The Exponential Function
Professor Strang explains how the "magic number e" connects to ordinary things like the interest on a bank account. The graph of y = e^x has the special ...
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PROFESSOR: Hi. Well, this is exponential day, the day for the function that only calculus could create, y is e to the x. And it couldn't have come from algebra because, however we approach e to the x, there's some limiting step. Something goes to 0. Something goes to infinity. I've got different ways to reach e to the x, but all of them involve that limiting process, which we haven't discussed in full. Let me come back at a later time to the whole theory, discussion of limits and just go forward here with this highly important function. And I'd like to start with its most important property, which is-- so it has this remarkable property that its slope is equal to itself. That's what is special about e to the x. The slope is equal to the function. Now, ...
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PROFESSOR: Hi. Well, this is exponential day, the day for the function that only calculus could create, y is e to the x. And it couldn't have come from algebra because, however we approach e to the x, there's some limiting step. Something goes to 0. Something goes to infinity. I've got different ways to reach e to the x, but all of them involve that limiting process, which we haven't discussed in full. Let me come back at a later time to the whole theory, discussion of limits and just go forward here with this highly important function. And I'd like to start with its most important property, which is-- so it has this remarkable property that its slope is equal to itself. That's what is special about e to the x. The slope is equal to the function. Now, ...
