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PROFESSOR: Hi. Well, I hope you're ready for second derivatives. We don't go higher than that in many problems, but the second derivative is an important-- the derivative of the derivative is an important thing to know, especially in problems with maximum and minimum, which is the big application of derivatives, to locate a maximum or a minimum, and to decide which one it is. And I can tell you right away, locating a maximum, minimum, is the first derivative's job. The first derivative is 0. If I have a maximum or a minimum, and we'll have pictures, somewhere in the middle of my function I'll recognize by derivative equals 0. Slope equals 0, that the function is leveling off, either bending down or bending up, maximum or minimum. OK, and it's the second derivative that tells me which it is. The second derivative tells me the bending of the graph. OK, so we now will have three generations. The big picture of calculus started with two functions: the ...

PROFESSOR: Well, I hope you appreciate that we have inducted you into some real magic, the magic of building languages, really building new languages. What have we looked at? We've looked at an Escher picture language: this language invented by Peter Henderson. We looked at digital logic language. Let's see. We've looked at the query language. And the thing you should realize is, even though these were toy examples, they really are the kernels of really useful things. So, for instance, the Escher picture language was taken by Henry Wu, who's a student at MIT, and developed into a real language for laying out PC boards based just on extending those structures. And the digital logic language, Jerry mentioned when he showed it to you, was really extended to be used as the basis for a simulator that was used to design a real computer. And the query language, of course, is kind of the germ of prologue. So we built all of these languages, they're all based o...

PROFESSOR: Well, I hope you appreciate that we have inducted you into some real magic, the magic of building languages, really building new languages. What have we looked at? We've looked at an Escher picture language: this language invented by Peter Henderson. We looked at digital logic language. Let's see. We've looked at the query language. And the thing you should realize is, even though these were toy examples, they really are the kernels of really useful things. So, for instance, the Escher picture language was taken by Henry Wu, who's a student at MIT, and developed into a real language for laying out PC boards based just on extending those structures. And the digital logic language, Jerry mentioned when he showed it to you, was really extended to be used as the basis for a simulator that was used to design a real computer. And the query language, of course, is kind of the germ of prologue. So we built all of these languages, they're all based o...