User-defined functions are fundamental building blocks in MATLAB, allowing you to encapsulate reusable code, improve program organization, and enhance readability. They enable you to break down complex problems into smaller, manageable parts, making your engineering and scientific research more efficient and robust.

A user-defined function in MATLAB is a script file that performs a specific task. It accepts input arguments, processes them, and returns output arguments. This modular approach is crucial for developing complex algorithms and simulations.

A typical MATLAB function has the following structure:

function [outputArg1, outputArg2, ...] = functionName(inputArg1, inputArg2, ...)
    % Function body: code to perform the task
    % Assign values to output arguments
    outputArg1 = ...;
    outputArg2 = ...;
end

• Function Definition Line:
  code

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  function [outputArg1, ...] = functionName(inputArg1, ...)

  defines the function's name, inputs, and outputs.
• H1 Line: The first comment line after the function definition is the H1 line, which is displayed by the
  code

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  help

  command.
• Help Text: Subsequent comment lines provide detailed documentation.
• Function Body: Contains the MATLAB statements that execute the function's logic.
• End Statement: Marks the end of the function.

Once a function is defined and saved in a

.m

Let's create a function to calculate the area of a circle.

Create a file named

circleArea.m

function [area] = circleArea(radius)
    % CIRCLEAREA Calculates the area of a circle.
    %   AREA = CIRCLEAREA(RADIUS) calculates the area of a circle
    %   with the given RADIUS.
    
    area = pi * radius^2;
end

To call this function, you would type in the Command Window:

myCircleArea = circleArea(10);

This will compute the area of a circle with a radius of 10 and store the result in the variable

myCircleArea

To write effective and maintainable MATLAB functions:

• Descriptive Names: Use clear and descriptive names for functions and variables.
• Comments: Include a H1 line and detailed help text to explain the function's purpose, inputs, and outputs.
• Single Responsibility: Design functions to perform one specific task.
• Avoid Global Variables: Pass all necessary data through input and output arguments.
• Error Handling: Consider adding checks for invalid input arguments.