I know Dr. Jerison won't be able to see this comment, but I just really want to say that, even though Dr. Jerison probably have vaguely guessed his impact from this Calculus course. But he would never know how MANY chinese students have their calculus SAVED by him. In fact this MIT OCW project has world impact, it will be a monument of the early Internet age
oh, these're beautiful, the arc length curves, we just were told to memorize the formulas, while learning them, in highschool, it's eato understand, thank you, Professor🌞
Honestly I think there should be people moderating the comments section that delete those judgmental comments. The students have rights to learn in a safe environment. Asking “stupid” questions is an integral part of learning as much as making mistakes. It’s just sad to see students swallow their doubts bcs they worry about how they look in front of others. So if you know the answers to the questions, shut up and watch the video without being a judgmental jerk.
To everyone being rude to the student, he's actually not completely off like you wrongly assume. Because if you have parentheses around the number in the superscript/exponent it can be used to denote a higher order derivative, like f⁽⁵⁾(x) can be used instead of the much less readable f'''''(x).
Great video, but misleading title. "Parametric Equations" in the name, and 40/45 minutes are about arc length and surface area? I kept waiting for the Parametric Equations topic to kick in I didn't realize the video was almost over.
I guess that if you rotate your axes in order to align one of the new coordinate-axis with the axis of revolution, you'll be able to easily solve the problem using the already-known strategy.
It has been given in the previous lectures to find volume aboit x and y axis. Volume of rotation.. And u can just make a change of axis. It is messy but we can solve it if we have a lot of patience.
I think he's actually not very sympathetic with students but he masters the subject and I find his explanations very enlightening, and hear him increases my knowledge and understanding a lot.
not very sympathetic with students?? you haven't seen all of his lectures at mit opencourseware, i strongly disagree with you. also you don't know him in real life, it's not enough to judge someone on a 50 min video
I obviously don't know as much maths as Prof David, but isn't the illustration (I call it illustration) between relationship of arc length of circle,# and angle circular? The arc length, in standard trig or elementary calculus, is already DEFINED. Further, to arrive the the arcsin, the trigonometric derivation trick was used. So proof is circular. But it is good demonstration of geometric interpretation. This "proof" reminds me of attempt to define addition using sets and powersets. Interesting but not useful for all practicle purpose.
Yeah theres an equivalent notation in the function notation two but it contains parentheses f^(2) (x) (the 2's little), yeah nothing much, just thought it was funny, but it does happen- smart people can derp moment sometimes XD.
We recommend you look at the OCW Scholar version of this course: ocw.mit.edu/courses/mathematics/18-01sc-single-variable-calculus-fall-2010. It has problems sets with solutions, so you can check your work. Best wishes on your studies!
here you go down to problem set and find which task were given to each lecture: ocw.mit.edu/courses/18-01-single-variable-calculus-fall-2006/pages/assignments/ and here you find homework with solutions(as a bonus there are supplementary notes): math.mit.edu/~jorloff/suppnotes/suppnotes01-01a/index-01A.html
If you know anything about the university system it doesn't matter if you got a 5 on the AP exam or learned it in middle school, you still have to take it as a lower div, no exceptions. James Rockford
Hannah At MIT you can receive credit for 18.01 if you score high enough on the AP exam. Here are the details: math.mit.edu/academics/undergrad/first/index.php
Am I the only one who doesn't seem think mr jerison isn't a good teacher? I mean compared to the brilliant herbert gross and christine breiner he seems to not be able to connect with us students and get what might be difficult or need more to students. In one of the lectures he couldn't even understand that the student who asked a question had a problem with negative numbers n that's the freakin basics .. PS I totally get this a purely subjective thing.
I know Dr. Jerison won't be able to see this comment, but I just really want to say that, even though Dr. Jerison probably have vaguely guessed his impact from this Calculus course. But he would never know how MANY chinese students have their calculus SAVED by him. In fact this MIT OCW project has world impact, it will be a monument of the early Internet age
oh, these're beautiful, the arc length curves, we just were told to memorize the formulas, while learning them, in highschool, it's eato understand, thank you, Professor🌞
MIT, thank you so much. This is truly a gift.
Professor Jerison, thank you so much for giving such a fascinating calculus series!
God bless MIT and professor Jerison!
Honestly I think there should be people moderating the comments section that delete those judgmental comments. The students have rights to learn in a safe environment. Asking “stupid” questions is an integral part of learning as much as making mistakes. It’s just sad to see students swallow their doubts bcs they worry about how they look in front of others.
So if you know the answers to the questions, shut up and watch the video without being a judgmental jerk.
Lol where the hell did you make up this "right" to learn in a safe environment. Snowflake.
@@Antonio_Serdar well, I didn’t make it up. It’s called basic human decency and common sense which I suggest you brush up on.
To everyone being rude to the student, he's actually not completely off like you wrongly assume. Because if you have parentheses around the number in the superscript/exponent it can be used to denote a higher order derivative, like f⁽⁵⁾(x) can be used instead of the much less readable f'''''(x).
I think you're supposed to use greek numerals to denote derivatives. So it would be f^{V}(x)
@@thebrucecyou i have seen all three of the notations being used
Thank you. I've just learned that a few days ago, and you helped me to understand it better.
Props to Saurav Bastola, ua-cam.com/channels/7hkeE-LRyzietNCecWnHLg.html for the listed topics.
