Numerical differentiation in MATLAB - Mini Project: Build & Apply

Numerical differentiation

📖 Scenario: You are working as a data analyst and need to find the rate of change of a function at specific points using numerical methods. This is useful when you have data points but no explicit formula for the function.

🎯 Goal: Build a MATLAB program that calculates the numerical derivative of a function at given points using the forward difference method.

📋 What You'll Learn

Create a vector of x values

Create a vector of corresponding y values for the function y = x^2

Define the step size h

Calculate the numerical derivative using the forward difference formula

Print the resulting derivative vector

💡 Why This Matters

🌍 Real World

Numerical differentiation helps estimate rates of change when you only have data points, such as measuring speed from position data.

💼 Career

Data analysts, engineers, and scientists often use numerical differentiation to analyze experimental or simulation data where formulas are unknown.

1

Create the data vectors

Create a vector called x with values 1, 2, 3, 4, 5. Then create a vector called y where each element is the square of the corresponding x value.

MATLAB

% Your code here

Need a hint?

Use the dot operator .^ to square each element of x individually.

2

Define the step size

Create a variable called h and set it to 1, which is the difference between consecutive x values.

MATLAB

x = [1, 2, 3, 4, 5];
y = x.^2;
% Your code here

Need a hint?

The step size h is the difference between two consecutive x values.

3

Calculate the numerical derivative

Create a vector called dy_dx that stores the numerical derivative of y with respect to x using the forward difference formula: dy_dx(i) = (y(i+1) - y(i)) / h for i from 1 to 4.

MATLAB

x = [1, 2, 3, 4, 5];
y = x.^2;
h = 1;
% Your code here

Need a hint?

Use a for loop from 1 to length of y minus 1. Calculate the difference quotient inside the loop.

4

Display the derivative

Use disp to print the vector dy_dx which contains the numerical derivatives.

MATLAB

x = [1, 2, 3, 4, 5];
y = x.^2;
h = 1;
dy_dx = zeros(1, length(y)-1);
for i = 1:length(y)-1
    dy_dx(i) = (y(i+1) - y(i)) / h;
end
% Your code here

Need a hint?

Use disp(dy_dx) to show the derivative values.