BlackTshirtMathProfessor
BlackTshirtMathProfessor
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Absolute max and min values Problem 1 (Multivariable Calculus)
This problem goes over how to find the absolute maximum and absolute minimum values of a function of two variables on a closed, bounded region. It's very similar to how this is done in calculus 1, where you check the values of the function at the critical points and endpoints of the interval. Now, the boundary of a region is a curve.
Looking for a specific problem or topic? Try checking my website:
www.blacktshirtmathprofessor.com/videos
Переглядів: 32 765

Відео

Quiz 3 Spring 2022 (Calculus 2)
Переглядів 5232 роки тому
This quiz focuses on finding volume for solids using the washer and shell methods. If you want to attempt this, give yourself about 10 minutes. Calculus 2, Spring 2022 00:00 Problems 00:18 Problem 1 05:55 Problem 2 Looking for a specific problem or topic? Try checking my website: www.blacktshirtmathprofessor.com/videos
Peculiar Property of Definite Integrals Problem 2 (The Art of Integration)
Переглядів 3 тис.2 роки тому
Now that we know about Weierstrass substitution we can come back to another integral that we can evaluate with the peculiar property/ The King Rule. This problem is short because we have access to some powerful techniques. After a little bit of algebraic simplification we reduce our integral to one that we previously evaluated using Weierstrass substitution, which is linked below. A Peculiar Pr...
Weierstrass Substitution Problem 1 (The Art of Integration)
Переглядів 2,6 тис.2 роки тому
This is our first definite integral that we'll solving using Weierstrass substitution. The only new part that we haven't covered so far in The Art of Integration is how to convert the limits, which we go over right in the beginning. All of the other conversions for sin x and dx are the same. With a little bit of algebra for a partial fraction decomposition this integral is then a piece of cake!...
Integral of 1dx using Weierstrass Substitution (The Art of Integration)
Переглядів 9562 роки тому
The integral of 1dx is a beast of a problem! Thankfully, Weierstrass substitution makes it trivial. Just kidding: this integral is really simple and you already know the answer, x C. Thankfully, Weierstrass substitution gives us the same result. Weierstrass Substitution - Introduction: ua-cam.com/video/VwL1Kl4Ruv4/v-deo.html The Art of Integration is an ongoing series where we evaluate integral...
Quiz 2 Spring 2022 (Calculus 2)
Переглядів 3472 роки тому
This quiz focuses on area between curves. If you want to attempt this, give yourself about 10 minutes. Calculus 2, Spring 2022 00:00 Problems 00:18 Problem 1 05:41 Problem 2 Looking for a specific problem or topic? Try checking my website: www.blacktshirtmathprofessor.com/videos
Quiz 1 Spring 2022 (Calculus 2)
Переглядів 6332 роки тому
This quiz focuses on substitution. If you want to attempt this, give yourself about 10 minutes. Calculus 2, Spring 2022 00:00 Problems 00:18 Problem 1a 01:48 Problem 1b 04:14 Problem 1c Looking for a specific problem or topic? Try checking my website: www.blacktshirtmathprofessor.com/videos
Integral of sec x with Weierstrass Substitution (The Art of Integration)
Переглядів 3,9 тис.2 роки тому
The integral of sec x is usually taught by using a non-obvious trick: multiplying and dividing by sec x tan x. Here, we go through an alternate way to solve the integral of sec x by making use of Weierstrass substitution. Make sure that you're comfortable with the conversions for dx, sin x, and cos x in terms of t first, which I have linked below: Weierstrass Substitution - Introduction: ua-cam...
Weierstrass Substitution - Introduction (The Art of Integration)
Переглядів 5 тис.2 роки тому
After a short break the Art of Integration is back with an introduction to the world's sneakiest substitution, Weierstrass substitution. While the substitution is non-obvious it is similar to some earlier problems that we've solved using trigonometric tricks, which are linked below. Trigonometric Tricks Problem 1: ua-cam.com/video/jTewu2JZxlQ/v-deo.html Weierstrass substitution is typically use...
Peculiar Property of Definite Integrals Problem 1 (The Art of Integration)
Переглядів 2,4 тис.3 роки тому
This is a beast of an integral! Good luck trying to find an antiderivative for this function. Fortunately, we now have access to the peculiar property of definite integrals known as the King Rule. Once we apply this property the rest of the work is applying basic properties of logarithms and some trig identities. You'll definitely want to be familiar with the peculiar property, linked below, be...
