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BlackTshirtMathProfessor
United States
เข้าร่วมเมื่อ 17 พ.ย. 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
มุมมอง: 34 253
วีดีโอ
Quiz 3 Spring 2022 (Calculus 2)
มุมมอง 5372 ปีที่แล้ว
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)
มุมมอง 3.1K2 ปีที่แล้ว
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)
มุมมอง 2.7K2 ปีที่แล้ว
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)
มุมมอง 9882 ปีที่แล้ว
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: th-cam.com/video/VwL1Kl4Ruv4/w-d-xo.html The Art of Integration is an ongoing series where we evaluate integra...
Quiz 2 Spring 2022 (Calculus 2)
มุมมอง 3532 ปีที่แล้ว
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)
มุมมอง 6432 ปีที่แล้ว
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)
มุมมอง 4.1K2 ปีที่แล้ว
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: th-cam...
Weierstrass Substitution - Introduction (The Art of Integration)
มุมมอง 5K2 ปีที่แล้ว
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: th-cam.com/video/jTewu2JZxlQ/w-d-xo.html Weierstrass substitution is typically us...
Peculiar Property of Definite Integrals Problem 1 (The Art of Integration)
มุมมอง 2.5K3 ปีที่แล้ว
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)
มุมมอง 12K3 ปีที่แล้ว
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)
มุมมอง 1.4K3 ปีที่แล้ว
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)
มุมมอง 2K3 ปีที่แล้ว
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)
มุมมอง 3.3K3 ปีที่แล้ว
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)
มุมมอง 1.3K3 ปีที่แล้ว
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)
มุมมอง 46K3 ปีที่แล้ว
Chain Rule with the Quotient Rule Problem 3 (Calculus 1)
Chain Rule with the Quotient Rule Problem 2 (Calculus 1)
มุมมอง 13K3 ปีที่แล้ว
Chain Rule with the Quotient Rule Problem 2 (Calculus 1)
Chain Rule with the Quotient Rule Problem 1 (Calculus 1)
มุมมอง 7K3 ปีที่แล้ว
Chain Rule with the Quotient Rule Problem 1 (Calculus 1)
Chain Rule with the Product Rule Problem 3 (Calculus 1)
มุมมอง 49K3 ปีที่แล้ว
Chain Rule with the Product Rule Problem 3 (Calculus 1)
Chain Rule with the Product Rule Problem 2 (Calculus 1)
มุมมอง 1.1K3 ปีที่แล้ว
Chain Rule with the Product Rule Problem 2 (Calculus 1)
Chain Rule with the Product Rule Problem 1 (Calculus 1)
มุมมอง 3723 ปีที่แล้ว
Chain Rule with the Product Rule Problem 1 (Calculus 1)
The Super Gaussian Integral (The Art of Integration)
มุมมอง 3.1K3 ปีที่แล้ว
The Super Gaussian Integral (The Art of Integration)
Shortcuts for the Chain Rule - General Power Rule and General Exponential Rule (Calculus 1)
มุมมอง 8933 ปีที่แล้ว
Shortcuts for the Chain Rule - General Power Rule and General Exponential Rule (Calculus 1)
The Chain Rule with Trig Functions (Calculus 1)
มุมมอง 1.3K3 ปีที่แล้ว
The Chain Rule with Trig Functions (Calculus 1)
The Chain Rule with Exponential Functions (Calculus 1)
มุมมอง 8783 ปีที่แล้ว
The Chain Rule with Exponential Functions (Calculus 1)
The Chain Rule - Identifying the Outer and Inner Functions (Calculus 1)
มุมมอง 5K3 ปีที่แล้ว
The Chain Rule - Identifying the Outer and Inner Functions (Calculus 1)
Second Derivative with Trig Functions Problem 1 (Calculus 1)
มุมมอง 1.3K3 ปีที่แล้ว
Second Derivative with Trig Functions Problem 1 (Calculus 1)
Quotient Rule with Trig Functions Problem 2 (Calculus 1)
มุมมอง 3403 ปีที่แล้ว
Quotient Rule with Trig Functions Problem 2 (Calculus 1)
Quotient Rule with Trig Functions Problem 1 (Calculus 1)
มุมมอง 6713 ปีที่แล้ว
Quotient Rule with Trig Functions Problem 1 (Calculus 1)