Mathematics - Multivariable Calculus - Lecture 22

Multivariable Calculus
Instructor: Edward Frenkel

Course website: http://math.berkeley.edu/~frenkel

Category:

Education

Tags:

• uc
• berkeley
• ucberkeley
• webcast.berkeley
• cal
• Fall
• 2009
• mathematics
• calculus
• multivariable

[SvenJoelStefan]

thank you for an excellent course! Great job Frenkel!

[fortunaaudacesiuvat]

Amazing lecture

[velvetfish1]

@humanbeing61

I think he means that the plane, although a 2-dimensional object, can occupy an orientation such that any point on the plane must be represented by three independent numbers, that is an x, a y, and a z component. This would typically be the case any time the plane is not parallel to the xy, xz, or yz planes.

[velvetfish1]

Another issue that wasn't discussed was that at the top of the canted membrane, what happens when the space available in the normal direction is less than the length of n (ie the boundary of the pipe and outside the domain would seem to impede flow). Consequently, I found this example more confusing than helpful in understanding, what I believe was a central focus of the lecture, to demonstrate how to calculate the flux across the membrane in a direction normal to the membrane.

[velvetfish1]

Of the lectures so far, I found that Prof. Frenkel's usually clear style seemed to break down, or perhaps at least my understanding of the presentation did. In the case of the flow through the canted membrane on a pipe, I did not understand how the delta S component did not change, since the long axis of the pipe had become stretched (major axis of the ellipse, where as the minor axis stayed the same, making for a greater surface area.

[humanbeing61]

Dear Mr. Frenkel you should explain your examples more and more. It is not enough at all what you did. 10x

[humanbeing61]

i am just wondering what do you mean by plane in three dimensional space. there is a mistake because it is more easier to deal with plane as two dimensional space.

[tucense]

I need a few more examples..

[KartKing4ever]

O.O...................to be precise lol asianz