Matlab & Mathematics Questions

 

Part A.

Choose a mathematical formula that comes from a real world application (try to get one you use in one of your other courses). Your formula should have at least two parameters. Select two parameters of interest so that your formula can be thought of as a function of two variables.

Implement your function in Scilab along with some explanatory text (for example what the function value represents, what the parameters are, units etc). In your submission discuss the domain and range of your function. Your function should be different from everyone else’s.                                         Your written submission should clearly show the results obtained and commentary along with the listing of the function you have written.

 

 

Part B.

Write a Scilab script file to plot the vector field

 

 

~

F (x, y) =

-1

 

2p (x2 + y 2 )

((qx + ky)i + (qy kx) j),

k, q = 2p ,

-1 £ x £ 1,

-1 £ y £ 1.

 

 

~

F is a basic model of the velocity field of a hurricane where k is the vortex strength and q is the sink

strength.

What happens to the hurricane velocity vector field when you keep q fixed and vary k? What about if you keep k fixed and vary q.

Your written submission should clearly show the results obtained and with the listing of the functions you have written.

 

 

Part C.

In Scilab generate the measurement data by the following commands x=0:100

y=((3*sin(%pi*x/10))^2)./x

 

Using Scilab write functions to implement the integration of the data between x= o and x=100 using the Trapezoidal Rule and Simpson’s Rule. Using intervals of (x) as 10,5,1 for both functions compare and comment on the accuracy of the results obtained.

Your written submission should clearly show the results obtained and commentary on the comparison along with the listing of the functions you have written.

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