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ee20-f10-hw01 - Problem Set 1 EECS 20N Structure and...

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EECS 20N: Structure and Interpretation of Signals and Systems Department of EECS University of California Berkeley Problem Set 1 Issued: 11 September 2010 Due: 17 September 2010, 6pm I believe that excessive admiration for the work of great minds is one of the most unfortunate preoccupations of intellectual youth—along with a conviction that certain problems cannot be attacked, let alone solved, because of one’s relatively limited abilities. Inordinate respect for genius is based on a commendable sense of fairness and modesty that is difficult to censure. However, when foremost in the mind of a novice, it cripples initiative and prevents the formulation of original work . . . Admittedly, certain concepts in science appear to be so complete, brilliant, and enduring that they seem to be the fruit of an almost divine intuition, springing forth perfect like Minerva from the head of Jupiter. However, the well-deserved admiration for such accomplishments would be considerably diminished were we aware of all of the time and effort, patience and perseverance, trials, cor- rections, and even mishaps that worked hand in hand to produce the final success—contributing almost as much as the investigator’s genius. a a Excerpts from Advice for a Young Investigator , by Santiago Ram´ on y Cajal, trans- lated by Neely Swanson and Larry W. Swanson, The MIT Press, 1999, ISBN: 0-262- 68150-1. Policy Statement We encourage you to collaborate, but only in a group of up to five current EECS 20N students. On the solution document that you turn in for grading, you must write the names of your collaborators below your own; each teammate must submit for our evaluation a distinct, self-prepared solution document containing original contributions to the collaborative effort. Please write neatly and legibly, because if we can’t read it, we can’t grade it. Unless we explicitly state otherwise, you will receive full credit only if you explain your work succinctly, but clearly and convincingly. Typically, we evaluate your solutions for only a subset of the assigned problems. A priori, you do not know which subset we will grade. It is to your advantage to make a bona fide effort at tackling every assigned problem. If you are asked to provide a “sketch,” it refers to a hand-drawn sketch, well- labeled to indicate all the salient features—not a plot generated by a computing device. 1
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On occasion, a problem set contains one or more problems designated as “op- tional.” We do NOT grade such problems. Nevertheless, you are responsible for learning the subject matter within their scope. Overview This problem set is designed to strengthen your mathematical foundations. In par- ticular, you will get practice with complex numbers and their arithmetic and complex variables and their algebra; you will also tiptoe into the realm of complex-valued func- tions (with more to come later). This problem set also explores some of the salient properties of the Dirac delta.
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