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Unformatted text preview: EECS 20N: Structure and Interpretation of Signals and Systems Department of EECS University of California Berkeley Problem Set 2 Issued: 18 October 2009 Due: 27 October 2009, 6pm Euler, a Swiss born mathematician who spent his career in Berlin and St. Petersburg, had an extraordinary in uence on all areas of mathematics, physics, and engineering. Not only was the importance of his discoveries unparalleled, their sheer quantity is also overwhelming. Opera Omnia , the still incomplete record of Euler's collected works, currently runs to over seventy-three volumes, six hundred pages each. The last seventeen years of Euler's life, between his return to St. Petersburg in 1766 and his death at the age of 76, were rather tumultuous. Yet, despite many personal tragedies, about half of his works were written during these years. These include a 775-page treatise on the motion of the moon, an in uential algebra textbook, and a three-volume discussion of integral calculus, completed while he continued to publish an average of one mathematics paper per week in the journal of the St. Petersburg Academy. The amazing thing is that he barely wrote or read a single line during this time. Having partially lost his sight soon after re- turning to St. Petersburg in 1766, Euler was left completely blind after a failed cataract operation in 1771. The thousands of pages of theorems were all dictated from memory. a a Excerpts from Linked: How Everything Is Connected to Everything Else and What It Means for Business, Science, and Everyday Life , by Albert-L aszl o Barab asi, published by Plume, a member of Penguin Group (USA) Inc., 2003, ISBN: 0-452-28439-2. 1 Policy Statement We encourage you to collaborate, but only in a group of up to ve 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 e ort. 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 de e ort at tackling every assigned problem. If we ask you 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. 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....
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