Matlab - Maclaurin series -n00b

[k1dd101]

Hi,
I have a problem, and I have no idea how to get started. I tried to follow tutorial on their website but it doesn't seems to help.
Here is my problem:

Derive the constant, linear, and quadratic terms in the Maclaurin series of the function f(x,y)= sin(x+y) cos(x-y).

This is what I have done so far:

>> syms x y
>> a=sin(x+y);
>> b=cos(x-y);
>> syms z
>> z=a*b
z = cos(x - y)*sin(x + y)
>> T=taylor(z,3);

---- After this I'm completely lost-----

>> xd=1:.05:3; yd=1:.05:3; zd=subs(a*b,{a,b},{[0 1; -1 0], [1 -1; -2 1]})

zd =
[ 0, -1]
[ 2, 0]

...using MATLAB for the first time.
Thanks in advance!

 

[mmwave]

Hi there,

I understand that you are having trouble deriving the constant, linear, and quadratic terms in the Maclaurin series of the function f(x,y)= sin(x+y) cos(x-y). Let me provide some guidance on how you can approach this problem.

Firstly, it's great that you have started by defining the variables x and y as symbolic variables using the "syms" command. This allows you to perform symbolic operations on them.

Next, you have defined the function f(x,y) as the product of sin(x+y) and cos(x-y). Now, to find the Maclaurin series of this function, you will need to use the "taylor" command in MATLAB. This command takes in the function and the number of terms you want in the series as inputs and returns the Maclaurin series.

In your case, you have correctly used the "taylor" command by specifying the function and the number of terms as 3. This means that the Maclaurin series of f(x,y) will have 3 terms. However, you have not assigned this series to a variable, so let's do that now.

You can assign the series to a variable, let's call it "S", by using the following command:
>> S=taylor(z,3);

Now, to find the constant, linear, and quadratic terms in this series, you can use the "coeffs" command. This command takes in the series and the variable you want to find the coefficients of as inputs and returns the coefficients in the form of a vector.

In your case, you want to find the coefficients of "S" with respect to "x", so you can use the following command:
>> coeffs(S,x)

This will return a vector with the constant, linear, and quadratic terms of the Maclaurin series of f(x,y).

I hope this helps you get started on solving your problem. If you have any further questions, please feel free to ask. Good luck!