Preflight assignment 13


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  1. Explain in your own words what "Fourier's trick" is, both mathematically and conceptually.



  2. We made an analogy in class between "expanding a vector in a basis" and "expanding a function with a Fourier Series". Did you understand that argument, did it make some sense to you, or did you get lost? In your own words, try to articulate that analogy - how do you think about it?


  3. In my lecture notes (labeled "PDF - page 10") at the bottom (and p. 11 at the top), I make a claim that if a function of x only (here, lets just call that f(x)) plus a pure function of y only (here, call that g(y)), add up to 0, i.e. f(x)+g(y)=0, then each function must in fact just be a constant (and, they must be the SAME constant, except opposite in sign) Boas makes the same argument on page 622 (in the big long paragaph after eq 2.4) Read that passage of Boas. It may seem a little dense (?) but it's the key to the method of separation of variables, and requires some thought. Explain it to us in your own words!



  4. Following up on the last question. If you solve a PDE in three dimensions, you might discover that f(x)+g(y)+h(z)=0 (where f, g, and h are different functions). What (if anything) could you conclude about the three functions? (Will the argument be the same as above, or is it different? ) Be as specific as you can.




  5. Please submit a question you have about the reading assigned for the upcoming class. What seemed hard, was something confusing, what would you like us to spend class time on? If you can't come up with any question, how about a comment - (did anything strike you as interesting? )
    Reminder: the reading assignments are on our course calendar


    Thanks for your time.

Optional! - below is a space for any additional relevant comments, thoughts, or suggestions you have.




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