01 direction fields, existence and uniqueness of solns

01 direction fields, existence and uniqueness of solns -...

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Unformatted text preview: 18.03 Lecture #1 Sept. 9, 2009: notes I’ll try to prepare notes summarizing what I did say, and sometimes also things that I should have said during each lecture. Probably this should not be a substitute for your own notes (I personally need to take notes in order to stay awake) but it is intended to be helpful as a reference or if you happen to miss a lecture. I will be happy to hear suggestions about what is or is not useful. First thing that I forgot to say: you’ll need access to the supplementary notes Differential equations: Notes and Exercises . A lot of the homework will be taken from there; many points are very clearly explained in an MIT-friendly fashion; there is a wonderful supply of well-designed practice problems; and the solutions provided are more detailed than those in the text. You can buy the notes at Copy Tech in the basement of Building 11, or see them online (link on the 18.03 home page). About printing out the homework problems: you may find it convenient to do the problem sets using only a screen image of the problem set (since in any case you are often just pointed to a problem in the text or the notes). The solutions provided will include the problem statements, so you might want to print out only the solutions to keep. In class, I said that a typical differential equation arises from a problem involving something measurable that is changing in a way you can understand. Modelling the problem means making an equation that describes approximately your understanding: that says how to write the rate of change in each possible state of the system. Initial conditions say how the system starts out. From these two pieces of information (how the system starts, and how it changes) you can hope to understand all of its behavior....
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01 direction fields, existence and uniqueness of solns -...

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