Thanks M.I.T. for making these lectures available to us. It is enlightening to see such talented teachers teach. It is mentally stimulating to think about these concepts. It is satisfying to learn.
The thing I love about math, is that it is totally independent of the world. Although mathematics does have applicaitons in many aspects of reality, it doesnt necessarily say anything about it. So math in itself is really formless, and a playground for people to tinker around in. Where everyone can enjoy and express new ideas.
@MikeDunn The names aren't fancy, they're explanatory. Single variable calculus is just what the name says it is, calculus involving only one variable. I'm sure you can figure out the other one. Calc 1 or calc 2 don't tell you what the subject is actually about.
You have to understand the point of reducing the integral, which is ofcourse to solve it. If you reduce to n = 0, you have the integral of e^x which is e^x. Using negative values of n makes the problem no easier. In other words, can you integrate e^x/x directly?
Well the integral of a y = 2πex is actually a line with slope λ = 2πe . Also it evaluates y = 0 for x = 0 & y= 2πe for x = 1. Clearly the integral from 0 to 1 of this function will be just the area of a triangle. I hope i helped :D .
Fact 1:- 2 * pi * e = circumference (top cylinder) and 2 * pi * e * x = volume (top of cylinder). (note you will need to subtract the bottom part from the top afterwards to complete the integral) Fact 2:- e is the radius or height and x is the base which when equal to 1 (lower limit e ^ 0) by Pythagoras theorem; solving the integral is the same as the area of a right-angle triangle and equal to 1/2 * base x height, scaled by a factor of two since the shell has a right and a left triangle when swept around.
@MikeDunn That's good and all for people in the US, but you must realise that as an online thing it will be accessed from people outside the US such as myself to who "calc 1" has no meaning.
@ 49:17 when he writes (-1) is actually correct. Why's it +1 when -e0 is -(1) seeing as e0 is 1? Great lecture though, seriously interesting. Makes me kind of want to do Mathematics in University, and I know this is just one lecture, but it doesn't seem to be as hard as I thought it would be. I guess it's just the fact that most people hate Math and find it super difficult, but I found this lecture enjoyable! Lol, sometimes can't believe I'm one to love Maths...
20:30 Where is the dx comes from? from d(u*v)/dx=u*dv/dx+v*du/dx get d(u*v)=u*dv+v*du, the integrate both side, ∫1d(u*v)=∫u*dv+∫v*du, finally we get u*v=∫u*dv+∫v*du
THIS PROFEESOR OF MATHEMATICS IS NICE I WANT TO GIVE HIM TIPS BEING A STUDENT PLEASE SIR ALWAYS ATTEMPT THOSE QUESTIONS WHICH YOU SOLVE ON BLACK BOARD OTHERWISE DON'T ATTEMPT I LIKED YOUR WAY OF TEACHING BUT YOU WILL GET SOME TIME TO BE PROFESSOR WALTER LEWIN HE WAS LEGEND YOU SHOULD SEE HIS LECTURES TO TEACH STUDENTS AS AN EXAMPLE I LOVE TO BE AN AUSTRONAUT TO WATCH YOUR PROGRAMMES
What does calc 1 mean? What does it tell you about the course? What I do know is that single variable calculus means we are integrating and diffrentraiting with respect to one variable. Single/Multi variable is more descriptive and actually describes what you learn.
Thanks M.I.T. for making these lectures available to us. It is enlightening to see such talented teachers teach. It is mentally stimulating to think about these concepts. It is satisfying to learn.
The thing I love about math, is that it is totally independent of the world. Although mathematics does have applicaitons in many aspects of reality, it doesnt necessarily say anything about it. So math in itself is really formless, and a playground for people to tinker around in. Where everyone can enjoy and express new ideas.
Hi everybody! I have eventually reached here!🎉 Thanks MIT for giving such opportunity to listen to the wonderful lessons!
Partial fractions starts at 0:45 until 18:20, which is also important.
woohoo integration by parts...how exciting...reminds me of the lecture I had a week ago!
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
Integration using the Reduction Formula starts at 27:45
16:40 you can also use the special integration formula
1/a * arctan(u/a) at that point
Dang, this professor does every portion of the problem so quick that it would take me a little while to do each portion.
@MikeDunn The names aren't fancy, they're explanatory. Single variable calculus is just what the name says it is, calculus involving only one variable. I'm sure you can figure out the other one. Calc 1 or calc 2 don't tell you what the subject is actually about.
Thanks ❤️🤍
Hello! Why is Professor stop reducing n to zero (30:22) if actually we can continue reducing to negative numbers, e.g. n=-1,-2,-3.
