Calculus 3 Lecture 14.7: TRIPLE Integrals Over Regions with CYLINDRICAL or SPHERICAL Coord.

Calculus 3 Lecture 14.7: TRIPLE Integrals Over Regions with CYLINDRICAL or SPHERICAL Coord: How (and why) to change regions into Cylindrical or Spherical Coordinates and perform the resultant triple integral. Also discussed are examples of Center of Mass and Moments of Inertia.

[seenathgooding]

Spherical Co-ordinates start @2:08:30 if anyone needed to know like I did.

[junior]

7:00 Ex 1
26:38 Ex 2 region bound by two functions (Good example to figure which is small or bigger function)
42:05 Ex 3 C.O.M
1:22:10 Ex 4 C.O.M
1:43:30 Ex 5 Moments of inertia problem
2:08:00 Intro spherical coordinates
2:19:00 Ex 6 Using spherical coordinates. p-simple instead of Z-simple.

Note: p is ALWAYS positive. The angle is ALWAYS between 0 and pi. Thetha is ALWAYS 0 to 2pi.

2:36:20 Ex 7 spherical coordinates
2:50:00 Ex 8 Bound by two functions
3:02:00 Ex 9

[josue]

Professor Leonard: “Head nod if you’re ok with that”
Me at home: *nods*

[justinallred]

skip to 1:10:17 for a blessing from Professor Leonard

[milessanders]

This man brought me back from a 56 to a 90. You know a person is special when they can revive your confidence in the face of something seemingly impossible. Forever grateful to you!

[albertnoven]

Stopped going to class. One video from Professor Leonard is worth one hundred of those lectures I get from my college. We live in wonderful times when lectures like this are accessible to so many people all around the world.

[keldonchase]

8:00 - Example 1
27:14 - Example 2
42:00 - Example 3
1:22:49 - Example 4
1:45:42 - Example 5
2:19:31 - Example 6
2:37:04 - Example 7
2:51:16 - Example 8
3:02:43 - Example 9

[KingMiiidas]

Reminds me of a Calc professor I had at Mesa Community; 3 hour classes taught by a professor who was both passionate and thorough with a conviction to give us an education worth the cost of tuition. He had a 2 hour drive to campus but showed up to class every day with a smile on his face. Hardest class I've ever taken but also the most satisfying. Glad to see there's more professors like him out there.

[sukainahasan]

These videos are so incredibly helpful, my entire calc class here in Pakistan relies on them to get through exams.
I want to send you a big bouquet of flowers and a packet of tight t shirts to say thanks!!!

[aaronguerrero]

Whats Up Professor Leonard!
I just want to thank you sincerely . Its crazy to think that my whole Calculus journey was altered by a man I will probably never meet. You've allowed to me to actually understand the concepts, and now in multivariable, begin to tap into my creative side of math. Absolutely TREMENDOUS! Can't thank you enough... I can only live with your passion for math to truly show my appreciation. Cheers Prof. L. Hope everything is well!

[globalevents]

This is my final section of Calculus 3! Thank you for the work, and dedication you put in to these videos. As you know, you have helped thousands of students achieve mathematical greatness, and every one of us will say that you are the best to do it. <3

[graceless]

Literally got more from you than my own professor. He just doesn't seem to get as excited as you. He also doesn't tell us these little tricks. Now it may be because we're online and it's covid season and my lectures are only 50 minutes but this has been so helpful and makes me feel less dumb. Thank you!

[lukedimitriades]

You help visualize and understand when most teachers just write down the formulas and do examples. And for that I applaud you sir

[ahmedrateb]

at 3:12:09, the correct answer for the volume is 8pi/3 not pi/3, this can be proven by the fact that the desired object is a true cone with a circle base at z=2 with a radius of 2 and the apex of the cone is at the origin so the height of the cone is 2. using the formula for the volume of the cone v=1/3*pi*r^2*h, you get 8pi'3

[obadam.]

Is it just me who got 8π/3 instead of π/3 @ 3:12:06

[pastelshoal]

This is my last week of calc 3 and god do I wish I just skipped out on lectures and watched these. The examples he does are not nearly as complex as what we do at my uni, but the way the material is presented is super informative and really gives me an idea of how to approach these problems and what they mean. Thank you!!

[Omegas]

When Prof. Leonard is the savior of your grade.

[cesargodoy]

I passed calc 3 in the summer (1 month) and it was all thanks to professor leonard :D

[THE_CRYPT_CLLECTR]

I'm over here nodding and raising my hands like I am physically your classroom haha =P... thanks for the knowledge, Professor! Super appreciated!

[cubby]

I am setting at an 86% in my Multivariable Calculus class. Hopefully, I can maintain that or maybe go higher. This has been a really tough class. The videos are really helpful and I wouldn't be doing this well if it wasn't for them. Thank you very much.