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Unformatted text preview: Codes and outputs for HW 6 21.1) by hand, I have it with me 21.2) % Calculates the Left, Right, and Trapezoidal estimations of the %Integral % of f(x) from a to b. function [L R T] = myints(f,a,b,n) format long x = linspace(a,b,n+1); y = f(x); L = 0; R = 0; dx = (ba)/n; %since we intend for the evaluation points to be evenly %spaced for i = 1:n L = L + y(i); R = R + y(i+1); end L = L*dx; R = R*dx; T = (L+R)*.5; Results: >> [L R T] = myints(f,1,2,4) L = 1.166413628918445 R = 1.269967019511719 T = 1.218190324215082 >> [L R T] = myints(f,1,2,100) L = 1.216879128301471 R = 1.221021263925202 T = 1.218950196113336 22.1) by hand, I have this with me 22.2) % Calculates the Left, Right, and Trapezoidal estimations of the %Integral % of f(x) from a to b. function M = mymidpoint(f,a,b,n) format long x = linspace(a,b,n+1); y = f(x); M = 0; for i = 1:n M = M + ((y(i)+y(i+1))/2)*(x(i+1)  x(i)); end Results >> M = mymidpoint(f,1,2,4) M = 1.218190324215082 >> M = mymidpoint(f,1,2,100) M = 1.218950196113336 22.3) function S = mysimpson(f,a,b,n) if rem(n,2) ~= 0 error( 'n must be even' ) end x = linspace(a,b,n+1); y = f(x); S = 0; w = ones(n+1,1); for i = 2:n if rem(i,2)==0 w(i)=4; else w(i)=2; end S = S + w(i)*y(i); end S = (S + y(1) + y(n+1))*((ba)/(3*n)); Results: >> S = mysimpson(f,1,2,4) S = 1.218945156857086 >> S = mysimpson(f,1,2,100) S = 1.218951416480312 23.1) Since 3 (3) = 6, selecting m = 60 would let h = .1 and because 2 (2) = 4, letting n = 40 would also let k = .1; thereby producing the following image: 23.2) The following creates the coordinates for t riangles in a hexagonal region with a...
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 Spring '08
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