1. 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

2. >>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=
Sub simpson_Click ()
80 a = .5: b = 1: m = 2 …
85 f = Sqr(x) * Cos(x)
End Sub
c) With computer (Visual Basic)

3. 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

4. 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) ^ * 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

5. 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= kN are known? A b F

6. A b F with Matlab clc;clear
Sample Solutions: A b F
with Matlab
clc;clear
A=[ ; ; ; ];
b=[-0.466;0;-6.557;4.353];
F=inv(A)*b
FJD= kN
FFD= kN
FCD= kN
FFC= kN

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