I also want to point out something that most people would forget: the cameraman is very professional, always got the timing correct. It's really not a trivial work! The cameraman has to listen thoroughout the lecture and keep focusing on the right thing. A big thank you to the camera man as well!
5/32 is the probability of x-1/2 (5/24)/(4/3) are the areas Probability is so more interesting that the integration formulas (what I'm doing at school)
THANK YOU! I tried to calculate it to make sure I was getting everything so far and couldn't figure out what went wrong EDIT : Oops, they address it later in the lecture, patience really is a virtue :)
interesting, testing -1 < x < 1/2 probability is 27/32. Sum of probalities for x range -1 < x < 1/2 and 1/2 < x < 1 27/32 + 5/32 is 1. It is proof of probality range - 1 up to 1.
41:42 : "it turns out to be 5/18, we won't do it"..... yeah I think they should have done it XD. I also think it's (5/24)/(4/3), which makes (5/32) as the final answer.
Shouldn't the small amount of heat required to raise the temperature of water be something like dQ= mcdT, where m=density*volume and c is the specific heat capacity of water?? Why does he just write energy = temp*volume?
-I was wondering the same thing. Maybe fictional laws of thermodynamics for the sake of understanding calculus?- -EDIT: Nvm, I got it. The integral computes the total rise in temperature. And he just measures how much energy it takes to rise the temperature bu that much.- EDIT AGAIN: I'm Jon Snow.
Still have a question for examples 2 and 3. Are the integral wrt x in ex2 and integral wrt theta in ex3 the area of the semi-sphere? why they are not equal？
Not the "total energy" because the water already had energy at the beginning. It is the total energy needed to raise the temperature to the requested point.
Why does the method for Ex 3 have dtheta, it makes sense to me when you find the integral wrt dx you multiply the function by dx to form a series of rectangles, but why are we multiplying the height given by sintheta by the angle?
sin theta = opp/ hyp , where opp is the height and hyp is r=1. So height = sin theta. And if you need to find the avg of height, you can integral sin theta d theta then multiply by 1/(b-a)
He added up temperatures from all hights of the volume BUT then he multiplied each of these temperatures with the infinitesimal volume that has that temperature. So temperatures that a larger volume have counts more
I am watching this lectures, I understand them, but when I go to solve the Psets, seems I dont know shit.... anyone having the same issue with the Psets?
I don´t think ppl will respond to this as most of the comments are from years ago, but anyway. I didn´t understand the "conversion factors" when he got 40pi to be 125(1000) kcal. I´m studying for economics so it would be nice to learn some more science as well as calculus :)
That's dimentional analysis bro... Maybe if look for that kind of convertion in google you'll find out. But I can tell you it won't be hard to understand
In the formula Q=density×volume×specific heat×temp difference....he used density as 1g/cm^3, volume in m^3(because he choose height and radius in m), specific heat as 1cal/g degree Celsius, and temp difference as degree Celsius...thus doing calculation we get heat in units of (cal m^3)/cm^3.......((g×m^3×cal×degree Celsius)/g×cm^3×degree Celsius)... That is final answer is 40π cal m^3/cm^3 which equal 40π×10^6 cal and hence 40π×1000 kcal which approximate to 125×1000kcal
I also want to point out something that most people would forget: the cameraman is very professional, always got the timing correct. It's really not a trivial work! The cameraman has to listen thoroughout the lecture and keep focusing on the right thing. A big thank you to the camera man as well!
I have really enjoyed Dr. Jerison's lectures. His sense of humor is wicked.
Thank you MIT for making this marvel an open courseware !!!
its amazing that he can do the lesson in a fun and creative way with real problems and great humor..awesome lecture again
Great guy, these materials are very informative and provide a great insight
to share this quality of things is incredible
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
20:28 When you raise your hand but your professor pretends you are invisible.
5/32 is the probability of x-1/2
(5/24)/(4/3) are the areas
Probability is so more interesting that the integration formulas (what I'm doing at school)
THANK YOU! I tried to calculate it to make sure I was getting everything so far and couldn't figure out what went wrong
EDIT : Oops, they address it later in the lecture, patience really is a virtue :)
Great lecture and professor!
14:24 This clarifies the difference between Examples 2 and 3. Just shows how unintuitive some probability problems can be.
Brilliant lecture, as always
Yeah the result at 41:40 should be 5/32 or 15,6 %.
'I was the little brother' lol, great lecture as always
Spoilers!
Good Job Professor
interesting, testing -1 < x < 1/2 probability is 27/32.
