Lec 26: Spherical coordinates; surface area | MIT 18.02 Multivariable Calculus, Fall 2007

[@moeezart835]

I never thought I would understand spherical coordinates! This guy makes it easssyyyy

[@sandar15]

Mr. Denis made me able to pass my final Multivariable Calculus exam... He's the boss!!!

[@kittycat1768]

"How many of you have seen spherical coordinates before?" *Half the class raise their hands* "I see that's not very many." - The legendary Auroux, 2007

[@deeptochatterjee532]

Shabit Hassan Actually, it was only at least 1/4 of them

[@alexhudson502]

Lecture 1: Dot Product Lecture 2: Determinants Lecture 3: Matrices Lecture 4: Square Systems Lecture 5: Parametric Equations Lecture 6: Kepler's Second Law Lecture 7: Exam Review (goes over practice exam 1a at 24 min 40 seconds) Lecture 8: Partial Derivatives Lecture 9: Max-Min and Least Squares Lecture 10: Second Derivative Test Lecture 11: Chain Rule Lecture 12: Gradient Lecture 13: Lagrange Multipliers Lecture 14: Non-Independent Variables Lecture 15: Partial Differential Equations Lecture 16: Double Integrals Lecture 17: Polar Coordinates Lecture 18: Change of Variables Lecture 19: Vector Fields Lecture 20: Path Independence Lecture 21: Gradient Fields Lecture 22: Green's Theorem Lecture 23: Flux Lecture 24: Simply Connected Regions Lecture 25: Triple Integrals Lecture 26: Spherical Coordinates Lecture 27: Vector Fields in 3D Lecture 28: Divergence Theorem Lecture 29: Divergence Theorem (cont.) Lecture 30: Line Integrals Lecture 31: Stokes' Theorem Lecture 32: Stokes' Theorem (cont.) Lecture 33: Maxwell's Equations Lecture 34: Final Review Lecture 35: Final Review (cont.)

[@gamalmostafa5681]

god bless you.

[@navs8603]

The ending of this lecture to reference Black hole was mind blowing !!!

[@SultanInStem-t3i]

these lectures are the best. Only he bothered to explain how to obtain dv. Bravo!

[@hongyuzhang5631]

I have to say: his explanation is so god damn clear!

[@pabloastoreca8726]

A lecture without Aurox's magical erasings 😔

[@xTheUndeadzx]

His lecture is so clear!

[@hamsinideshmukh]

refer to the spherical coorinate system taught in a best way eva till 13:57

[@JAGAMTec]

I wish he was my teacher, what a nice class. excelent

[@Dra60oN]

At 32:04 there was actually a question, someone actually raised a hand up.

[@dtalmood]

Oh my god literally this guy is smart, my professor just throws information on the white board with no explanation

[@denisespinoza2597]

Thank you Professor Denis Auroux

[@yunlongosterxia2768]

great professor. that is why mit is mit. --comment from a freshman from cuhksz

[@priyanshubansal6776]

thanks to camera man and mit who put his time in making this lecture

[@jankipatel2392]

Nice ..... Very nice explaination sir.... Brilliant

[@topilinkala1594]

Spherical cap of radius r and height h: pi*(h^2)*(3r-h)/3. Radius r is the radius of the sphere, not of the cap. Here r=1 and h=1-1/sqrt(2) which gives the answer. My HP-50g gives it as (8-5*sqrt(2))*pi/12 which is the same that was on the lecture. Personally I don't like roots in denominators in answers.

[@Originalimoc]

This lecture literally get me addicted 😁

[@legacies9041]

@ 38:30 it is technically India and not China! India is right on the other side of Boston

[@joebrinson5040]

Thank you MIT

[@the_eternal_student]

In the first triple integral problem, what does he mean the entire z is used? the shaded portion does not form a vertical circle.

[@toastertastic]

I won't pay attention in class, but I'll watch 3 of these in a row and actually make an effort to learn.

