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Lecture 2 Notes

# l3 l2w22 w3 al3 and so on w1 l1 l2 l1w12

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Unformatted text preview: A Idea: Make a square with area A n༆  Real task: Make a sequence of increasingly square rectangles, each with area A Insight Through Computing 2 1/28/14 Idea: How to make a rectangle “more square”? n༆  W If a square and a rectangle both have area A … L L1 = (L+W)/2 n༆  W1 = A/L1 then A is between the length and width of the rectangle W1 L1 Insight Through Computing Repeat: 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... W1 L1 L2 = (L1+W1)/2 W2 = A/L2 Lecture 1 9 Insight Through Computing Square Root Conclusions •  Algorithm via simple geometry •  Reduces to a simple formula •  Looks complicated, but code is simple Roots Quadratic equation ax 2 + bx + c = 0 What is the formula for the roots? Insight Through Computing Insight Through Computing 3 1/28/14 Roots Roots Quadratic equation ax 2 + bx + c = 0 What is the formula for the roots? − b ± b 2 + 4ac r= 2a •  Let’s solve Insight Through Computing Insight Through Computing x 2 + 5x + 6 = 0 •  Using Matlab Script % Quad1 % Solves a b c d r1 r2 = = = = = = Programming Basics Variables and Expressions Assignment Statements Built- In Functions Script Execution Comments Keyboard Input Formatting Output x^2 + 5x + 6 = 0 1; 5; 6; sqrt(b^2 -4*a*c); (-b - d)/(2*a) (-b + d)/(2*a) Insight Through Computing Insight Through Computing Script A sequence of instructions. The order of the instructions is important. A script is a program. Insight Through Computing Comments % Quad1 % Solves a b c d r1 r2 = = = = = = x^2 + 5x + 6 = 0 1; 5; 6; sqrt(b^2 - 4*a*c); (-b - d)/(2*a) (-b + d)/(2*a) Insight Through Computing 4 1/28/14 Arithmetic Expressions Comments Begin with the “%” symbol. Goes to the end of the line. Facilitate the reading and understanding of the script. Insight Through Computing % Quad1 % Solves a b c d r1 r2 = = = = = = 1; 5; 6; sqrt(b^2 - 4*a*c); (-b - d)/(2*a) (-b + d)/(2*a) Insight Through Computing Arithmetic Expression Built- In Functions % Quad1 % Solves A recipe that results in the production of a number. Insight Through Computing a b c d r1 r2 = = = = = = x^2 + 5x + 6 = 0 1; 5; 6; sqrt(b^2 - 4*a*c); (-b - d)/(2*a) (-b + d)/(2*a) Insight Through Computing Built- In Functions Variables % Quad1 % Solves These are “packagings” of more advanced calculations. Some examples: log, exp, sin, cos,… Insight Through Computing x^2 + 5x + 6 = 0 a b c d r1 r2 = = = = = = x^2 + 5x + 6 = 0 1; 5; 6; sqrt(b^2 - 4*a*c); (-b - d)/(2*a) (-b + d)/(2*a) Insight Through Computing 5 1/28/14 Assignment Statements Variables •  A variable is a “box” that holds a numerical value % Quad1 % Solves •  It has a name •  The name must begin with a letter •  Upper and lower cases are distinguished. Can...
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