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BlackTshirtMathProfessor
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Добавлен 17 ноя 2020
I'm a professor of mathematics at a community college in the United States. I like to wear black t-shirts under my flannels.
I hope you enjoy the content!
- BTMP
www.blacktshirtmathprofessor.com/
blacktshirtmathprofessor
Channel updates are posted on my website and previews are on my Instagram account.
I hope you enjoy the content!
- BTMP
www.blacktshirtmathprofessor.com/
blacktshirtmathprofessor
Channel updates are posted on my website and previews are on my Instagram account.
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
Looking for a specific problem or topic? Try checking my website:
www.blacktshirtmathprofessor.com/videos
Просмотров: 26 392
Видео
Quiz 3 Spring 2022 (Calculus 2)
Просмотров 4662 года назад
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)
Просмотров 2,5 тыс.2 года назад
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)
Просмотров 2,2 тыс.2 года назад
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)
Просмотров 8142 года назад
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: ruclips.net/video/VwL1Kl4Ruv4/видео.html The Art of Integration is an ongoing series where we evaluate integra...
Quiz 2 Spring 2022 (Calculus 2)
Просмотров 3032 года назад
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)
Просмотров 5602 года назад
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)
Просмотров 3,2 тыс.2 года назад
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: ruclip...
Weierstrass Substitution - Introduction (The Art of Integration)
Просмотров 4 тыс.2 года назад
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: ruclips.net/video/jTewu2JZxlQ/видео.html Weierstrass substitution is typically us...
Peculiar Property of Definite Integrals Problem 1 (The Art of Integration)
Просмотров 2 тыс.2 года назад
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)
Просмотров 10 тыс.3 года назад
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)
Просмотров 8333 года назад
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)
Просмотров 1,2 тыс.3 года назад
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)
Просмотров 2,1 тыс.3 года назад
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)
Просмотров 1,2 тыс.3 года назад
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)
Просмотров 30 тыс.3 года назад
Chain Rule with the Quotient Rule Problem 3 (Calculus 1)
Chain Rule with the Quotient Rule Problem 2 (Calculus 1)
Просмотров 6 тыс.3 года назад
Chain Rule with the Quotient Rule Problem 2 (Calculus 1)
Chain Rule with the Quotient Rule Problem 1 (Calculus 1)
Просмотров 2,9 тыс.3 года назад
Chain Rule with the Quotient Rule Problem 1 (Calculus 1)
Chain Rule with the Product Rule Problem 3 (Calculus 1)
Просмотров 20 тыс.3 года назад
Chain Rule with the Product Rule Problem 3 (Calculus 1)
Chain Rule with the Product Rule Problem 2 (Calculus 1)
Просмотров 5053 года назад
Chain Rule with the Product Rule Problem 2 (Calculus 1)
Chain Rule with the Product Rule Problem 1 (Calculus 1)
Просмотров 1933 года назад
Chain Rule with the Product Rule Problem 1 (Calculus 1)
The Super Gaussian Integral (The Art of Integration)
Просмотров 3 тыс.3 года назад
The Super Gaussian Integral (The Art of Integration)
Shortcuts for the Chain Rule - General Power Rule and General Exponential Rule (Calculus 1)
Просмотров 5013 года назад
Shortcuts for the Chain Rule - General Power Rule and General Exponential Rule (Calculus 1)
The Chain Rule with Trig Functions (Calculus 1)
Просмотров 6603 года назад
The Chain Rule with Trig Functions (Calculus 1)
The Chain Rule with Exponential Functions (Calculus 1)
Просмотров 3303 года назад
The Chain Rule with Exponential Functions (Calculus 1)
The Chain Rule - Identifying the Outer and Inner Functions (Calculus 1)
Просмотров 4,4 тыс.3 года назад
The Chain Rule - Identifying the Outer and Inner Functions (Calculus 1)
Second Derivative with Trig Functions Problem 1 (Calculus 1)
Просмотров 1,1 тыс.3 года назад
Second Derivative with Trig Functions Problem 1 (Calculus 1)
Quotient Rule with Trig Functions Problem 2 (Calculus 1)
Просмотров 2143 года назад
Quotient Rule with Trig Functions Problem 2 (Calculus 1)
Quotient Rule with Trig Functions Problem 1 (Calculus 1)
Просмотров 4473 года назад
Quotient Rule with Trig Functions Problem 1 (Calculus 1)
This is also equal to b-a/2 as pi/2-0 /2 =pi/4.
