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PROFESSOR: Find our final solution, we just have to match the equations. So Psi continues at x equals a. And what do we have? Well from two, you have cosine of ka. And from four you would have a equals e to the minus ka. This is the value of this-- so the interior solution at x equals a must match the value of the exterior solution of k equals a. Psi prime must be continuous at x equals a as well. Well what is the derivative of this function? It's minus the sine of this. So it's minus k sine of kx, that becomes ka, is equal to the derivative of that one, which is minus Kappa A e to that minus Kappa little a. Two equations, and how many unknowns? Well there's A and some information about Kappa and k. And the easiest way to eliminate that is to divide them. So you divide the bottom equation by this equation. So what do we get? Divide the bottom by the top. Minus k and and the minuses cancel, we can cancel those minus signs and you get k tan ka is equal to Kappa....

It's not unusual to find that an application is organized as multiple communicating processes. What's the advantage of using multiple processes instead of just a single process? Many applications exhibit concurrency, i.e., some of the required computations can be performed in parallel. For example, video compression algorithms represent each video frame as an array of 8-pixel by 8-pixel macroblocks. Each macroblock is individually compressed by converting the 64 intensity and color values from the spatial domain to the frequency domain and then quantizing and Huffman encoding the frequency coefficients. If you're using a multi-core processor to do the compression, you can perform the macroblock compressions concurrently. Applications like video games are naturally divided into the "front-end" user interface and "back-end" simulation and rendering engines. Inputs from the user arrive asynchronously with respect to the simulation and it's...