Calculate the integral with; a) Trapezoidal rule b) Simpson’s rule

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Presentation transcript:

Calculate the integral with; a) Trapezoidal rule b) Simpson’s rule Sample Solutions: Calculate the integral with; a) Trapezoidal rule b) Simpson’s rule c) With computer (Visual Basic), take m=2, n=4. a) Trapezoidal rule: Divide into for equal section between 0.5 and 1. k θ f 0.5 0.6205 1 0.625 0.6411 2 0.75 0.6337 3 0.875 0.5996 4 0.5403

>>I=int('sqrt(tet)*cos(tet)',0.5,1);vpa(I,5) I=0.30796 Sample Solutions: b) Simpson’s rule: with Matlab >>I=int('sqrt(tet)*cos(tet)',0.5,1);vpa(I,5) I=0.30796 Sub simpson_Click () 80 a = .5: b = 1: m = 2 … 85 f = Sqr(x) * Cos(x) End Sub c) With computer (Visual Basic)

a) Lagrange interpolation (manually) with computer Sample Solutions: The pressure values of a fluid flowing in a pipe are given in the table for different locations . Find the pressure value for 5 m. a) Lagrange interpolation (manually) with computer Location (m) 3 8 10 Pressure (atm) 7 6.2 6 a) with Lagrange interpolation b) For computer solution, the file li.txt is arranged as follows and the code Lagr.I is run. li.txt 3 3,7 8,6.2 10,6 5

x=0.6786 y=0.3885 x=0.6786, y=0.3885 Sample Solutions: How do you find x and y values, which satisfy the equations? Sub newtonrn_Click () 40 n = 2 … 41 xb(1) = 1: xb(2) = 1: xh(1) = .001: xh(2) = .001 45 '---- Error equations ----------- a(1, 1) = 2 * Cos(2 * xb(1)) - 3: a(1, 2) = 3 * xb(2) ^ 2 a(2, 1) = 2 * xb(1): a(2, 2) = 2 * xb(2) + 1 b(1) = -(Sin(2 * xb(1)) + xb(2) ^ 3 - 3 * xb(1) + 1) b(2) = -(xb(1) ^ 2 + xb(2) ^ 2 + xb(2) - 1) 46 '-------------------- End Sub x=0.6786 y=0.3885 with Matlab: >>[x,y]=solve('sin(2*x)+y^3=3*x-1','x^2+y=1-y^2') x=0.6786, y=0.3885

Sample Solutions: As a result of the equilibrium conditions, the equations given below are obtained for a truss system. How do you calculate the member forces FJD, FFD, FCD and FFC if FCK=6.157 kN and FCB=-3.888 kN are known? A b F

A b F with Matlab clc;clear Sample Solutions: A b F with Matlab clc;clear A=[-1 -0.707 -0.894 0;0 -0.707 -1 0;3 0 0 2.365;0 0 0.894 1]; b=[-0.466;0;-6.557;4.353]; F=inv(A)*b FJD= 1.5429 kN FFD= -14.3701 kN FCD= 10.1596 kN FFC= -4.7297 kN

Find the roots of the polynomial. Sample Solutions: Find the roots of the polynomial. with Matlab >> p=[3 0 5 6 -20] >> roots(p) ans = -1.5495 0.1829 + 1.8977i 0.1829 - 1.8977i 1.1838 >>ezplot('3*t^4+5*t^2+6*t-20',-2,2)