/problem-sheets
Timestamps:
0:00 - Intro
1:24 - Vectors
1:55 - Scalars
2:26 - Standardising Vectors
2:54 - Cartesian Vectors
3:55 - Magnitude and Direction
5:20 - Polar Vectors
5:51 - Adding and Subtracting vectors
11:01 - Scalar multiplication
12:52 - Vector Line Equation
16:14 - Vector Notation
Переглядів: 1 378

Відео

Parametric and Implicit Differentiation (visualised)
Переглядів 13 тис.2 роки тому
Parametric and Implicit differentiation are the sneakiest tools for combating derivatives! It allows us to solve difficult differentiation problems with ease by utilising the Chain Rule in very sneaky ways! Explore what's really happening with Parametric and Implicit differentiation! Differentiation video: ua-cam.com/video/HNDIS_mZb0E/v-deo.html Problem Sheet: mathacy.com/problem-sheets Timesta...
The function that solves every Integration question | Weierstrass Substitution | tan(x/2)
Переглядів 7 тис.2 роки тому
The Ghost Substitution (commonly known as the Weierstrass or Half-Angle Tangent Substitution) is one of the 'sneakiest substitutions' in mathematics. The Ghost Substitution utilizes a very clever and useful property about trigonometric functions which allows us to solve complex calculus related problems. In this video, we visually explain how we can intuitively define the circle using the Ghost...
Integration by substitution (visualised)
Переглядів 19 тис.3 роки тому
Integration by substitution is one of the most powerful tools for combating integrals! It allows us to transform a difficult integral into a significantly easier one. In this video we visually show what actually happens when you perform a substitution and how to properly use integration by substitution. Integration video: ua-cam.com/video/vcEmFspb8ZU/v-deo.html Problem Sheet: mathacy.com/proble...
Integration by parts (visualised)
Переглядів 37 тис.3 роки тому
Integration by parts is one of the most useful tools for finding integrals! In this video we cover what it is, how it works and we also show what is VISUALLY happening! Integration by parts is the product rule for Integration. It allows us to find the integral of functions multiplied together and it is a super interesting solution to a geometrical problem! Problem Sheet: mathacy.com/problem-she...
Integration
Переглядів 14 тис.3 роки тому
Integration is one of the beautiful pillars of calculus. It revolves around the idea of doing the opposite of differentiation, an anti-differentiation. Sounds straight forward right? However, there is an unbelievable connection which revolutionized mathematics entirely! That result is that anti-differentiation is equivalent to the area under a curve. In this video we take a deep dive into integ...
Differentiation - The Chain Rule
Переглядів 13 тис.3 роки тому
The Chain Rule is one of most important rules in differentiation and allows us to find the derivative of composite functions. This rule alone allows to differentiate an infinite number of different functions and combined with the product rule, allows us to solve almost every differentiation problem! Chain Rule Problem Sheet: mathacy.com/problem-sheets Timestamps: 00:00 - Intro 00:16 - The Compo...
UNBELIEVABLE: 1 x 2 x 3 x 4 x ... = √2π | Infinity Factorial / Product of Natural Numbers
Переглядів 14 тис.3 роки тому
Astounding! The product of all natural numbers (or counting numbers) is equal to √2π. In this video we go through how this result is derived a take a look at the super famous Riemann-zeta function and use it to formulate this result and we will utilise our arsenal of differentiation. Disclaimer: There are many areas in this video that 'break' mathematics, such as taking the derivative of an inf...
Differentiation - Product Rule (and Quotient Rule)
Переглядів 27 тис.3 роки тому
The product rule is one of the most useful tools for differentiating functions multiplied by other functions. This beautiful rule allows us to differentiate a practically infinite number of functions! We also take a deep dive into the quotient rule which allows us to find the derivative of functions divided by other functions! You don't wanna miss this! Problem Sheet: mathacy.com/videos/differe...
What is e and ln(x)? (Euler's Number and The Natural Logarithm)
Переглядів 619 тис.3 роки тому
Euler's Number, e, is one of the most prominent constants in mathematics and exponential functions are some of the most important in maths. In this video: we take a deep dive into what Euler's Number is, what exponential functions are and how to differentiate them and we take a look at the super important natural logarithm, ln(x). Website: mathacy.com Timestamps: 0:00 - Intro 0:27 - Compound in...
Differentiating sin(x), cos(x) and tan(x)
Переглядів 11 тис.3 роки тому
Trigonometric functions are some of the most fundamental functions in mathematics. In this session we learn how what the derivatives of sin(x), cos(x) and tan(x) are and prove it via first principles. These classic functions form a very beautiful relationship, you don't want to miss this one! Proof of tan(x): mathacy.com/videos/differentiation-playlist Concrete proof: mathacy.com/videos/differe...
Stationary Points (Turning Points)
Переглядів 18 тис.4 роки тому
Stationary Points (Turning Points)
Differentiation
Переглядів 43 тис.4 роки тому
Differentiation