Pofessor Black Shirt, you are one of the best math presenter on youtube. I am a retired EE who spends a lot of time on youtube math channels, guys like you are realy saving guys like me from getting dementia. Your explation of the gamma function is very clear that even an old guy like me have no problem understanding your lecture, keep up the good work.
Thank you so much for sharing these tips and tricks
You are AWESOME!!!!
Excellent tutorial. I enjoyed watching and learning from this tutorial. Thanks.
Excellent tutorial
Let's integrate by parts multiple times and then derive formula for product in terms of Gamma function
That sounds crazy. I’m in!
@@BlackTshirtMathProfessor It maybe helpful Look , when you solving odes like Legendre , Chebyshev, Hermite,Bessel using power series (Frobenius) method you will get recurrence relation for coefficients This recurrence relation can be sometimes expressed as product and later this product can be expressed in terms of Gamma function so we are able to write general form of solution using series
great intuition, thanks!
I can’t take credit for it. I remember learning this from one of my professors 20 years ago.
Unfortunately it is very tricky. In writing another comment I got confused when r was between 0 and -1. Looking at the general geometric series of a+ar+ar²+ar³+... then odd powers of r would be negative. Another problem arises as n approaches infinity ("at infinity" is nonsense) then 1-r^n approaches in value up to 1. The finite formula approaches in value down to a as n approaches infinity. It is reasonable to assume that as n approaches infinity that 1/n is 0, but assuming is not always reasonable. Nonstandard Analysis says they are the same, I disagree. Infinity is incomplete, inconsistent and imprecise.
As you say in the video, SHUT UP and learn where your formula comes from. The formula for the sum of a finite geometric series is; a*(1-r^n)/(1-r) where n is a natural > 1, r!=1 and an if n=1. This formula was obtained by multiplying the series by r, using standard algebraic manipulations to obtain the result, valid for all r except 9/9, excuse me 1. Ok, what happens as n approaches infinity. n becomes very large and 1-r^n becomes a very large absolute number if r is greater than 1. Not helpful. If r is 1, "an" then becomes "a" times larger than n. a*(1-r^n)/(1-r) r<1 and n approaching infinity. 1-r^n becomes very close to 1 and the sum becomes very close to a/(1-r). The question becomes, is the Archimedean property violated.? Infinity is incomplete, inconsistent and imprecise.
I did all of this in a previous video, bro.
@@BlackTshirtMathProfessor thanks for the reply. I have not yet found that video. I am only commenting on the topic of "Does ".99..."=1. The biggest problem in non-standard Analysis is the treatment of infinity and the "place notation" of real numbers in different bases. What are limits? Do they have to equal the entity they refer to? There is no such reality as "at infinity". I am trying to rely on basics. The definition of rational numbers is the ratio of two integers. 9/9 does not define ".99...". Integers do not have nonzero digits to the right of the radix point in base place number notation. (Weak arg but still logical as base place notation is universally used for numbers) Are the real numbers a continuum? Can decimal place notation represent each number in the continuum. Is it really a paradox that a runner can't pass a finish line if he only get ½ way there at a time.
ruclips.net/video/HVcSEuy0DRs/видео.htmlsi=Ga_nZCrivGxabAlD
@@BlackTshirtMathProfessor JohnTheBonehead is a troll. He has been posting his hilarious nonsense everywhere for at least a year.
Revising for calculus 2 and your videos have been extremely concise on each topic! Thanks a ton
wonderful explanation, i appreciate the efforts.
