ode_dreamin_ch1_5-02-07_rev20110510tue[2] - ODE DREAMIN...

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ODE DREAMIN’ CHAPTER 1 OPENING REMARKS (5-02-07) by Doug Jones ode_dreamin_ch1_5-02-07[1].doc Page 1 of 2 50 dy y dx  (1.1) is a differential equation , because it is an equation with a derivative in it ! It’s actually an ordinary differential equation (that’s where “ODE” comes from). A solution to (1.1) is a function,   fx , with the property that if I “plug it into” the LHS (left - hand side) of (1.1) and “ do the math,” it simplifies down to the RHS (right -hand side), which in this problem is zero. Many times, especially in the early- going, I’ll write or   x instead of f or () for a solution, so don’t let this notation surprise you. My claim, now, is that   5 x xe (1.2) is a solution to (1.2). How did I come up with that function? That’s one big question ! That’s the meat of this course, and we’ll partially answer that question during the next 10 weeks. However, the short answer is that we use the “McBee Method” – we ask it! That is, we ask the differential equation, “What is your solution?” And then we listen very carefully. Many times it will answer us!
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This note was uploaded on 12/30/2011 for the course MAP 2302 taught by Professor Jones during the Summer '11 term at Tallahassee Community College.

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ode_dreamin_ch1_5-02-07_rev20110510tue[2] - ODE DREAMIN...

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