Lecture 1: Rate of Change
Lecture 2: Limits
Lecture 3: Derivatives
Lecture 4: Chain Rule
Lecture 5: Implicit Differentiation
Lecture 6: Exponential and Log
Lecture 7: Exam 1 Review
Lecture 9: Linear and Quadratic Approximations
Lecture 10: Curve Sketching
Lecture 11: Max-min
Lecture 12: Related Rates
Lecture 13: Newton's Method
Lecture 14: Mean Value Theorem
Lecture 15: Antiderivative
Lecture 16: Differential Equations
Lecture 18: Definite Integrals
Lecture 19: First Fundamental Theorem
Lecture 20: Second Fundamental Theorem
Lecture 21: Applications to Logarithms
Lecture 22: Volumes
Lecture 23: Work, Probability
Lecture 24: Numerical Integration
Lecture 25: Exam 3 Review
Lecture 27: Trig Integrals
Lecture 28: Inverse Substitution
Lecture 29: Partial Fractions
Lecture 30: Integration by Parts
Lecture 31: Parametric Equations
Lecture 32: Polar Coordinates
Lecture 33: Exam 4 Review
Lecture 35: Indeterminate Forms
Lecture 36: Improper Integrals
Lecture 37: Infinite Series
Lecture 38: Taylor's Series
Lecture 39: Final Review
So Smiley You Make Available This Video Arc Length Surface Area and My Favourite the Parametric Equation
Good Job Professor
38:50
I think in this case , with rotation we would get volume with such strip.
For surface area the rotation method will not do , in mu opinion
Thanks ❤️🤍
Great video, but misleading title. "Parametric Equations" in the name, and 40/45 minutes are about arc length and surface area? I kept waiting for the Parametric Equations topic to kick in I didn't realize the video was almost over.
it was clearly stated at the intro 00:52 secs to be precise that the lecture would be about geometry in calculus
I Really Like The Video From Your Parametric equations, arclength, surface area
Why is arc length not included in volume of solid in revolution whereas it is used in surface area formula?
How can I calculate volumen of a solid of revolution generated by a curve turned aroun an inclined line?
I guess that if you rotate your axes in order to align one of the new coordinate-axis with the axis of revolution, you'll be able to easily solve the problem using the already-known strategy.
It has been given in the previous lectures to find volume aboit x and y axis. Volume of rotation.. And u can just make a change of axis. It is messy but we can solve it if we have a lot of patience.
min 25:04 it would have been worth mentioning that the resulting integral is a mix of real + imaginary components
Everything is real in that integral...
I think he's actually not very sympathetic with students but he masters the subject and I find his explanations very enlightening, and hear him increases my knowledge and understanding a lot.
not very sympathetic with students?? you haven't seen all of his lectures at mit opencourseware, i strongly disagree with you. also you don't know him in real life, it's not enough to judge someone on a 50 min video
Awesome..Its much helpful.
I obviously don't know as much maths as Prof David, but isn't the illustration (I call it illustration) between relationship of arc length of circle,# and angle circular? The arc length, in standard trig or elementary calculus, is already DEFINED. Further, to arrive the the arcsin, the trigonometric derivation trick was used. So proof is circular. But it is good demonstration of geometric interpretation.
This "proof" reminds me of attempt to define addition using sets and powersets. Interesting but not useful for all practicle purpose.
I am having trouble understanding how the area element came out to be as 2*pi*y*ds. If anyone gets it do tell.
Could anyone tell me why we usually take the doubly infinitesimal number to be 0 but here it is valid to write ds^2 =/= 0?
Yeah theres an equivalent notation in the function notation two but it contains parentheses f^(2) (x) (the 2's little), yeah nothing much, just thought it was funny, but it does happen- smart people can derp moment sometimes XD.
the confusion arises from leibniz notation where d^2/dx^2 would represent the second derivative. still pretty dumb question though aha
I didn't get it about the deeper understanding about radians! :(
I was wondering if a semicircle is differentiable at x=+1. I would say no, since it becomes minus infinity.
by definition, it's one of the cases which are not differentiable.
where can i find the homework for this class?
We recommend you look at the OCW Scholar version of this course: ocw.mit.edu/courses/mathematics/18-01sc-single-variable-calculus-fall-2010. It has problems sets with solutions, so you can check your work. Best wishes on your studies!
here you go down to problem set and find which task were given to each lecture:
ocw.mit.edu/courses/18-01-single-variable-calculus-fall-2006/pages/assignments/
and here you find homework with solutions(as a bonus there are supplementary notes):
math.mit.edu/~jorloff/suppnotes/suppnotes01-01a/index-01A.html
"Is f ' (x) squared the same as f "(x)?" asks an MIT student.
y= f'(x);
y^2 = dy/dx
y = -1/x + c
I think she got confused with what prof Miller told in lecture 4 when he said that some people use crazy notations for high order derivatives.
It's awesome
I agree. Some people don't need to be an ass.
do you mean d2/d^2x?
W. O. W. Nuff said.
no
7:15 affirmative action and quotas yay!
Or a student who is learning calculus in a calculus class. Not everyone learns a subject before taking a course on that subject.
you would think MIT students would learn this in highschool
If you know anything about the university system it doesn't matter if you got a 5 on the AP exam or learned it in middle school, you still have to take it as a lower div, no exceptions. James Rockford
Hannah At MIT you can receive credit for 18.01 if you score high enough on the AP exam. Here are the details: math.mit.edu/academics/undergrad/first/index.php
i must say some guys ask really stupid questions. i felt like the professor having hard time not to say that.
It made me realize that I'm smarter than 1 MIT student - for a minute, anyway.
Am I the only one who doesn't seem think mr jerison isn't a good teacher? I mean compared to the brilliant herbert gross and christine breiner he seems to not be able to connect with us students and get what might be difficult or need more to students. In one of the lectures he couldn't even understand that the student who asked a question had a problem with negative numbers n that's the freakin basics .. PS I totally get this a purely subjective thing.