How do I differentiate in MATLAB?

In summary, diff is a function in MATLAB that can be used to differentiate most functions with an appropriate step size. It can be overloaded and used to calculate derivatives numerically, as shown in the example with the sin function. The command also returns a vector with one less element. Alternatively, the gradient function can also be used for 1D problems, with additional syntaxes available for higher dimensional problems.
  • #1
Urmi Roy
753
1
I find that I don't have the symbolic toolbox. Due to this, I'm not being able to differentiate by using the usual 'diff' command. However, just as one can integrate numerically, by using the quad and quadl functions, is there no way to differentiate numerically on MATLAB (like using the ab initio method or something)?
 
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  • #3
You can use diff to differentiate most functions with an appropriate step size. For example,

Code:
h = 0.001;
x = -pi:h:pi;
y = sin(x);
z = diff(y)/h;

If you plot z, you will see that it is equal to cos(x). Similarly, you can use diff to calculate derivatives this way for other functions.

Just remember diff returns a vector with 1 less element.

Alternatively, you could use gradient, which returns a vector of the same size. For 1D problems this is a simple partial derivative. There are additional syntaxes available for higher dimensional problems (see http://www.mathworks.com/help/matlab/ref/gradient.html)
 
  • #4
Thanks for the info, Kreil! I can't imagine why I didn't see your post in all these days!
 
  • #5


There are a few options for differentiating in MATLAB without using the symbolic toolbox. One option is to use the finite difference method, where you approximate the derivative by calculating the slope of a small interval around a point. This can be done using the "gradient" function in MATLAB.

Another option is to use the "diff" function with a small step size to approximate the derivative numerically. This is similar to the ab initio method you mentioned.

You can also use the "polyfit" function to fit a polynomial curve to your data and then take the derivative of the polynomial to approximate the derivative of your original function.

Overall, while the symbolic toolbox may provide a more precise and analytical approach to differentiation, there are still ways to differentiate numerically in MATLAB without it. It may require some additional steps and approximations, but it is certainly possible.
 

1. How do I differentiate a function in MATLAB?

To differentiate a function in MATLAB, you can use the 'diff' function. This function takes in two arguments - the function that you want to differentiate and the variable you want to differentiate with respect to. For example, to differentiate the function f(x) = x^2 with respect to x, you would use the command 'diff(x^2, x)'.

2. Can I differentiate a vector or matrix in MATLAB?

Yes, you can differentiate a vector or matrix in MATLAB. The 'diff' function can take in a vector or matrix as its first argument, and will return the differentiated vector or matrix. However, the second argument must be the variable that you are differentiating with respect to.

3. How do I specify the order of differentiation in MATLAB?

To specify the order of differentiation in MATLAB, you can add a third argument to the 'diff' function. This argument represents the number of times you want to differentiate the function. For example, to differentiate the function f(x) = x^3 twice, you would use the command 'diff(x^3, x, 2)'.

4. What is the difference between symbolic and numerical differentiation in MATLAB?

In MATLAB, symbolic differentiation involves using the 'sym' function to create a symbolic expression, which can then be differentiated using the 'diff' function. This method is useful for obtaining exact expressions for derivatives. Numerical differentiation, on the other hand, involves using numerical methods to approximate derivatives at specific points. This method is useful when the function cannot be easily differentiated symbolically or when only the value of the derivative at a specific point is needed.

5. How do I plot the derivative of a function in MATLAB?

To plot the derivative of a function in MATLAB, you can first use the 'diff' function to obtain the differentiated function. Then, you can use the 'ezplot' function to plot the original function and the differentiated function on the same graph. You can also specify the range of values for the independent variable using the 'ezplot' function.

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