Question

1) Create a matlab function that calculates:

for

Name your function TwoVarFunc :

The inputs should be in the same order:

• xmin
• xmax
• ymin
• ymax
• N: n is the number of elements in the vector x and y

The ouputs should be in the same order:

• f_xy: is the calculated array f(x,y)
• f_xyMAX: should be the the maximum value of the function f(x,y).

Hint: to create vectors x and y look up the matlab built-in function linspace()

Hint 2: To get the maximum value in f_xy use the built-in function max()

Code to call function:

[f_xy,f_xyMAX] = TwoVarFunc(-4,4,-5,5,100)

2)

Using the function in Problem 1, calculate:

for :

Create the vectors x and y with 1000 values.

Create a subplot with 2 panes:

1. In the first pane, include a surface plot of f(x,y)
2. In the second pane, include a mesh plot of f(x,y)

Include axis labels and titles for both plots.

Answer 1

1.
% Matlab function file : TwoVarFunc.m
function [f_xy, f_xyMAX] = TwoVarFunc(xmin, xmax, ymin, ymax,N)
x = linspace(xmin,xmax,N);
y = linspace(ymin,ymax,N);
f_xy = (x'*y)./(sin(x)+cos(x));
f_xyMAX = max(max(f_xy));
end
%end of function

2.
% Matlab main script to use the function TwoVarFunc to get the value of the
% function and plot the surface and mesh plot
xmin = -4;
xmax = 4;
ymin = -7;
ymax = 7;
N = 1000;
x = linspace(xmin,xmax,N);
y = linspace(ymin,ymax,N);
[f_xy,f_xyMAX] = TwoVarFunc(xmin,xmax,ymin,ymax,N);
subplot(1,2,1);
surf(x,y,f_xy);
xlabel('X');
ylabel('Y');
zlabel('Z');
title('Surface plot of xy/(sin(x)+cos(x))')
subplot(1,2,2);
mesh(x,y,f_xy);
xlabel('X');
ylabel('Y');
zlabel('Z');
title('Mesh plot of xy/(sin(x)+cos(x))')
%end of script

Output:

Surface plot of xy/(sin(x)+cos(x)) Mesh plot of xy/(sin(x)+cos(x)) * 104 *104 2.5 2.5 2 1.5 1.5 0.5 0.5 Noy NO -0.5 -0.5 -1 -1.5 g 2 2 0 0 2