A Peculiar Property of Definite Integrals // The King Rule (The Art of Integration)
Переглядів 12 тис.3 роки тому
In this video we introduce a peculiar property of definite integrals that's known in some places as the King Rule. On our journey to evaluate difficult integrals we've needed to expand our mathematical toolbox to be able to increase our creative problem solving skills. We've used algebraic tricks, creative substitutions, and advanced results like Euler's formula and the gamma function. We're no...
Chain Rule Multiple Times Problem 3 (Calculus 1)
Переглядів 1,3 тис.3 роки тому
This is another really good problem: it involves the Chain Rule being applied multiple times and trig functions. We point out the common error here, which is misinterpreting the inside as tangent being multiplied by sine. By using our shortcuts for the Chain Rule, linked below, the work isn't that bad as long as you remember the trig derivatives. Shortcuts for the Chain Rule - General Power Rul...
Chain Rule Multiple Times Problem 2 (Calculus 1)
Переглядів 1,9 тис.3 роки тому
This is a really good problem on applying the Chain Rule multiple times. We start by making sure that you understand the power notation for trig functions. Once we see this we can identify the outer and inner functions and apply the Chain Rule the first time by using the shortcut that I call the General Power Rule. We then apply the Chain Rule again to find the derivative of cos(3x). This is a ...
Chain Rule Multiple Times Problem 1 (Calculus 1)
Переглядів 3,2 тис.3 роки тому
Finding the derivative of this function requires applying the Chain Rule multiple times. Notice that since we have e raised to a function we need to apply the Chain Rule (we can use the General Exponential Rule). Also, the inner function sin(2x) is a composite so we'll need to apply the Chain Rule again! The work isn't difficult but it's easy to get lost when applying several derivative rules t...
Integral with the Exponential and Floor Functions (The Art of Integration)
Переглядів 1,3 тис.3 роки тому
This is a spicy integral involving the floor function, the greatest integer less than or equal to x. At first glance this integral might seem difficult but there's a nice property that we can make use of: the floor function is constant over integer intervals [n, n 1]. From here we split the integral up into a sum of integrals over integer intervals and use some standard results from calculus 2....
Chain Rule with the Quotient Rule Problem 3 (Calculus 1)
Переглядів 45 тис.3 роки тому
Chain Rule with the Quotient Rule Problem 3 (Calculus 1)
Chain Rule with the Quotient Rule Problem 2 (Calculus 1)
Переглядів 12 тис.3 роки тому
Chain Rule with the Quotient Rule Problem 2 (Calculus 1)
Chain Rule with the Quotient Rule Problem 1 (Calculus 1)
Переглядів 6 тис.3 роки тому
Chain Rule with the Quotient Rule Problem 1 (Calculus 1)
Chain Rule with the Product Rule Problem 3 (Calculus 1)
Переглядів 46 тис.3 роки тому
Chain Rule with the Product Rule Problem 3 (Calculus 1)
Chain Rule with the Product Rule Problem 2 (Calculus 1)
Переглядів 1 тис.3 роки тому
Chain Rule with the Product Rule Problem 2 (Calculus 1)
Chain Rule with the Product Rule Problem 1 (Calculus 1)
Переглядів 3533 роки тому
Chain Rule with the Product Rule Problem 1 (Calculus 1)
The Super Gaussian Integral (The Art of Integration)
Переглядів 3,1 тис.3 роки тому
The Super Gaussian Integral (The Art of Integration)
Shortcuts for the Chain Rule - General Power Rule and General Exponential Rule (Calculus 1)
Переглядів 8503 роки тому
Shortcuts for the Chain Rule - General Power Rule and General Exponential Rule (Calculus 1)
The Chain Rule with Trig Functions (Calculus 1)
Переглядів 1,2 тис.3 роки тому
The Chain Rule with Trig Functions (Calculus 1)
The Chain Rule with Exponential Functions (Calculus 1)
Переглядів 7423 роки тому
The Chain Rule with Exponential Functions (Calculus 1)
The Chain Rule (Calculus 1)
Переглядів 8353 роки тому
The Chain Rule (Calculus 1)
The Chain Rule - Identifying the Outer and Inner Functions (Calculus 1)
Переглядів 5 тис.3 роки тому
The Chain Rule - Identifying the Outer and Inner Functions (Calculus 1)
Second Derivative with Trig Functions Problem 1 (Calculus 1)
Переглядів 1,3 тис.3 роки тому
Second Derivative with Trig Functions Problem 1 (Calculus 1)
Quotient Rule with Trig Functions Problem 2 (Calculus 1)
Переглядів 3253 роки тому
Quotient Rule with Trig Functions Problem 2 (Calculus 1)
Quotient Rule with Trig Functions Problem 1 (Calculus 1)
Переглядів 6313 роки тому
Quotient Rule with Trig Functions Problem 1 (Calculus 1)

