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L1intro - Introduction to Computing Using Matlab CS1112...

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Introduction to Computing Using Matlab CS1112 Fall 2009 (CIS1121) Professors C. Van Loan & D. Fan http://www.cs.cornell.edu/courses/cs1112/
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August 27, 2009 Lecture 1 2 Today’s lecture An illuminating problem CS1112 philosophies & syllabus What is computer programming? Choosing between CS111 2 & CS111 0 Course logistics/policies (highlights)
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August 27, 2009 Lecture 1 3 An illuminating problem: computing square roots Suppose A > 0 Observation: If A is the area of a square, then I can just measure the side length—that is Idea: Make a square with area A Real task: Make a sequence of increasingly square rectangles, each with area A A
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August 27, 2009 Lecture 1 4 How to make a rectangle “more square”? If a square and a rectangle both have area A then is between the length and width of the rectangle A
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A/L Recipe: L new = (L + A/L) / 2 Current: Next: L L new A/L new An improvement strategy The average of the length and width.
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August 27, 2009 Lecture 1 6 A Matlab program to make “increasingly square” rectangles % The first rectangle... L1 = A; W1 = 1; % The second rectangle... L2 = (L1+W1)/2; W2 = A/L2; % The third rectangle... L3 = (L2+W2)/2; W3 = A/L3; % and so on...
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The progression of rectangles Length Width 9.000000000000000 1.000000000000000 5.000000000000000 1.800000000000000 3.400000000000000 2.647058823529412 3.023529411764706 2.976653696498055 3.000091554131380 2.999908448662588 3.000000001396984 2.999999998603016
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August 27, 2009 Lecture 1 8 Some conclusions from square root finding problem It paid to have a geometric sense A complicated computation was reduced to a sequence of elementary calculations A program is like a formula (or sequence of formulas)
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August 27, 2009 Lecture 1 9 Course Goals Develop your “ computational senses ,” senses that you need in computer problem-solving Develop a facility with the Matlab programming environment
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August 27, 2009 Lecture 1 10 A sense of geometry
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A sense of complexity What is the best itinerary to visit Boston, Miami, LA, Dallas ? 3! = 6 possibilities Add Seattle, NYC Austin, Denver 7! = 5040 If a computer can process 1 billion itineraries a second, how long does it take to solve a 100-city problem?
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August 27, 2009 Lecture 1 13 A sense of randomness and probability Random walk Brownian motion in water
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August 27, 2009 Lecture 1 14 A sense of approximation & error 1/3 = .33333…
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August 27, 2009
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