midterm_07 - EE263 Oct 2627 or Oct 2728 2007 Prof S Boyd...

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EE263 Prof. S. Boyd Oct. 26–27 or Oct. 27–28, 2007. Midterm exam This is a 24 hour take-home midterm. Please turn it in at Bytes Cafe in the Packard building, 24 hours after you pick it up. Please read the following instructions carefully. You may use any books, notes, or computer programs ( e.g. , Matlab), but you may not discuss the exam with anyone until Oct. 29, after everyone has taken the exam. The only exception is that you can ask the TAs or Stephen Boyd for clarification, by emailing to the staff email address. We’ve tried pretty hard to make the exam unambiguous and clear, so we’re unlikely to say much. Please address email inquiries to [email protected] . This forwards the mail to the professor and the TAs. In particular, please do not use Stephen Boyd’s or the TAs’ individual email addresses. Since you have 24 hours, we expect your solutions to be legible, neat, and clear. Do not hand in your rough notes, and please try to simplify your solutions as much as you can. We will deduct points from solutions that are technically correct, but much more complicated than they need to be. Please check your email a few times during the exam, just in case we need to send out a clarification or other announcement. It’s unlikely we’ll need to do this, but you never know. Attach the official exam cover page (available when you pick up or drop off the exam, or from the midterm info page) to your exam, and assemble your solutions to the problems in order, i.e. , problem 1, problem 2, . . . , problem 5. Start each solution on a new page. Please make a copy of your exam before handing it in. We have never lost one, but it might occur. When a problem involves some computation (say, using Matlab), we do not want just the final answers. We want a clear discussion and justification of exactly what you did, the Matlab source code that produces the result, and the final numerical result. Be sure to show us your verification that your computed solution satisfies whatever properties it is supposed to, at least up to numerical precision. For example, if you compute a vector x that is supposed to satisfy Ax = b (say), show us the Matlab code 1
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that checks this, and the result. (This might be done by the Matlab code norm(A*x-b) ; be sure to show us the result, which should be very small.) We will not check your numerical solutions for you, in cases where there is more than one solution. In the portion of your solutions where you explain the mathematical approach, you cannot refer to Matlab operators, such as the backslash operator. (You can, of course, refer to inverses of matrices, or any other standard mathematical construct.) Some of the problems are described in a practical setting, such as signal processing, communications, or control. You do not need to understand anything about the ap- plication area to solve these problems . We’ve taken special care to make sure all the information and math needed to solve the problem is given in the problem description.
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