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

Lecture 26: Spherical coordinates; surface area.
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[@moeezart835]

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

[@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.

[@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

[@navs8603]

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

[@pabloastoreca8726]

A lecture without Aurox's magical erasings 😔

[@JAGAMTec]

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

[@hongyuzhang5631]

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

[@Dra60oN]

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

[@xTheUndeadzx]

His lecture is so clear!

[@hamsinideshmukh]

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

[@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 :)

[@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.

[@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

[@jankipatel2392]

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

[@belthazor000]

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

[@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

[@LambdaJuuichi]

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

[@legacies9041]

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

[@bobkameron]

great lecture!

[@sachinruffneck]

fantastic lecturer

[@joebrinson5040]

Thank you MIT

[@Originalimoc]

This lecture literally get me addicted 😁

[@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

[@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.

[@edwarddi3833]

this guy is amazing!

[@jankipatel2392]

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

[@douglaslee7034]

Yes

[@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?

[@romshamangla8159]

wonderful!

[@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..

[@clapika999]

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

[@Originalimoc]

Toan Ngo Didn't use caption. Nice catch.

[@not_amanullah]

Thanks ❤🤍

[@ormazar9017]

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

[@memojedi]

this guy is great!!!

[@audreydaleski1067]

Unit circle, p=1.

[@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

[@ycz6]

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

[@not_amanullah]

This is helpful ❤️🤍

[@anandrukh]

thank you SIR

[@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.

[@booitsivilly]

This lecture video is amazing!

[@user-ff8nw4wl9h]

Thank you verhhy much))))

[@imegatrone]

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

[@deeptochatterjee532]

Why, on every video?

[@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?

[@audreydaleski1067]

Cospiover4=cospiover4

[@user-rm6rb3tp5u]

24:41

[@debunker1905]

this is entertaining

[@shawnnyhus2193]

note to self -a

[@jameshopkins3541]

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

[@kavoos1000]

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

[@yoadknux]

hmm, attrachon

[@flowewritharoma]

cool mit

[@daniel_liu_it]

这是日本友人么😏

[@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 😂

[@deeptochatterjee532]

Damn, his jokes are just not landing.

[@yagol777]

Lol. Me too