Introduction

Mathematical modeling is the process of using math to represent, analyze, and solve problems from the real world. It’s like building a bridge between what happens around us and the language of mathematics.

Why Do We Model?

Models help us understand complex systems, make predictions, and test ideas in a safe, mathematical way. Whether you're estimating how fast a car travels or predicting how diseases spread, math models are everywhere.

The Modeling Cycle

The modeling process usually follows these steps:

1. Understand the Problem
2. Formulate a Model
3. Compute or Solve
4. Interpret Results
5. Validate and Refine the Model

Types of Models

• Physical Models: Small-scale versions or simulations (e.g., a globe for Earth).
• Mathematical Models: Equations or formulas that mimic real situations.

Benefits

• Save time and resources.
• Make predictions about future events.
• Test scenarios without any real-world risk.