Why Mathematical Modelling?

Why Mathematical Modelling?

Mathematical modelling is the process of translating a real-world problem into mathematical language, solving it, and interpreting the solution back in context. It is not about solving word problems mechanically; it requires physical insight — understanding the underlying laws and choosing appropriate symbols to compare mathematical results with practical values.

The Need for Mathematical Modelling

Many problems cannot be solved by direct measurement or observation. For example:

• Width of a river — you cannot stretch a tape across it.
• Height of a tower — you cannot climb to the top to measure.
• Mass of the Earth — you cannot put it on a scale.
• Population of India in 2020 — you cannot wait until then to count.
• Volume of blood in a person — you cannot drain all the blood.
• Optimal angle for shot-put — depends on many variables (height of thrower, air resistance, gravity).
• Temperature of the Sun's surface — impossible to measure directly.
• Why heart patients avoid lifts — involves physiology and pressure changes.

In each case, mathematics provides a way to estimate or compute the answer using known laws and relationships.

The Core Idea

Mathematical modelling involves:

1. Identifying the real-world problem and the quantities involved.
2. Making assumptions to simplify the situation (e.g., ignoring air resistance, assuming uniform density). …