# SLSEEC 2012-2013 Theme – Mathematical Modelling

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Mathematical modelling is the process of transformation of a physical situation into mathematical analogies with appropriate conditions.

Physical situations need some physical insight into the problem. Then it is solved by using various mathematical tools like percentage, area, surface area, volume, time and work, profit and loss, differential equations, probability, statistics, linear, nonlinear programming, etc. It is a multi-step process involving identifying the problem, constructing or selecting appropriate models, fighting out what data need to be collected, deciding number of variables and predictors to be chosen for greater accuracy, testing validity of models, calculating solution and implementing the models. It may be an iterative process where we start from a crude model and gradually refine it until it is suitable for solving the problem and enables us to gain insight and understanding of the original situation. It is an art, as there can be a variety of distinct approaches to the modeling, as well as science, for being tentative in nature.

In mathematical modelling, we neither perform any practical activity nor interact with the situation directly, e.g. we do not take any sample of blood from the body to know the physiology, and still our mathematical tools reveal the actual situations. The rapid development of high speed computers with the increasing desire for the answers of everyday life problems have led to enhanced demands of modelling almost every area. The objective of this sub-theme is to help children to analyse how mathematical modelling can be used to investigate objects, events, systems and processes.

It can be visualized by Fig. 1.

The exhibits/models in this sub-theme may pertain to:

• mathematical modelling to solve various problems of our everyday life/ environment related problems
• mathematical modelling and computer simulation of climate dynamics/ production of weather phenomena based on a number of predictors
• mathematical modeling in physical geography such as rotation and revolution of earth, precession and equinoes etc.
• mathematical modelling to predict orbital path of comets, meteors and other minor planets
• mathematical modelling to show how disease might spread in human in the event of epidemics/bioterrorism
• mathematical modelling to predict the devastating effects of wars/nuclear explosions
• mathematical modelling to show spread of forest fire depending on the types of trees, weather and nature of the ground surface
• mathematical modelling to demonstrate the action of medicines in human system
• mathematical modelling of the working of heart, brain, lungs, kidneys, bones and endocrine system
• computer diagnosis of human diseases
• mathematical modelling of fluid flow in drain, spillways, rivers, etc.
• using mathematical modelling and computer simulation to improve cancer therapy/wound healing/tissues formation/ corneal wound healing
• mathematical modelling of intracelular biochemical reactions and metabolisms
• mathematical modelling to describe traffic flow/stock market options
• studies of storage and retrieval techniques for computer systems
• data manipulation and information management techniques
• statistics and random number problems
• developing video games
• mathematical modelling for increasing production of crops
• mathematical modelling on balance of carbon cycle
• mathematical modelling on social insects such as honeybees, termites etc. to know how they use local information to generate complex and functional patterns of communication
• mathematical modelling of maximum speed in fibre optic links
• mathematical modelling of highly abstract problems arising from control and communication processes in the brain
• mathematical modelling of urban city planning

• Fig. 1: A Mathematical Model

• mathematical modelling to prevent an unwanted future/to understand various natural and unnatural phenomena
• mathematical modelling to show the effect of climate changes/global warming
• mathematical modelling for predicting future population and knowing the impact of population
• mathematical modelling for increasing production of crops etc.

State Level Science and Environment Exhibitions for Children 2012 – 2013 Complete Information

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• mathematical model to predict orbital paths middle school
• mathematical model to predict orbital paths of objects in sky
• mathematical modelling is a process

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