The first example [Transparancy 1] could be solved by inspection, without actually having to calculate any integrals. This is, of course, the most pleasant kind of problem to solve! (Look for one on your final exam.)
Flux integrals were talked about. We referred back to the definition of flux in Lecture 14.
An application from Thermodynamics was presented [Transparancy 2], showing how to calcuate the heat flowing through a surface. This expression was obtained from integrating Fourier's Law. A specific example was given, involving an insulated hot water pipe [Transparancies 2 and 3]. An expression was found for the steady-state temperature of the insulator as a function of distance.
The next application was from Electrostatics, and involved Gauss's Law [Transparancy 4]. An example was given, in which Gauss's Law was used to calculate the electric field of an infinite sheet [Transparancies 4 and 5]. It turns out that this electric field is independent of the distance from the sheet.
(You will find two versions -- a "screen" version, which is 400 pixels wide and a corresponding number of pixels long, at a resolution of 100 by 100 dots per inch, and a "print" version, which is generally between 8 and 8.5 inches wide and up to 11 inches long, also at a resolution of 100 by 100 dots per inch. The screen versions generally have a file size of between 60 and 75 K, which downloads reltively quickly. The print versions generally have a file size of between 170 and 225 K, which takes a bit longer to download.)