[@bobkameron]

great lecture!

[@belthazor000]

i wish to have a lecture like that in my university..

[@LambdaJuuichi]

Damn this guy is amazing D: he explains really good.

[@not_amanullah]

Thanks ❤🤍

[@lindsaywaterman2010]

Since for pi/4 it is part of a sphere, shouldn't the top be curve like the icecream on the top of the cone?

[@sachinruffneck]

fantastic lecturer

[@ormazar9017]

What is the form of the line element on the surface of the sphere? Can we transform it to Cartesian coordinates?

[@not_amanullah]

This is helpful ❤️🤍

[@edwarddi3833]

this guy is amazing!

[@jankipatel2392]

Lecture on higher order differential equations are available??????

[@douglaslee7034]

Yes

[@ycz6]

Is there no interactive transcript on this one? I'm not seeing it...

[@timleungck]

whats the point for me to paying for my host uni.. I cant understand what they were saying and i have to come up to attend lecture from other uni

[@memojedi]

this guy is great!!!

[@xinyuli9423]

50:49 "If the earth collapsed to a black hole at the center of the earth with the same mass, you wouldn't notice the difference immediately" LMAO

[@kemae]

Actually, if the magnetic field is maintained, and you can walk on the shell surface of the earth as usual, there'd be no significant difference

[@SPRINGGREEN813]

@@kemae Can you explain how?

[@ashreesatapathy4836]

why is phi limited from 0 to 180

[@abdulrahmant8095]

Because in z-axis thing are diffirent than x and y axiis. In z-axis you go with your angle in both dirextion at the same time so 90 degrees in z-axis is like 180 degrees in x-axis & y-axis so 1 rev. will be equal to 180 degrees not 360 I hope that answered your question..

[@romshamangla8159]

wonderful!

[@swaggerchegger98]

The Einstein field equations state that the superpostion principle will not work on gravitational fields. So using the formulas at ~41min wouldn't take relativity into consideration :)

[@clapika999]

in the script i think it should have meant "secant"?

[@Originalimoc]

Toan Ngo Didn't use caption. Nice catch.

[@booitsivilly]

This lecture video is amazing!

[@anilthapa6290]

can anybody explain why he place the solid in z plane with 0 x and 0 y, it is the plane where direction of force is directed.

[@mauriciobarda]

Because of the simmetry, the force exerted by all the particles in the direction of positive and negative x and y cancel out each other, and only the net force exerted in the Z direction is doing an atraction to the mass little-m.

[@audreydaleski1067]

Unit circle, p=1.

[@봄여율-u9f]

24:41

[@antoniomranz]

Good explanation but the convention for letters assigned to angles (phi, theta) is different to the more usual one . Theta, usually is used for the angle from z-axis

[@anandrukh]

thank you SIR

[@Muleslover]

0:52 3D

[@ЧингисханЧимбаев]

Thank you verhhy much))))

[@imegatrone]

I Really Like The Video From Your Spherical coordinates surface area.

[@deeptochatterjee532]

Why, on every video?

[@debunker1905]

this is entertaining

[@jameshopkins3541]

NI SIQUIERA SIRVE PARA CALCULAR EL VOLUMEN DE LA ESFERA MENOS PARA PROBLEMAS MAS COMPLICADOS.

[@shawnnyhus2193]

note to self -a

[@kavoos1000]

plane or plain? :))))))) just kidding he is the best and i am thankfull for what he is teaching so bright and clear..

[@audreydaleski1067]

Cospiover4=cospiover4

[@flowewritharoma]

cool mit

[@daniel_liu_it]

这是日本友人么😏

[@yoadknux]

hmm, attrachon

[@jojoblazer777]

I totally thought phi = pi/4 was a plane heh. . . Woops.

[@daniel_liu_it]

Why did he take the example of China rather than French 😂

[@yagol777]

Lol. Me too

[@deeptochatterjee532]

Damn, his jokes are just not landing.