You teach very well man, Tnx
This helped a lot
outstanding sir ....hats off
You are doing gods work brother thank you
❤
Thanks from India 🇮🇳🫶
I don't know if you are reading the comments right now, but if you are, I must say that you have a great channel. I am a physics Olympian and sometimes math can be difficult for me. I came across your channel on reddit while looking for a good resource on differential equations, your videos are very explanatory and the integrals you solved were the ones I couldn't solve and they helped me a lot in this regard. You uploaded your last video 1 year ago, it is very sad that a channel like yours has few views. I know it is impertinent to say this, but please continue uploading videos. I am sure you will be trending one day, because you deserve it. Have a nice day
Thank you! As a former physics student myself, this makes me really happy to see that you found some of my videos useful. I do still actively reply to comments but I haven’t been able to make time for recording new videos after some things changed in my personal life. I’m still planning to get back to it at some point.
@@BlackTshirtMathProfessor Thank you for responding to my comment, I respect your decision. I want you to know that if you come back, I'm sure there will be a lot of fans like me who will support your videos😁. Have a nice day.
gracias por la magnifica explicación ,saludos desde México
You can do the same thing with hyperbolic functions using e^x=cosh(x)+sinh(x). Instead of matching the real and imaginary components in the equality, you match the even and odd components.
Very very clear! And the right speed: I can follow, and it is not too slow! And you convey your fascination for math! Just great!
Thanks for the new and simple way of finding INTEGRATION BY PARTS .....!!!
Asombroso!
As always, a wonderful video. Fractional derivatives are a fascinating concept that I hadn't thought of before. It was also enormously helpful to link it with the gamma function, which I only learned about yesterday.
It has truly brightened my day to stumble onto this channel. After a long search, I came upon this extremely clear and thorough description of the gamma function. Continue doing what you're doing; you are a great instructor.
Loved and subscribed !!!!
But you don't agree with the result. Your channel shows that you are a crackpot.
Mr perfect ❤
Thank you, doing my physics degree with many gap years from my A levels. Your channel is very hlpful
vine con mi mono choro, robale todo
Y only say that tan(x)=sin(x)/cos(x) Then say u=cos(x) So -du=sin(x)dx So the resultant integral was -∫(ln(u)/u)du With the simple substitution v=ln(u) and dv=du/u and working it the result is ln²(u)/2+c=ln²(cos(x))/2+c
Probably is not the best method, but I use x=tan⁴(θ), dx=4tan³(θ)sec²(θ)dθ So I get the integral of tan⁵(θ)dθ And is not bad with the identity of tan²(θ)=sec²(θ)-1 The integral give me tan⁴(θ)-2tan²(θ)+4ln|sec(θ)|+c tan⁴(θ)=x 2tan²(θ)=2√(x) 4ln|sec(θ)|=4ln|√(1+√(x))|=2ln|1+√(x)|=2ln(1+√(x)) So x-2√(x)+2ln(1+√(x))+c
Easier to understand, thank you so much❤
Γ(z)= ∫₀ ᪲ tᶻ⁻¹ e⁻ᵗ dt
The clarity of your whiteboard script is very helpful.
Interesting. I wonder what real applicaions are on the horizon with fractional derivatives.
thank you very much! ive been struggling on the chain rule in my course
tysm i was about to kms over this
bout to watch, if it doesnt help me, im doin it.
this was awesome and very helpful thanks
Thanks from Afghanistan
I want you as my teacher lol
Great work! Easy to understand
of course much simpler and clear path
extremely helpful video, thank you so much!
why do we split the boundary as top and bottom and not left and right?
You could but you would need to solve for x instead of y
the shortcuts part in the end is very nice
Do Lagrange multipliers work for this?
Yes, but only for checking for maximum/minimum values on the boundary of the region. The constraint would be x^2 + y^2 = 16
@@BlackTshirtMathProfessorso the process would be to use Lagrange multipliers to find the candidates on the boundary, and then find other critical points where it could occur?
That’s right!
amazing
how is root 2 the outer function in the very first example
👍👍