КОМЕНТАРІ

  • @ananthakrishnank3208
    @ananthakrishnank3208 День тому

    1:10 Just came for this second. Got it, thanks!

  • @Delodg
    @Delodg 2 дні тому

    I don’t understand how e^x grows faster than x^100. I put it in and x^100 was always bigger

  • @nikolaspareschi
    @nikolaspareschi 3 дні тому

    Maybe you should consider changing the tone of your voice, avoid hitting these high pitches. The video was amazing.

  • @hdbrot
    @hdbrot 5 днів тому

    For a long time I struggled to understand the structural reason why composition of functions turns into multiplication. That is, why is multiplication the natural thing to do? And why is the formula so asymmetric, while it‘s totally nice for addition for example, where it‘s just (f + g)' = f' + g'. My confusion was resolved when I learned that taking the tangent space at a point is a functor from pointed manifolds to vector spaces.

  • @ahmoin
    @ahmoin 5 днів тому

    you know this video is gonna be good when its just titled "Vectors"

  • @Lordversus44
    @Lordversus44 5 днів тому

    This video is incredible. It is well explained and clear. Never seen so much professionalism and precision in a video like this. Thank you!! 🎉

  • @ahmoin
    @ahmoin 5 днів тому

    i wish i saw this video in algebra 2 and precalc

  • @EHMM
    @EHMM 8 днів тому

    analytic continuation is cool :)

  • @BigGod23-321
    @BigGod23-321 10 днів тому

    ❤❤

  • @Haggdjdndbxhdjnjff
    @Haggdjdndbxhdjnjff 12 днів тому

    good

  • @sammyisanna4367
    @sammyisanna4367 14 днів тому

    How did we cancel the x in 8:55 ???

  • @not.xanjay
    @not.xanjay 16 днів тому

    5:49 isnt that the answer, xcos(x)+sin(x)+c ???

  • @mangeshjirapure9154
    @mangeshjirapure9154 17 днів тому

    What a easy explanation 👍

  • @jacobperalta3379
    @jacobperalta3379 20 днів тому

    Bro there is no h in the letter h.😂 It is just „atch“ not „hatch“ Perfect video but this was a little trigger for me😂😂

  • @mintusaren895
    @mintusaren895 22 дні тому

    Why e can be others, unknown.

  • @mihisarakaveesha8954
    @mihisarakaveesha8954 26 днів тому

    The best explanation for 'e' I've seen. Superb Work 😊

  • @middlemanning
    @middlemanning 28 днів тому

    Freaking goat

  • @ChimaevMikelson
    @ChimaevMikelson Місяць тому

    wow

  • @a1184zxc
    @a1184zxc Місяць тому

    DA BEST MATHS Channel is back!

  • @Rickidicki
    @Rickidicki Місяць тому

    Will you marry me?

  • @FreemanArno
    @FreemanArno Місяць тому

    Young Linda Anderson Maria Smith Ronald

  • @Bitmaker64
    @Bitmaker64 Місяць тому

    holy shit, this genuinely feels so obvious now that you explained how it works, but this is literally never clicked for me. I am the definition of mnd blown rn.

  • @AntoinetteSusie-r3m
    @AntoinetteSusie-r3m Місяць тому

    Moore Kimberly Thompson Deborah Williams Joseph

  • @PatrickPerez-o1b
    @PatrickPerez-o1b Місяць тому

    Johnson Laura Taylor Betty Harris Deborah

  • @mwerensteijn
    @mwerensteijn Місяць тому

    Thank you so much!