Sum of probalities for x range -1 < x < 1/2 and 1/2 < x < 1
27/32 + 5/32 is 1. It is proof of probality range - 1 up to 1.
dang he even covers part of continuous distribution what an amazing lecture.
Oh there is someone taking the lectures with me. The comments are so old i thought I'm alone. Anyways HI pal.
@@jpnewshazaribagh8130 You're not only the one who is taking lectures in the future :D
41:42 : "it turns out to be 5/18, we won't do it"..... yeah I think they should have done it XD. I also think it's (5/24)/(4/3), which makes (5/32) as the final answer.
This is helpful ❤️🤍
Thanks 🤍❤️
Great course!
Shouldn't the small amount of heat required to raise the temperature of water be something like dQ= mcdT, where m=density*volume and c is the specific heat capacity of water?? Why does he just write energy = temp*volume?
-I was wondering the same thing. Maybe fictional laws of thermodynamics for the sake of understanding calculus?-
-EDIT: Nvm, I got it. The integral computes the total rise in temperature. And he just measures how much energy it takes to rise the temperature bu that much.-
EDIT AGAIN: I'm Jon Snow.
Because c= 1 cal/g.ºC, for the water.
And the density of the water is 1 g/ml.
Still have a question for examples 2 and 3. Are the integral wrt x in ex2 and integral wrt theta in ex3 the area of the semi-sphere? why they are not equal？
14:40 but which formula I have to use to find the centre of mass ?
T= 100 - 30 y, as y get higher T get lower.
8:00 isn't it the integration of the area of semicircle 🤔
08•48 can anyone express this integration without using geometry
thanks a lot
i was the little sister and I got a dart right between the eyes, up about a half inch. probability is 1.
the integral on the witch's cauldron example simply gives the total energy inside the cauldron right? loved this lecture!
Not the "total energy" because the water already had energy at the beginning. It is the total energy needed to raise the temperature to the requested point.
Why does the method for Ex 3 have dtheta, it makes sense to me when you find the integral wrt dx you multiply the function by dx to form a series of rectangles, but why are we multiplying the height given by sintheta by the angle?
sin theta = opp/ hyp , where opp is the height and hyp is r=1. So height = sin theta. And if you need to find the avg of height, you can integral sin theta d theta then multiply by 1/(b-a)
Why does the comparison between average height with respect to arclength gives lower value than with respect to x one?
Is the answer in the probability task 5/32 ?
yes
Yup. It is. www.wolframalpha.com/input/?i=(integral+from+1%2F2+to+1+(1-x%5E2)dx)%2F(integral+form+-1+to+1+(1-x%5E2)dx)
Thanks for posting, yeah I also got 5/32.
That's what I calculated.
anyone know how you would calculate the probability of x being greater than or equal to 1/2?
At 41:40 it should be 5/32
can someone tell me why did he integrated T and Volume ? what formula used ?
He added up temperatures from all hights of the volume BUT then he multiplied each of these temperatures with the infinitesimal volume that has that temperature. So temperatures that a larger volume have counts more
44:48 5/32
I Really Like The Video Work, average value, probability From Your
I am watching this lectures, I understand them, but when I go to solve the Psets, seems I dont know shit.... anyone having the same issue with the Psets?
what is difference between practice exam and exam on this page? ocw.mit.edu/courses/mathematics/18-01-single-variable-calculus-fall-2006/exams/
Thermodynamic
like it like it like it !!!!!!!!!!!!!!!!
The average 0 to 1 value of skin covered by awesome tattoos under David Jerison's lecture shirts is probably 1
I don´t think ppl will respond to this as most of the comments are from years ago, but anyway. I didn´t understand the "conversion factors" when he got 40pi to be 125(1000) kcal.
I´m studying for economics so it would be nice to learn some more science as well as calculus :)
He already had 40pi * 1000 kcal and 40pi is approx. 125.664 so approx. 125.......hope that helped
That's dimentional analysis bro... Maybe if look for that kind of convertion in google you'll find out. But I can tell you it won't be hard to understand
In the formula Q=density×volume×specific heat×temp difference....he used density as 1g/cm^3, volume in m^3(because he choose height and radius in m), specific heat as 1cal/g degree Celsius, and temp difference as degree Celsius...thus doing calculation we get heat in units of (cal m^3)/cm^3.......((g×m^3×cal×degree Celsius)/g×cm^3×degree Celsius)... That is final answer is 40π cal m^3/cm^3 which equal 40π×10^6 cal and hence 40π×1000 kcal which approximate to 125×1000kcal
candy bars lol