Why numerical computation solves real problems in MATLAB - See It in Action

Why numerical computation solves real problems

📖 Scenario: Imagine you are an engineer who needs to calculate the stress on a bridge beam under different loads. The exact math formulas are complex and hard to solve by hand. Numerical computation helps you find good approximate answers quickly using a computer.

🎯 Goal: You will create a simple MATLAB program that uses numerical computation to estimate the square root of a number. This shows how computers solve problems that are difficult to do exactly by hand.

📋 What You'll Learn

Create a variable called number with the value 25

Create a variable called tolerance with the value 0.0001

Use a while loop to approximate the square root of number using the Babylonian method

Print the final approximate square root stored in approx_sqrt

💡 Why This Matters

🌍 Real World

Engineers and scientists use numerical computation to solve complex problems like stress analysis, fluid flow, and electrical circuits where exact formulas are too hard or impossible to solve by hand.

💼 Career

Knowing numerical methods and programming helps you work in fields like engineering, data science, finance, and research where computers solve real-world problems efficiently.

1

DATA SETUP: Create the initial number variable

Create a variable called number and set it to 25.

MATLAB

% Create a variable called number and set it to 25
% Your code here

Need a hint?

Use number = 25; to create the variable.

2

CONFIGURATION: Add a tolerance variable for accuracy

Create a variable called tolerance and set it to 0.0001.

MATLAB

number = 25;
% Create a variable called tolerance and set it to 0.0001
% Your code here

Need a hint?

Use tolerance = 0.0001; to set the accuracy level.

3

CORE LOGIC: Use a while loop to approximate the square root

Create a variable approx_sqrt and set it to number / 2. Then use a while loop to improve approx_sqrt using the Babylonian method until the difference between approx_sqrt^2 and number is less than tolerance. Use the formula: approx_sqrt = (approx_sqrt + number / approx_sqrt) / 2;

MATLAB

number = 25;
tolerance = 0.0001;
% Initialize approx_sqrt and use a while loop to improve it
% Your code here

Need a hint?

Start with half the number, then repeat improving the guess until close enough.

4

OUTPUT: Display the approximate square root

Write a disp statement to print the text 'Approximate square root:' followed by the value of approx_sqrt.

MATLAB

number = 25;
tolerance = 0.0001;
approx_sqrt = number / 2;
while abs(approx_sqrt^2 - number) > tolerance
    approx_sqrt = (approx_sqrt + number / approx_sqrt) / 2;
end
% Display the approximate square root
% Your code here

Need a hint?

Use disp(['Approximate square root: ', num2str(approx_sqrt)]) to show the result.