  • @ONeilPoppy-l1k
    @ONeilPoppy-l1k Місяць тому

    Harris Brian Taylor Jessica Thomas Laura

  • @Pulipatismitanaga
    @Pulipatismitanaga Місяць тому

    10th class student be like : ah man out of syllabus

  • @Unitarian-Astronomer
    @Unitarian-Astronomer Місяць тому

    Subscribed!

  • @Arycke
    @Arycke Місяць тому

    6:02 , the indefinite integral should have had abs value around f(x), bc f(x)=x+1 has negative f(x) values. I.e. ln|(x+1)| + C, where x ≠-1 Original function had domain (-inf,-1)U(-1,+inf) You get an anti derivative at every point defined in the original domain.

    • @Arycke
      @Arycke Місяць тому

      Still an awesome visualization. Thanks for this, sir.

  • @HousmanTim-m8j
    @HousmanTim-m8j Місяць тому

    Thompson Daniel Young Matthew Lee Christopher

  • @TyrelleBarker
    @TyrelleBarker 2 місяці тому

    All i heard was haych

  • @MelvilleAlbert-h2j
    @MelvilleAlbert-h2j 2 місяці тому

    White Michael Rodriguez Kimberly Hernandez Anthony

  • @balaakhilan
    @balaakhilan 2 місяці тому

    gauss found this when he was a kid

  • @fatlip8315
    @fatlip8315 2 місяці тому

    Anything times the rate of decay, equals everything adds up to what it adds up to until it decays and isn't what it once was. Even the universe expanding times the rate of decay, means the universe isn't expanding much more then it decays. What would be a good way to explain the rate of decay in a mathematical formulation.

  • @threety-three5091
    @threety-three5091 2 місяці тому

    i have one question, if f(x) and g(x) are parametric equations to each other, when thinking about the graph formed, the integrals you are calculating wont really be the integrals of the functions themselves, but rather some representation of them to fit into the parametric equation. Can someone explain why this works?

  • @juzbecoz
    @juzbecoz 2 місяці тому

    Zeta enters

  • @OConnorCarr-b7l
    @OConnorCarr-b7l 2 місяці тому

    Thomas Paul Johnson Barbara Anderson Susan

  • @AdaHurley-h3q
    @AdaHurley-h3q 2 місяці тому

    Dickinson Mall

  • @PeggyCecil-z8h
    @PeggyCecil-z8h 2 місяці тому

    Johnnie Summit

  • @TitusAfra-h5f
    @TitusAfra-h5f 2 місяці тому

    Lewis Betty Miller Ruth Anderson Nancy

  • @AntoinetteSusie-r3m
    @AntoinetteSusie-r3m 2 місяці тому

    Wilson Jennifer Taylor Jennifer Robinson Michael

  • @FieldWordsworth-m5n
    @FieldWordsworth-m5n 2 місяці тому

    Davis Sharon Gonzalez Kenneth Robinson Timothy

  • @ElectraBard-h3d
    @ElectraBard-h3d 2 місяці тому

    Brown Eric Garcia Elizabeth White Lisa

  • @padaddadada5417
    @padaddadada5417 2 місяці тому

    thank you for your video !!! But i have a question at 3:10 you rotate the x and y axis to calculate the area between y1 and y2 but what if instead of an exponential curve as here , we had a cos function then the cos function would be (rotated too ) and what sense would calculating the area under this curve have ?

  • @MorrisonOscar-u6l
    @MorrisonOscar-u6l 2 місяці тому

    Jones Kenneth Williams Robert Robinson Mark

  • @nicolasgobert8324
    @nicolasgobert8324 2 місяці тому

    Perfect Video ❤

  • @YuleTaylor-l8g
    @YuleTaylor-l8g 2 місяці тому

    Gonzalez Lisa Robinson Thomas Jones Jeffrey

  • @WhittierElliot-f3b
    @WhittierElliot-f3b 2 місяці тому

    Taylor Larry Taylor Margaret Johnson William

  • @themegaruler
    @themegaruler 2 місяці тому

    funny beginning i laughed

  • @BenBernice-i5y
    @BenBernice-i5y 2 місяці тому

    Rau Extension