КОМЕНТАРІ

  • @homamthewise6941
    @homamthewise6941 2 дні тому

    Thanks 👍

  • @lessName1
    @lessName1 2 дні тому

    The rule is so weird and confusing yet he explained it in the most easiest and understandable way. Thank you, sir!

  • @eunicekimani6464
    @eunicekimani6464 3 дні тому

    Thanks

  • @StellaMuthoni-k3b
    @StellaMuthoni-k3b 5 днів тому

    Thankssss😊

  • @Nevertoolatetostart
    @Nevertoolatetostart 6 днів тому

    Thank you SOOOOO MUCHHHHHHHH!!!!!!!!!!!!

  • @PauloConstantino167
    @PauloConstantino167 8 днів тому

    but when you integrate the fractional derivative of X, you get the wrong result. So you need fractional integrals as well

  • @alexkotusenko
    @alexkotusenko 9 днів тому

    amazing video thank you

  • @A.-sd7wf
    @A.-sd7wf 11 днів тому

    Out of all the videos, this one helped me the most. Thanks!! I hope you come back to UA-cam and continue uploading.

  • @Makeupbymegan_6e23
    @Makeupbymegan_6e23 15 днів тому

    This is such a clear and well explained video, thank you so much!

  • @pepper5117
    @pepper5117 15 днів тому

    thanks james

  • @whyyat3470
    @whyyat3470 16 днів тому

    Please start making more videos. They are really well done and you passion for the subject is evident!

  • @omarsamy1144
    @omarsamy1144 16 днів тому

    you are amazing,idk how that video doesnt have too many like but id like to tell you that you are helping lots of students ,keep the amazing work

  • @RevocatusPaulC.P
    @RevocatusPaulC.P 17 днів тому

    Good job thank you very much

  • @landonmoore3550
    @landonmoore3550 19 днів тому

    I appreciate you using the u1 and u2 equations for variation of parameters instead of deriving and doing systems of equations. I have been looking for this. Also nice to combine two different topics to speed up my studies for finals. Good video!

  • @hibahstudio299
    @hibahstudio299 20 днів тому

    Where are you going it's been two years since u are not uploading sirr😢😢.Please do ur live vlog as a teacher since I want to be a lecture when I grownup.

  • @md.antikrahman2172
    @md.antikrahman2172 21 день тому

    May god bless you.

  • @brahim1brahim4311
    @brahim1brahim4311 25 днів тому

  • @khadijaSallau
    @khadijaSallau 26 днів тому

    It was -8 and +3, but you changed it when putting it in the equation. Why? Is it allowed because you want to cancel out?

  • @pierceandermann1011
    @pierceandermann1011 29 днів тому

    i fucks with this heavy

  • @blueschase11
    @blueschase11 Місяць тому

    So what does the value of e have to do with e^-infinity^2

  • @braveknight6857
    @braveknight6857 Місяць тому

    7:40 is there a typo ?

  • @jmilenyt
    @jmilenyt Місяць тому

    Your channel is just right in time before my calculus class. Thank you so much!

  • @FlipperSkipp
    @FlipperSkipp Місяць тому

    Good sir I will kiss you on the lips, thank you for your service

  • @diabetus129
    @diabetus129 Місяць тому

    4:15 wow this is exactly what i needed to hear lol

  • @itzorca3997
    @itzorca3997 Місяць тому

    goat

  • @chrischatergoon3207
    @chrischatergoon3207 Місяць тому

    Best explanation on UA-cam sir.

  • @rallyssuhfarias9560
    @rallyssuhfarias9560 Місяць тому

    this is the best video i have seen about the gamma function thank you so much! they always skip the integrals :( i always see this is my math book and i always got scaried but now i see that's not that complicated at all

  • @mathijs1987j
    @mathijs1987j Місяць тому

    Very nice problem and very clear presentation!

  • @Smdb6Z
    @Smdb6Z Місяць тому

    You are very good teacher ... Handsome too .

  • @joeanava851
    @joeanava851 Місяць тому

    can you explain how did you get the 8 and -3?

