Da Nang-10/2014

Natural Science Department – Duy Tan University

Lecturer: Ho Xuan Binh

MATHEMATICAL

MODELS

In this section, we will learn:

Mathematical models

Mathematical models  

MATHEMATICAL MODELS1Natural Science Department – Duy Tan University

A mathematical model is a mathematicalDescription — often by means of a function or an equation — of a real-world phenomenonsuch as:

*Size of a population*Demand for a product*Speed of a falling object*Life expectancy of a person at birth*Cost of emission reductions

PURPOSE2

Natural Science Department – Duy Tan University

The purpose of the model is to understand the phenomenon and, perhaps, to make predictions about future behavior.

Mathematical models  

PROCESS3Natural Science Department – Duy Tan University

The figure illustrates the process of mathematical modeling.

Mathematical models  

STAGE 14Natural Science Department – Duy Tan University

Given a real-world problem, our first task is to formulate a mathematical model.

Mathematical models  

STAGE 25Natural Science Department – Duy Tan University

The second stage is to apply the mathematics that we know—such as the calculus that will be developed throughout this book—to the mathematical model that we have formulated in order to derive mathematicalconclusions.

Mathematical models  

STAGE 36Natural Science Department – Duy Tan University

In the third stage, we take those mathematicalconclusions and interpret them as informationabout the original real-world phenomenon—byway of offering explanations or makingpredictions.

Mathematical models  

STAGE 47Natural Science Department – Duy Tan University

The final step is to test our predictions by checking against new real data.

If the predictions don’t compare well with reality, we need to refine our model or to formulate a new model and start the cycle again.

Mathematical models  

LOGO

Thank you for your attention