Math Modeling

Math Modeling focuses on the application of mathematical concepts to solve real-world problems through modeling and analysis.

Basic Concepts

Building Simple Models

Getting Started

Creating a simple model starts by identifying the key parts of a problem and making some assumptions to keep things manageable.

Making Assumptions

Assumptions are the choices you make to simplify reality. For example, ignoring air resistance when modeling a falling object makes the math easier.

Common Types of Simple Models

  • Linear Models: Assume a straight-line relationship between variables.
  • Proportional Models: When one quantity changes, another changes by a constant factor.

Steps to Build

  1. Pick the important variables.
  2. Decide how they are related.
  3. Write down a mathematical expression or equation.

Keep It Simple

Start with the most basic model and add complexity later as needed.

Examples

  • Using \(y = mx + b\) to model the cost of movie tickets as a function of the number of tickets bought.

  • Modeling a car's distance traveled with time using \(d = vt\).

In a Nutshell

Start with basic relationships and simple assumptions to build models.