    • @BlackTshirtMathProfessor
      @BlackTshirtMathProfessor Місяць тому

      To factor the denominator, find two numbers that multiply to -21 and add to 5: 8 and -3 work.

  • @servius6274
    @servius6274 Місяць тому

    THANKK YOU, Finally a professor that thoroughly explains the topic and doesnt skips steps and lays it out neatly 💪

    • @servius6274
      @servius6274 Місяць тому

      His channel needs more subs and exposure bc he explains the topics very clearly

    • @BlackTshirtMathProfessor
      @BlackTshirtMathProfessor Місяць тому

      You’re welcome, fellow mathematician!

    • @servius6274
      @servius6274 Місяць тому

      @@BlackTshirtMathProfessor Haha thank you, I was literally stuck on a Dif Eq problem but this video cleared the way, thank you 🙏

  • @konkcs4
    @konkcs4 Місяць тому

    you are good, thanks Black shirt professor. A professor with the cool name

  • @ayamusa1439
    @ayamusa1439 Місяць тому

    Is it also the answer be y’ = 3(1 + tan(sin x))^3 times sec x squared times sin x times cos x? I mean if it’s okay to include the sec x squared not just sec (sin x)

  • @gaBgaBigBy
    @gaBgaBigBy Місяць тому

    Beauty video - thanks for helping me understand

  • @Ewoshi22
    @Ewoshi22 Місяць тому

    THANK YOU! This really helped me for some of my derivative questions regarding product, quotient and chain rule, especially where you had to factor at the end!

  • @ysrdomain2702
    @ysrdomain2702 Місяць тому

    Very good and clear explanation, thanks a lot.

  • @IrdinaBlume
    @IrdinaBlume Місяць тому

    Hi sirr , I m just found your youtube channel and your explanation really clear tho with the math working really make me easier to understand❤️

  • @M.7
    @M.7 Місяць тому

    Lifesaver

  • @tanvec
    @tanvec Місяць тому

    28:39 The Gaussian integral definitely evaluates to \sqrt{\pi}, however you have half the Gaussian integral since the limits are from 0 to infinity. The answer you wrote down is still correct though due to the 2 out front. Just a minor thing. Great presentation overall!

  • @paperbeatsrock_
    @paperbeatsrock_ Місяць тому

    I am in awe at your ability to create a video explaining layered, complex subjects, all without any editing (save for the simple cut to write out the problem) AND while keeping it extremely digestible. Stellar work - even if you happen to use a script or a teleprompter to help, it's still a rare and hard-earned skill. Major props!

    • @BlackTshirtMathProfessor
      @BlackTshirtMathProfessor Місяць тому

      Thank you! I actually didn’t use a script or teleprompter. I just recreated what I do in my courses, which I’ve been teaching for 16 years. I strived to try to create a classroom-like feel by doing it all in one take.

  • @frankansari3457
    @frankansari3457 Місяць тому

    It is really interesting that π appears at so much unexpected places. 😃

    • @BlackTshirtMathProfessor
      @BlackTshirtMathProfessor Місяць тому

      Seeing mathematical concepts pop up in unexpected places is one of my favorite things about mathematics!

  • @mariel-janedeniegagamarcha9728
    @mariel-janedeniegagamarcha9728 Місяць тому

    wow can u make a lot of simplified step by step tutorial for calcuus, this is somehow way more clearer Thanks a lot!

  • @FRKNDOG
    @FRKNDOG Місяць тому

    hello! i've recently encountered a problem with both important mclaurin series in one equation, how can i decide which one to use?

  • @giancarlog.1
    @giancarlog.1 Місяць тому

    Very helpful video, thank you

  • @lego7535
    @lego7535 Місяць тому

    THANK YOU

  • @Twilightcentre
    @Twilightcentre Місяць тому

    THanks very much!! Really helpful!

  • @MANIRIHOINNOCENT-mc4lp
    @MANIRIHOINNOCENT-mc4lp 2 місяці тому

    thank you for this ,what about the ODE of 2rd order do not contain x or y explicitly?

  • @SonaDevi-f8e
    @SonaDevi-f8e 2 місяці тому

    Thnkuu so much sir it's help me alotttt from india thnku so much

  • @justalion2805
    @justalion2805 2 місяці тому

    Thank you sir

  • @justindesilva9
    @justindesilva9 2 місяці тому

    when khan academy, NancyPi and the chemsitry tutor couldnt save me, blacktshirt came for the rescue