Submit your script that does the following. Save the script as mydiff.m

Part 1

Write a script that takes the forward difference, backward difference, and central difference for the following x and y data points

x = 0:0.2:10;

y = sin(x);

Plot your results on one plot with the following lines

x vs. dy/dx found using the forward difference method with a solid blue line

x vs. dy/dx found using the backward difference method with a solid green line

x vs. dy/dx found using the central difference method with a solid red line

x vs. dy/dx using the actual derivative of y = sin(x), y = cos(x) with a black dotted line

Your plot should include an x axis label, y axis label, title, and legend

Use a linewidth of 2

Part 2

The derivative of

y = x sin(x2) + 1

is

dy/dx = sin(x2) + 2x2cos(x2)

In the same script create a second plot that plots from x = 0 to x = 10

the analytical solution to dy/dx using a step size of 0.01 (red solid line)

The numerical solution to dy/dx using the central difference method and a step size of 0.01 (black dotted line)

The numerical solution to dy/dx using the central difference method and a step size of 0.1 (blue dotted line)

The numerical solution to dy/dx using the central difference method and a step size of 0.5 (green dotted line)

Your plot should include an x axis label, y axis label, title, and legend

Use a linewidth of 2

Note: you can code the analytical derivative as

x = 0:0.01:10

Yprime = sin(x.^2) + 2*x.^2.*cos(x.^2)

If youre asking why do I need to put .^ instead of just ^?

This is because x^2 is the matrix multiplication x*x (which will yield an error if x is a 1D array because the inner dimensions will not match)

x.^2 will take each element of x and square that element

Essentially, x.^2 is doing the following:

x = 0:0.01:10

for i = 1:length(x)

X_squared(i) = x(i)*x(i);

end

Instead of typing the for loop above, we can just type X_squared = x.^2