## Introduction to Function Handles in MATLAB

Function handles in MATLAB are a powerful data type that allow programmers to store information about a function. The purpose of function handles is to provide a means of referring to a function in a more abstract way.

The function handle allows the programmer to pass functions as arguments, store functions in data structures, and use them in many other ways.

## Common Uses of Function Handles

One of the most common uses of function handles is for passing functions as arguments to other functions. This allows for the creation of more flexible and reusable code.

Function handles are also frequently used in integration and optimization functions, as well as in callback functions and local functions.

## Creating a Function Handle in MATLAB

To create a function handle in MATLAB, the programmer needs to use the “@” symbol followed by the name of the function. Here is an example of how to define a variable “my_defining_function” as a function handle:

“`

my_defining_function = @my_function

“`

## Using the Diff Function to Find the Derivative of Function Handles

The MATLAB language offers a powerful function for calculating the derivative of function handles. This function is called diff.

## Here is an example of how to use the diff function to find the derivative of a function handle:

“`

## syms x

f = @(x) x^2 + 3*x – 2;

df = diff(f(x))

“`

This code defines a function handle “f” with an equation that contains the variable “x” and then uses the diff function to find the derivative of “f”.

## Finding the Derivative of Symbolic Matrix Functions

A more complicated example is finding the derivative of a symmetric matrix function with respect to its parameters. Here is an example, this code defines a symmetric matrix function and then finds its derivative with respect to “x”.

“`

## syms x

S = sym(‘s’,[2 2]); % Create a 2-by-2 symbolic matrix

f = x*S^2 – 7*x*S + 2;

matlabFunction(f, ‘Vars’, {x, S})

dfds = diff(f, S)

“`

## Additional Examples for Practice

## Here are a few more examples for you to practice with:

Example #1: Find the derivative of this function handle:

“`

f = @(x) x.^2 + sin(x);

“`

Example #2: Find the derivative of this function handle:

“`

g = @(x) x.^3 + x^2 + x + 1;

“`

Example #3: Find the derivative of this matrix function handle:

“`

syms x;

M = sym(‘m’,[3 3]); % Create a 3-by-3 symbolic matrix

h = cos(x)*M + x^2*exp(M);

matlabFunction(h, ‘Vars’, {x, M})

dhdm = diff(h, M)

“`

## Conclusion

The use of function handles in MATLAB has a wide range of applications. They are an essential tool for any programmer using MATLAB, especially for developers who are looking for ways to create more flexible and reusable code.

With a little bit of practice, you can master the use of function handles and take your MATLAB programming to the next level. In conclusion, function handles are a powerful data type in MATLAB that allow programmers to store information about a function, providing a means of referring to a function in a more abstract way.

Function handles are frequently used for passing functions as arguments, in integration and optimization functions, as well as in callback functions and local functions. In this article, we covered the methods for finding the derivative of function handles, which is a common use of function handles.

We learned how to create a function handle in MATLAB, use the diff function to find the derivative of function handles, find the derivative of symmetric matrix functions, and provided additional examples for practice. By mastering the concept of function handles, programmers can improve the flexibility and reusability of their MATLAB code.