You have to understand the point of reducing the integral, which is ofcourse to solve it. If you reduce to n = 0, you have the integral of e^x which is e^x. Using negative values of n makes the problem no easier. In other words, can you integrate e^x/x directly?
This is exactly what I'm doing in class!
The G(n-1) function IS the integral of x^(n-1)*e^x.
At 47:43 how is the integral of 2pi * ex * dx equal to the area of a triangle?
Well the integral of a y = 2πex is actually a line with slope λ = 2πe . Also it evaluates y = 0 for x = 0 & y= 2πe for x = 1. Clearly the integral from 0 to 1 of this function will be just the area of a triangle. I hope i helped :D .
Fact 1:-
2 * pi * e = circumference (top cylinder) and 2 * pi * e * x = volume (top of cylinder).
(note you will need to subtract the bottom part from the top afterwards to complete the integral)
Fact 2:-
e is the radius or height and x is the base which when equal to 1 (lower limit e ^ 0) by Pythagoras theorem; solving the integral is the same as the area of a right-angle triangle and equal to 1/2 * base x height, scaled by a factor of two since the shell has a right and a left triangle when swept around.
@@hyungjoonpark83 You're welcome :) .
I had to look up the word recalcitrant
45:55 - shouldn't it be +2 (-2(-1) instead of -2?
No, -2 is right because [e*(1)^2-0-0+2*（0-1）]=e-2
thank you
integration of 1/x^2+2x+3 is =1/2^1/2 tan inverse of x+1/2^1/2
last lecture . awesome lecture.
I Really Like The Video Integration by parts, reduction formulae From Your
@MikeDunn That's good and all for people in the US, but you must realise that as an online thing it will be accessed from people outside the US such as myself to who "calc 1" has no meaning.
cal 1 is everything upto multivariable cal starting after alebra and trig from limits and continuity. SO its just a logistic of how its organized sir.
@ 49:17 when he writes (-1) is actually correct. Why's it +1 when -e0 is -(1) seeing as e0 is 1? Great lecture though, seriously interesting. Makes me kind of want to do Mathematics in University, and I know this is just one lecture, but it doesn't seem to be as hard as I thought it would be. I guess it's just the fact that most people hate Math and find it super difficult, but I found this lecture enjoyable! Lol, sometimes can't believe I'm one to love Maths...
I might be a late but +1 is correct because it's 0 - (-e^0) = e^0 = 1
The mic noise and hiss is distracting in this lecture, I hope someone could fix it ..
I am Sachin gothwal Mathematics of India very nice sir 🎉🎉
How come at 45:55 when -2*(-y) it's -2 instead of +2
+Thomas Lauritson Because he evaluates the function at e - the function evaluated at 1. [e] - [+2] = [e-2]
yes
F. how can every single lec can be quality guaranteed?
@ 50:18
Now I see, guess I made the same mistake. It is -1.
6:57 "aright" :D
ooh am i the first one in 2020 quarantine to reach here ;P
20:30 Where is the dx comes from? from d(u*v)/dx=u*dv/dx+v*du/dx get d(u*v)=u*dv+v*du, the integrate both side, ∫1d(u*v)=∫u*dv+∫v*du, finally we get u*v=∫u*dv+∫v*du
@markkerollos I know that, chief. But the rest of the country calls it "Calc 1" or "Calc 2", and people pretty much know what it is.
cool!
@nomchews I don't think you're qualified to be taking shots at an MIT professor.
ok... so mcdonalds it is
why this lecture is not being downloaded on Idm?
ask idm maybe?
the crackling in this video is annoying
IKR
The one guy who disliked....who r u??
THIS PROFEESOR OF MATHEMATICS IS NICE
I WANT TO GIVE HIM TIPS BEING A STUDENT
PLEASE SIR ALWAYS ATTEMPT THOSE QUESTIONS WHICH YOU SOLVE ON BLACK BOARD
OTHERWISE DON'T ATTEMPT
I LIKED YOUR WAY OF TEACHING BUT YOU WILL GET SOME TIME TO BE PROFESSOR WALTER LEWIN
HE WAS LEGEND
YOU SHOULD SEE HIS LECTURES TO TEACH STUDENTS AS AN EXAMPLE
I LOVE TO BE AN AUSTRONAUT TO WATCH YOUR PROGRAMMES
Single Variable Calculus? Multi-Variable Calculus? Can't we just say Calc 1, Calc 2, or Calc 3 instead of coming up with fancy names?
What does calc 1 mean? What does it tell you about the course? What I do know is that single variable calculus means we are integrating and diffrentraiting with respect to one variable. Single/Multi variable is more descriptive and actually describes what you learn.
Oh wait... this was 13 years ago 🤣🤣
@@TonyG-n1m That's ok. There's no time limit on a Reply.